├── .gitignore
├── HISTORY.md
├── LICENSE
├── Pipfile
├── README.md
├── colab_notebooks
├── summarization_example_transformers.ipynb
├── vid2cleantext_multi.ipynb
└── vid2cleantext_single_demo.ipynb
├── examples
├── TEST_folder_edition
│ ├── CITATIONS
│ ├── console_printouts_large_model.md
│ ├── dl_src_videos.py
│ ├── wav2vec2-large-v2clntxt_transc_metadata
│ │ ├── mit_matrices_sgd_000_vid2txt_Dec-18-2021_-20_metadata.csv
│ │ ├── mit_matrices_sgd_001_vid2txt_Dec-18-2021_-21_metadata.csv
│ │ ├── mit_matrices_sgd_002_vid2txt_Dec-18-2021_-21_metadata.csv
│ │ ├── mit_signals_000_vid2txt_Dec-18-2021_-21_metadata.csv
│ │ ├── mit_signals_001_vid2txt_Dec-18-2021_-21_metadata.csv
│ │ ├── mit_signals_002_vid2txt_Dec-18-2021_-21_metadata.csv
│ │ ├── mit_vibrations_and_waves_000_vid2txt_Dec-18-2021_-21_metadata.csv
│ │ ├── mit_vibrations_and_waves_001_vid2txt_Dec-18-2021_-22_metadata.csv
│ │ ├── mit_vibrations_and_waves_002_vid2txt_Dec-18-2021_-22_metadata.csv
│ │ └── mit_vibrations_and_waves_003_vid2txt_Dec-18-2021_-22_metadata.csv
│ └── wav2vec2-large-v2clntxt_transcriptions
│ │ ├── YAKE - all keys for batch Dec-18-2021_-22.csv
│ │ ├── mit_matrices_sgd_000_vid2txt_Dec-18-2021_-20_full.txt
│ │ ├── mit_matrices_sgd_001_vid2txt_Dec-18-2021_-21_full.txt
│ │ ├── mit_matrices_sgd_002_vid2txt_Dec-18-2021_-21_full.txt
│ │ ├── mit_signals_000_vid2txt_Dec-18-2021_-21_full.txt
│ │ ├── mit_signals_001_vid2txt_Dec-18-2021_-21_full.txt
│ │ ├── mit_signals_002_vid2txt_Dec-18-2021_-21_full.txt
│ │ ├── mit_vibrations_and_waves_000_vid2txt_Dec-18-2021_-21_full.txt
│ │ ├── mit_vibrations_and_waves_001_vid2txt_Dec-18-2021_-22_full.txt
│ │ ├── mit_vibrations_and_waves_002_vid2txt_Dec-18-2021_-22_full.txt
│ │ ├── mit_vibrations_and_waves_003_vid2txt_Dec-18-2021_-22_full.txt
│ │ ├── neuspell_results
│ │ ├── mit_matrices_sgd_000_vid_2_txt_dec_18202120_full_NSC_results.txt
│ │ ├── mit_matrices_sgd_001_vid_2_txt_dec_18202121_full_NSC_results.txt
│ │ ├── mit_matrices_sgd_002_vid_2_txt_dec_18202121_full_NSC_results.txt
│ │ ├── mit_signals_000_vid_2_txt_dec_18202121_full_NSC_results.txt
│ │ ├── mit_signals_001_vid_2_txt_dec_18202121_full_NSC_results.txt
│ │ ├── mit_signals_002_vid_2_txt_dec_18202121_full_NSC_results.txt
│ │ ├── mit_vibrations_and_waves_000_vid_2_txt_dec_18202121_full_NSC_results.txt
│ │ ├── mit_vibrations_and_waves_001_vid_2_txt_dec_18202122_full_NSC_results.txt
│ │ ├── mit_vibrations_and_waves_002_vid_2_txt_dec_18202122_full_NSC_results.txt
│ │ └── mit_vibrations_and_waves_003_vid_2_txt_dec_18202122_full_NSC_results.txt
│ │ └── results_SC_pipeline
│ │ ├── mit_matrices_sgd_000_vid_2_txt_dec_18202120_full_NSC_SBD.txt
│ │ ├── mit_matrices_sgd_001_vid_2_txt_dec_18202121_full_NSC_SBD.txt
│ │ ├── mit_matrices_sgd_002_vid_2_txt_dec_18202121_full_NSC_SBD.txt
│ │ ├── mit_signals_000_vid_2_txt_dec_18202121_full_NSC_SBD.txt
│ │ ├── mit_signals_001_vid_2_txt_dec_18202121_full_NSC_SBD.txt
│ │ ├── mit_signals_002_vid_2_txt_dec_18202121_full_NSC_SBD.txt
│ │ ├── mit_vibrations_and_waves_000_vid_2_txt_dec_18202121_full_NSC_SBD.txt
│ │ ├── mit_vibrations_and_waves_001_vid_2_txt_dec_18202122_full_NSC_SBD.txt
│ │ ├── mit_vibrations_and_waves_002_vid_2_txt_dec_18202122_full_NSC_SBD.txt
│ │ └── mit_vibrations_and_waves_003_vid_2_txt_dec_18202122_full_NSC_SBD.txt
└── TEST_singlefile
│ ├── base_v2clntxt_transc_metadata
│ └── president_john_f_kennedys_peace_speech_vid2txt_Dec-15-2021_-01_metadata.csv
│ ├── base_v2clntxt_transcriptions
│ ├── YAKE - all keys for batch Dec-15-2021_-01.csv
│ ├── neuspell_results
│ │ └── president_john_f_kennedys_peace_speech_vid_2_txt_dec_15202101_full_NSC_results.txt
│ ├── president_john_f_kennedys_peace_speech_vid2txt_Dec-15-2021_-01_full.txt
│ └── results_SC_pipeline
│ │ └── president_john_f_kennedys_peace_speech_vid_2_txt_dec_15202101_full_NSC_SBD.txt
│ ├── console_prinout_basemodel.md
│ ├── console_printout_largeWav2Vec2.md
│ ├── dl_src_video.py
│ ├── large_v2clntxt_transc_metadata
│ └── president_john_f_kennedys_peace_speech_vid2txt_Dec-15-2021_-01_metadata.csv
│ └── large_v2clntxt_transcriptions
│ ├── YAKE - all keys for batch Dec-15-2021_-01.csv
│ ├── neuspell_results
│ └── president_john_f_kennedys_peace_speech_vid_2_txt_dec_15202101_full_NSC_results.txt
│ ├── president_john_f_kennedys_peace_speech_vid2txt_Dec-15-2021_-01_full.txt
│ └── results_SC_pipeline
│ └── president_john_f_kennedys_peace_speech_vid_2_txt_dec_15202101_full_NSC_SBD.txt
├── helper
└── en-80k.txt
├── requirements.txt
├── setup.py
└── vid2cleantxt
├── __init__.py
├── audio2text_functions.py
├── transcribe.py
└── v2ct_utils.py
/.gitignore:
--------------------------------------------------------------------------------
1 |
2 | # common repo-related filetypes
3 |
4 | *.pdf
5 | *.xlsx
6 | *.csv
7 |
8 | # force-add notebooks and examples
9 | *colab_notebooks/
10 | *examples/
11 | *helper/
12 |
13 | # eggs
14 | */eggs/
15 | *.egg
16 |
17 |
18 | ### JupyterNotebooks ###
19 | # gitignore template for Jupyter Notebooks
20 | # website: http://jupyter.org/
21 |
22 | .ipynb_checkpoints
23 | */.ipynb_checkpoints/*
24 |
25 | # IPython
26 | profile_default/
27 | ipython_config.py
28 |
29 | # Remove previous ipynb_checkpoints
30 | # git rm -r .ipynb_checkpoints/
31 |
32 | ### Python ###
33 | # Byte-compiled / optimized / DLL files
34 | __pycache__/
35 | *.py[cod]
36 | *$py.class
37 | \__pycache__
38 | *__pycache__*
39 | # C extensions
40 | *.so
41 |
42 | # Distribution / packaging
43 | .Python
44 | build/
45 | develop-eggs/
46 | dist/
47 | downloads/
48 | eggs/
49 | .eggs/
50 | parts/
51 | sdist/
52 | var/
53 | wheels/
54 | pip-wheel-metadata/
55 | share/python-wheels/
56 | *.egg-info/
57 | .installed.cfg
58 | *.egg
59 | MANIFEST
60 |
61 | # PyInstaller
62 | # Usually these files are written by a python script from a template
63 | # before PyInstaller builds the exe, so as to inject date/other infos into it.
64 | *.manifest
65 | *.spec
66 |
67 | # Installer logs
68 | pip-log.txt
69 | pip-delete-this-directory.txt
70 |
71 | # Unit test / coverage reports
72 | htmlcov/
73 | .tox/
74 | .nox/
75 | .coverage
76 | .coverage.*
77 | .cache
78 | nosetests.xml
79 | coverage.xml
80 | *.cover
81 | *.py,cover
82 | .hypothesis/
83 | .pytest_cache/
84 | pytestdebug.log
85 |
86 | # Translations
87 | *.mo
88 | *.pot
89 |
90 | # Django stuff:
91 | *.log
92 | local_settings.py
93 | db.sqlite3
94 | db.sqlite3-journal
95 |
96 | # Flask stuff:
97 | instance/
98 | .webassets-cache
99 |
100 | # Scrapy stuff:
101 | .scrapy
102 |
103 | # Sphinx documentation
104 | docs/_build/
105 | doc/_build/
106 |
107 | # PyBuilder
108 | target/
109 |
110 | # Jupyter Notebook
111 |
112 | # IPython
113 |
114 | # pyenv
115 | .python-version
116 |
117 | # pipenv
118 | # According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
119 | # However, in case of collaboration, if having platform-specific dependencies or dependencies
120 | # having no cross-platform support, pipenv may install dependencies that don't work, or not
121 | # install all needed dependencies.
122 | #Pipfile.lock
123 |
124 | # poetry
125 | #poetry.lock
126 |
127 | # PEP 582; used by e.g. github.com/David-OConnor/pyflow
128 | __pypackages__/
129 |
130 | # Environments
131 | # .env
132 | .env/
133 | .venv/
134 | env/
135 | venv/
136 | ENV/
137 | env.bak/
138 | venv.bak/
139 | pythonenv*
140 |
141 | # Rope project settings
142 | *.log*
143 |
144 | # mkdocs documentation
145 | /site
146 |
147 | # mypy
148 | .mypy_cache/
149 | .dmypy.json
150 | dmypy.json
151 |
152 | # IDE
153 | .vscode
154 |
155 | # pytype static type analyzer
156 | .pytype/
157 |
158 | # operating system-related files
159 | # file properties cache/storage on macOS
160 | *.DS_Store
161 | # thumbnail cache on Windows
162 | Thumbs.db
163 |
164 | # profiling data
165 | .prof
166 |
167 | # IDE-related files
168 | .github
169 | .idea
170 |
171 | # local temp dirs
172 | scratch
173 | notebooks
174 | *audio_chunks*
175 | *test2*
176 |
177 | # media files
178 | *.mp4
179 | *.wav
180 | *.mov
181 | *.mp3
--------------------------------------------------------------------------------
/HISTORY.md:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/pszemraj/vid2cleantxt/2034489f538e22d62e508add517c45cc6093d85f/HISTORY.md
--------------------------------------------------------------------------------
/LICENSE:
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/Pipfile:
--------------------------------------------------------------------------------
1 | [[source]]
2 | url = "https://pypi.org/simple"
3 | verify_ssl = true
4 | name = "pypi"
5 |
6 | [packages]
7 | librosa = "~=0.8.1"
8 | wordninja = "~=2.0.0"
9 | psutil = "~=5.8.0"
10 | natsort = "~=7.1.1"
11 | pandas = "~=1.3.0"
12 | moviepy = "~=1.0.3"
13 | transformers = "~=4.15.0"
14 | numpy = "~=1.21.0"
15 | pydub = "~=0.24.1"
16 | symspellpy = "~=6.7.0"
17 | joblib = "~=1.0.1"
18 | torch = "~=1.9.0"
19 | tqdm = "~=4.43.0"
20 | plotly = "~=4.14.3"
21 | yake = "~=0.4.8"
22 | pysbd = "~=0.3.4"
23 | clean-text = "*"
24 | humanize = "~=3.13.1"
25 | neuspell = "~=1.0.0"
26 | openpyxl = ">=3"
27 | spacy = ">=3.0.0,<4.0.0"
28 | en-core-web-sm = {file = "https://github.com/explosion/spacy-models/releases/download/en_core_web_sm-3.0.0/en_core_web_sm-3.0.0.tar.gz"}
29 | GPUtil = "~=1.4.0"
30 | Unidecode = "~=1.3.2"
31 |
32 | [dev-packages]
33 |
34 | [requires]
35 | python_version = "3.8"
36 |
--------------------------------------------------------------------------------
/examples/TEST_folder_edition/CITATIONS:
--------------------------------------------------------------------------------
1 | # Citations for the MIT OpenCourseWare Videos
2 |
3 | ## Videos
4 |
5 | Lecture 13: Dispersive Medium, Phase Velocity, Group Velocity | Part II: Electromagnetic Waves | Physics III: Vibrations and Waves | Physics | MIT OpenCourseWare. (n.d.). Retrieved December 12, 2021, from https://ocw.mit.edu/courses/physics/8-03sc-physics-iii-vibrations-and-waves-fall-2016/part-ii-electromagnetic-waves/lecture-13/
6 |
7 | Lecture 24: Butterworth Filters | Video Lectures | Signals and Systems | MIT OpenCourseWare. (n.d.). Retrieved December 12, 2021, from https://ocw.mit.edu/resources/res-6-007-signals-and-systems-spring-2011/video-lectures/lecture-24-butterworth-filters/
8 |
9 | Lecture 25: Stochastic Gradient Descent | Video Lectures | Matrix Methods in Data Analysis, Signal Processing, and Machine Learning | Mathematics | MIT OpenCourseWare. (n.d.). Retrieved December 12, 2021, from https://ocw.mit.edu/courses/mathematics/18-065-matrix-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/video-lectures/lecture-25-stochastic-gradient-descent/
10 |
11 | ## Course Pages
12 |
13 | Yen-Jie Lee. 8.03SC Physics III: Vibrations and Waves. Fall 2016. Massachusetts Institute of Technology: MIT OpenCourseWare, . License: Creative Commons BY-NC-SA.
14 |
15 | Gilbert Strang. 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning. Spring 2018. Massachusetts Institute of Technology: MIT OpenCourseWare, . License: Creative Commons BY-NC-SA.
16 |
17 | Alan Oppenheim. RES.6-007 Signals and Systems. Spring 2011. Massachusetts Institute of Technology: MIT OpenCourseWare, . License: Creative Commons BY-NC-SA.
18 |
--------------------------------------------------------------------------------
/examples/TEST_folder_edition/dl_src_videos.py:
--------------------------------------------------------------------------------
1 | """
2 | dl_src_video.py - Download source videos from dropbox.
3 |
4 | All videos are under creative commons license and are cited in CITATIONS file in this working directory.
5 |
6 | link to folder containing all videos : https://www.dropbox.com/sh/0u3easov5bygo5l/AACXWZ_gXhAsSTHg64FYsjf5a?dl=0
7 |
8 | In case of dropbox server issues, please refer to original URLs in CITATIONS file.
9 | """
10 | import requests
11 | import os
12 | from os.path import join
13 | from tqdm.auto import tqdm
14 |
15 | multi_test = {
16 | "MIT_MatricesSGD_000.mp4": "https://www.dropbox.com/s/9b0j41zf3jaswv2/MIT_MatricesSGD_000.mp4?dl=1",
17 | "MIT_MatricesSGD_001.mp4": "https://www.dropbox.com/s/691qsessxsbzbvz/MIT_MatricesSGD_001.mp4?dl=1",
18 | "MIT_MatricesSGD_002.mp4": "https://www.dropbox.com/s/tqzn5ocnx0rghw7/MIT_MatricesSGD_002.mp4?dl=1",
19 | "MIT_Signals_000.mp4": "https://www.dropbox.com/s/bgyk0azwp67rbvn/MIT_Signals_000.mp4?dl=1",
20 | "MIT_Signals_001.mp4": "https://www.dropbox.com/s/uufiecjos44vh4d/MIT_Signals_001.mp4?dl=1",
21 | "MIT_Signals_002.mp4": "https://www.dropbox.com/s/zuyiqbqw2fn3tb8/MIT_Signals_002.mp4?dl=1",
22 | "MIT_VibrationsAndWaves000.mp4": "https://www.dropbox.com/s/laeo90gjdlqffn2/MIT_VibrationsAndWaves000.mp4?dl=1",
23 | "MIT_VibrationsAndWaves001.mp4": "https://www.dropbox.com/s/8s9vwohtlyseoq9/MIT_VibrationsAndWaves001.mp4?dl=1",
24 | "MIT_VibrationsAndWaves002.mp4": "https://www.dropbox.com/s/7rpg5nxcvzd0m9x/MIT_VibrationsAndWaves002.mp4?dl=1",
25 | "MIT_VibrationsAndWaves003.mp4": "https://www.dropbox.com/s/whwe8qydcnmkgf1/MIT_VibrationsAndWaves003.mp4?dl=1",
26 | } # contains all videos for the example
27 |
28 |
29 | def download_single_file(link, filename):
30 | """Download a single file from a remote server."""
31 | local_name = join(os.getcwd(), "examples", "TEST_folder_edition", filename)
32 | if os.path.exists(local_name):
33 | print(f"\nFile {filename} already exists. Skipping download.")
34 | return
35 | print("\nDownloading file...")
36 | with open(local_name, "wb") as f:
37 | f.write(requests.get(link).content)
38 | print(f"\nDownload of {filename} complete.")
39 |
40 |
41 | if __name__ == "__main__":
42 | pbar = tqdm(total=multi_test.__len__(), desc="Downloading example videos")
43 | for filename, link in multi_test.items():
44 | download_single_file(link, filename)
45 | pbar.update(1)
46 | pbar.close()
47 |
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/examples/TEST_folder_edition/wav2vec2-large-v2clntxt_transc_metadata/mit_matrices_sgd_002_vid2txt_Dec-18-2021_-21_metadata.csv:
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1 | orig_file,num_audio_chunks,chunk_len_sec,input_dur_mins,date_of_transc,full_text,num_chars,word_count
2 | MIT_MatricesSGD_002.mp4,53,15,13.25,Dec-18-2021_-21,"WELL LET'S LET ME ACTUALLY TELL YOU THEN ABOUT RATHER THAN THE THE PROOF I THINK I'LL SHARE THE PROOF WITH GILL BECAUSE THE PROOF THAT I WANT WANTED TO ACTUALLY SHOW YOU GIVES A PROOF OF
3 | THE STOCASTIC GRADIENT IS WELL BEHAVED ON BOTH CONVEX AND NON CONVEX PROBLEMS AND THE PROOF I WANTED TO SHOW WAS FOR THE NON CONVEX CASE BECAUSE IT APPLIES TO NEURAL NETWORK SO YOU MAY BE CURIOUS ABOUT THAT PROOF AND REMARKABLY THAT PROOF IS MUCH SIMPLER THAN THE CASE OF CONVEX
4 | PROBLEMS SO LET ME JUST MENTION SOME VERY IMPORTANT POINTS ABOUT SARCASTIC RADIENT SO EVEN THOUGH THIS METHOD HAS BEEN AROUND SINCE NINETEEN FIFTY ONE EVERY DEEP LEARNING TOOLKIT HAS IT AND WE ARE STUDYING IT IN CLASS THERE ARE STILL GAPSBET
5 | IN WHAT WE CAN SAY THEORETICALLY AND WHAT HAPPENS IN PRACTICE AND I'LL SHOW YOU THOSE GAPS ALREADY AND ENCOURAGE YOU TO THINK ABOUT THOSE IF YOU WISH SO LET'S LOOK BACK AT OUR PROBLEM AND TELL YOU ABOUT TWO VARIANTS SO HERE ARE THE TWO VARIANTS I'M GOING
6 | ASK IF ANY OF YOU IS FAMILIAR WITH THESE VARIANTS IN SOME WAY OR OTHER SO LET'S I JUST CALLED IT FEASIBLE HERE THERE ARE NO CONSTRAINTS SO YOU START WITH ANY RANDOM FACTOR OF YOUR CHOICE IN DEEP NETWORK TRAIN
7 | YOU HAVE TO WORK HARDER AND THEN THIS IS THE ITERATION YOU RUN RIGHT OPTION ONE AND OPTION TWO SO OPTION ONE SAYS THAT WAS THE IDEA WE HAD IN CLASS RANDOM LY PICK SOME TRAINING DATA POINT USE ITS DORCASTIC GRADIENT
8 | WELL WHAT DO WE MEAN BY RANDOM LY PICK THE MOMENT YOU USE THE WORD RANDOM YOU HAVE TO DEFINE WHAT'S THE RANDOM NESS SO ONE RANDOM NESS IS UNIFORM PROBABILITY
9 | AND TRAINING DATA POINTS THAT IS ONE'S RANDOMNESS THE OTHER VERSION IS YOU PICK A TRAINING DATA POINT WITHOUT REPLACEMENT SO SO WITH REPLACEMENT MEANS YOU KNOW JUST UNIFORMLY AT RANDOM EACH TIME
10 | DRAW A NUMBER FROM ONE THROUGH N USE THAT SARCASTIC RADIENT MOVE ON WHICH MEANS THE SAME POINT CAN EASILY BE PICKED TWICE ALSO AND WITHOUT REPLACEMENT MEANS IF YOU'VE PICKED U POINT NUMBER THREE YOU'RE NOT GOING TO PICK IT AGAIN UNTIL YOU'VE
11 | THROUGH THE ENTIRE TRAINING DATA SET THOSE ARE TWO TYPES OF RANDOMNESS WHICH VERSION WOULD YOU USE THERE IS NO RIGHT OR WRONG ANSWER TO THIS I'M JUST TAKING A POLE
12 | WHAT WOULD YOU USE THINK THAT YOU'RE WRITING A PROGRAMME FOR THIS AND MAYBE THINK REALLY PRAGMATICALLY PRACTICALLY THAT'S ENOUGH OF AN HIN WHICH VERSION WOULD YOU USE I'M JUST CURIOUS
13 | WHO WOULD USE ONE PLEASE RAISE HANDS O WHO AND THE THE EXCLUSION THE COMPLIMENT THEREOF OR I DON'T KNOW MAYBE SOME PEOPLE ARE UNDECIDED WHO WOULD USE TOO VERY FEW PEOPLE WO
14 | OK HOW MANY OF YOU USE THE NEURAL NETWORK TRAINING TOOL KITS LIKE DENSE FLO PIT TORCH WHAT NOT WHICH VERSION ARE THEY USING
15 | ACTUALLY EVERY PERSON IN THE REAL WORLD IS USING VERSION TOO ARE YOU REALLY GOING TO RANDOMLY GO THROUGH YOUR RAM EACH TIME TO PICK RANDOM POINTS THEY'LL KILL YOUR G P PERFORMANCE LIKE ANYTHING
16 | WHAT PEOPLE DO IS TAKE A DATA SET USE A PRE SHUFFLE OPERATION AND THEN JUST WHOOP STREAM THROUGH THE DATA WHAT DOES STREAMING THROUGH THE DATA MEAN WITHOUT REPLACEMENT SO ALL THE TOOLKITS ACTUALLY ARE USING THE WITHOUT REPLACEMENT ER
17 | EVEN THOUGH INTUITIVELY THE RE JUS UNIFORM RANDOM FEELS MUCH NICER AND THAT FEELING IS NOT ILL FOUNDED BECAUSE THAT'S THE ONLY VERSION WE KNOW HOW TO ANALYZE MATHEMATICALLY SO EVEN FOR THIS METHOD EVERYBODY STUDIES IT THERE
18 | AN PAPERS ON IT THE VERSION THAT IS USED IN PRACTICE IS NOT THE VERSION WE KNOW HOW TO ANALYZE IT'S A MAJOR OPEN PROBLEM IN THE FIELD OF STOCASTIC GRADIENT TO ACTUALLY ANALYZE THE VERSION THAT WE USE IN PRACTICE THIS KIND OF
19 | RISING BUT IT'S WITHOUT REPLACEMENT MEANS NON IID PROBABILITY THEORY AND NON IIDE PROBABILITY THEORY IS NOT SO EASY THAT'S THE ANSWER O K SO THE OTHER VERSION IS THIS MINE BATCH IDEA WHICH
20 | MENTIONED REALLY EARLY ON IS THAT RATHER THAN PICK ONE RANDOM POINT I'LL PICK A MINNIE BATCH SO I HAD A MILLION POINTS EACH TIME INSTEAD OF PICKING ONE MAYBE I'LL PICK
21 | TEN OR HUNDRED OR THOUSAND OR WHAT HAVE YOU SO THIS AVERAGES THINGS AVERAGING THINGS REDUCES THE VARIANTS SO THIS IS ACTUALLY A GOOD THING CAUSE THE MORE QUANTITIES YOU AVERAGE THE LESS NOISE YOU HAVE THATS
22 | KIND OF WHAT HAPPENS IN PROBABILITY RIGHT SO WE PICK A MINNIE BATCH AND THE SARCASTIC ESTIMATE NOW IS THIS YOU KNOW NOT JUST A SINGLE GRADIENT BUT AVERAGED OVER A MINNIE BATCH
23 | SO MINI BATCH OF SIZE ONE IS THE PURE VANILLA S G D MINNI BATCH OF SIZE N IS NOTHING OTHER THAN PURE GRADIENT DESCENT SOMETHING IN BETWEEN IS WHAT PEOPLE ACTUALLY USE AND AGAIN THE THEORETICAL ANALYSIS ONLY EX
24 | IF THE MINNIE BATCH IS PICKED WITH REPLACEMENT NOT WITHOUT REPLACEMENT SO ONE OF THE REASONS ACTUALLY A VERY IMPORTANT THING IN THEORY YOU DON'T GAIN TOO MUCH IN TERMS OF COMPUTATIONAL GAINS ON CONVERGENCE
25 | PEED BY USING MANY MATCHES BUT MINY BATCHES ARE REALLY CRUCIAL SPECIALLY IN YOUR DEEP LEARNING GPU STYLE TRAINING BECAUSE THEY ALLOW YOU TO DO THINGS IN PARALLEL EACH THREAD OR EACH CORE OR SUB
26 | OR OR SMALL CHIP OR WHAT HAVE YOU DEPENDING ON YOUR HARDWARE CAN BE WORKING WITH ONE SORCASTIC RADIANT SO MINNI BATCHES THE LARGER THE MINNIE BATCH THE MORE THINGS YOU CAN DO IN PARALLEL SO MINNI BATCHES ARE GREATLYEXPLOT
27 | BY PEOPLE TO ER GIVE YOU A CHEAP VERSION OF PARALELISM AND WHERE DOES THE PARALLELISM HAPPEN YOU CAN THINK THAT EACH CORE COMPUTES A SARCASTIC GRADIENT SO THE HARD PART IS NOT
28 | ADDING THESE THINGS UP AND MAKING THE UPDATE TO X THE HARD PART IS COMPUTING A SARCASTIC GRADIENT SO IF YOU CAN COMPUTE TEN THOUSAND OF THOSE IN PARALLEL BECAUSE YOU HAVE TEN THOUSAND CORES GREAT FOR YOU AND THAT'S THE REASON PEOPLE LOVE USING MANE
29 | ACHES BUT A NICE SIDE REMARK HERE THIS IS ALSO THIS BRINGS US CLOSE TO THE RESEARCH EDGE OF THINGS AGAIN THAT WELL YOU'D LOVE TO USE VERY LARGE MINNIE BADGES SO THAT YOU CAN FULLY MAX OUT ON THE PARA
30 | ISM AVAILABLE TO YOU RIGHT MAYBE YOU HAVE A MULTI GEP SYSTEM IF YOUARNO FRIENDS WITH ENVY DEAR GOGA I ONLY HAVE LIKE TWO GPS BUT DEPENDS ON HOW MANY GPS YOU HAVE YOU'D LIKE TO REALLY MAX OT ON PARALLELISM SO THAT YOU CAN REALLY
31 | UNCH THROUGH BIG DATA SETS AS FAST AS POSSIBLE BUT YOU KNOW WHAT HAPPENS WITH VERY LARGE MINNY BATCHES SIFYO HAVE VERY LARGE MINNI BATCHES STARCASTIC GRADIENT STARTS LOOKING MORE LIKE
32 | FULL GRADIENT DESCENT WHICH IS ALSO CALLED BACH GRADIENT DESCENTTHAT'S NOT A BAD THING THAT'S AWESOME FOR OPTIMIZATION BUT IT IS A WEIRD CONUNDRUM THAT HAPPENS IN TRAINING DEEP NERAL NETWORKS
33 | THIS TYPE OF PROBLEM WE WOULDN'T HAVE FOR CONVEX OPTIMIZATION BUT IN DEEP NURALET WECAUS THIS REALLY DISTURBING THING HAPPENS THAT IF YOU USE THESE VERY LARGE MANY BATCHES YOUR METHOD STARTS RESEMBLING RADIANT DESCENT THAT MEANS IT DECREASES NOISE
34 | MUCH SO THAT THIS REGION OF CONFUSION SHRINKS SO MUCH WHICH ALL SOUNDS GOOD BUT IT ENDS UP BEING REALLY BAD FOR MACHINE LEARNING THAT'S WHAT I SAID THAT IN MACHINE LEARNING YOU WANT SOME REGION OF UNCERTAINTY AND WHAT IT
35 | MEANS ACTUALLY IS A LOT OF PEOPLE HAVE BEEN WORKING ON THIS INCLUDING AT BIG COMPANIES THAT IF YOU REDUCE THAT REGION OF UNCERTAINTY TOO MUCH YOU END UP OVER FITTING YOUR NEURAL NETWORK
36 | AND THEN IT STARTS SUCKING IN ITS TEST DATA UNSEEN DATA PERFORMANCE SO EVEN THOUGH FOR PARALLELISM PROGRAMMING OPTIMIZATION THEORY BIG MINNI BATCH IS AWESOME
37 | TUNATELY THERE PRICE TO BE PAID THAT IT HURTS YOUR TEST ERROR PERFORMANCE AND THEY'RE ALL SORTS OF METHODS PEOPLE ARE TRYING TO COOK UP INCLUDING A SHRINKING ETA
38 | INGLY OR CHANGING NEURA NETWORK ARCHITECTURE AND ALL SORTS OF IDEAS YOU CAN COOK UP YOUR IDEAS FOR YOUR FAVOURITE ARCHITECTURE HOW TO MAKE A LARGE MINNIE BATCH WITHOUT HURTING THE FINAL PERFORMANCE BUT IT'S STILL SOMEWHAT OF AN OPEN QUESTION ON HOW TO OPTIMIL
39 | ECT WHICH MENI HOW LARGE YOUR MANY BATS SHOULD BE SO EVEN THOUGH THESE IDEAS ARE SIMPLE YOU SEE THAT EVERY SIMPLE IDEA LEADS TO AN ENTIRE SUB AREA OF S G D
40 | HERE ARE PRACTICAL CHALLENGES PEOPLE HAVE VARIOUS HERISTICS FOR SOLVING THESE CHALLENGES YOU CAN COOK UP YOUR OWN BUT IT'S NOT THAT ONE IDEA ALWAYS WORKS SO IF YOU LOOK AT S G D WHAT ARE THE
41 | IN PARTS THE MOVING PARTS IN GD THE GRADIENTS STACASTIC GRADIENTS THE STEP SIZE THE MINNI BATCH SO HOW SHOULD I PICK STEP SIZES VERY NON TRIVIAL PROBLEM DIFFERENT DEEP LEARNING TO
42 | S MAY HAVE DIFFERENT WAYS OF AUTOMATING THAT TUNING BUT IT'S ONE OF THE PAINFUL THINGS WHICH MINNY BATCH TO USE WITH REPLACEMENT WITHOUT REPLACEMENT I ALREADY SHOWED YOU BUT WHICH MINNY BATCH SHOULD I USE HOW LARGE THAT SHOULD BE AGAIN NOT
43 | EASY QUESTION TO ANSWER HOW TO COMPUTE STARCASTIC GRADIENTS DOES ANYBODY KNOW HOW STARCASTIC GRADIENTS ARE COMPUTED FOR DEEP NETWORK TRAINING ANYBODY KNOW THERE ISA
44 | FAMOUS ELGARITHM CALLED BACK PROPAGATION THAT BACK PROPAGATION ELGRITHM IS USED TO COMPUTE A SINGLE STARCASTIC GRADIENT SOME PEOPLE USE THE WORD BACK PROP TO MEAN ASJIDDY BUT WHAT BACK PROP REALLY MEANS IS SOME
45 | SOME KIND OF ALGORISM WHICH COMPUTES FOR YOU A SINGLE SARCASTIC GRADIENT AND HENCE YOUKNOW THIS R TENSER FLUED CETRA THESE TOOLKISS THEY COME UP WITH ALL SORTS OF WAST AUTOMATE THE COMPUTATION OF A GRADIENT BECAUSE REALLY THAT'S THE MAIN THING
46 | AND THEN OTHER IDEAS LIKE RADIENT CLIPPING AND MOMENTUM ET CETERA THE BUNCH OF OTHER IDEAS AND THE THEORETICAL CHALLENGES I MENTIONED TO YOU ALREADY PROVING THAT IT WORKS THAT IT ACTUALLY SOLVES WHAT IT SET OUT TO DO UNFORTUNATELY I WAS TOO SLOW
47 | COULDN'T SHOW YOU THE AWESOME FIVE LINE PROOF THAT I HAVE THAT S GD WORKS FOR NEWRAL NETWORKS AND THEORETICAL ANALYSIS AS I SAID IS REALLY LAGGING MY PROOF ALSO USES THE WID
48 | CEMENT AND THE WITHOUT REPLACEMENT VERSION WHICH IS THE ONE THAT IS ACTUALLY IMPLEMENTED O THERE'S VERY LITTLE PROGRESS ON THAT THERE IS SOME PROGRESS THERE'S A BUNCH OF PAPERS INCLUDING FROM OUR COLLEAGUES THAT IMIGHTY BUT IT'S QUITE
49 | AND THE BIGGEST QUESTION WHICH MOST OF THE PEOPLE IN MACHINE LEARNING ARE CURRENTLY EXCITED ABOUT THESE DAYS IS STUFF LIKE WHY DOES S GD WORK SO WELL FOR NEURAL NETWORKS WE
50 | THIS SCRAPPY OPTIMIZATION METHOD IT VERY RAPIDLY DOES SOME FITTING DATA IS LARGE NEURO NETWORK IS LARGE AND THEN THIS NEURO NETWORK ENDS UP HAVING GREAT CLASSIFICATION PERFORMANCE WHY IS THAT HAPPENING THAT'S CALLED TRYING TO EXPLAIN
51 | BUILD A THEORY OF GENERALIZATION WHY DOES AN S G D TRAINED NEURA NETWORK WORK BETTER THAN NEURAL NETWORKS TRAIN WITH MORE FANCY OPTIMIZATION METHODS IT'S A MYSTERY AND MOST OF THE PEOPLE WHO TAKE INTEREST IN THEORETICAL MACHINE LEARNING AND STATISTICS
52 | THAT IS ONE OF THE MYSTERIES THEY ARE TRYING TO UNDERSTAND SO I THINK THAT'S MY STORY OF S JIDDY AND THIS IS THE PART WE SCAP BUT ITS SOKE THE THE INTUITION BEHIND US JDDYS MUCH MORE IMPORTANT THAN THIS
53 | SO I THINK WE CAN THANK YOU CLOSE MAYBEWER THE ROOF OR MONDAYS EXACTLY I THINK SO THAT
54 | HEY'LL BE GREAT
55 | ",10599,1912
56 |
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/examples/TEST_folder_edition/wav2vec2-large-v2clntxt_transc_metadata/mit_signals_002_vid2txt_Dec-18-2021_-21_metadata.csv:
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1 | orig_file,num_audio_chunks,chunk_len_sec,input_dur_mins,date_of_transc,full_text,num_chars,word_count
2 | MIT_Signals_002.mp4,21,15,5.25,Dec-18-2021_-21,"THE FILTHE FILTER THAT WE OBTAINED BY MAPPING THE BUTTERWORTH FILTER TO A DIGITAL FILTER THROUGH THE BIOLINEAL TRANSFORMATION IN FACT FALLS OFF IN FREQUENCY
3 | MUCH MORE RAPIDLY THAN THE ONE THAT WE GOT THROUGH IMPULSE AND VARIANCE A QUESTION IS WHY NOW ONE THOUGHT THAT MIGHT COME TO MIND AS WELL IMPULSE AND VARIANCE AS ALIASING THE BIOLINEAR TRANSFORM
4 | AN DOESN'T HAVE ALIASING THAT MUST BE A CONSEQUENCE OF ALIASING IN FACT THAT'S NOT THE REASON ALIASING AS IT TURNS OUT IN THIS PARTICULAR DESIGN IS WA WAS RELATIVELY MINIMAL IN THE IMPULSE AND VARIANT DESIGN
5 | THE REASON HAS TO DO WITH THIS NON LINEAR MAPPING IN THE BILINEAR TRANSFORMATION FROM THE CONTINUOUS TIME FREQUENCY TO THE DISCREET TIME FREQUENCY KEEP IN MIND THAT
6 | THROUGH THAT MAPPING AS YOU START WALKING AROUND THE UNIT CIRCLE AND MOVING UP THE JEOMEGA AXIS AS YOU MOVE UP THE JEOMEGA AXIS YOU HAVE TO MOVE FASTER AND FASTER AND FASTER AND FASTER AND WHAT'S IN
7 | NOUS TIME FREQUENCY AND INFINITY IS WHAT YOU GET TO IN THE DISCREET TIME FREQUENCY BY THE TIME YOU GET AROUND TO PI SO IN FACT WHAT WE'RE LOOKING AT IS AS AS WE LOOK OUT ALONG THIS
8 | QUENCY AXIS IS WE'RE SEEING HIGHER AND HIGHER AND HIGHER FREQUENCIES IN THE CONTINUOUS TIME FILTER BY THE TIME WE GET TO PI WE SHOULD IN FACT BE IN THE CONTINUOUS
9 | TIME FILTER EQUIVALENTLY OFF TO INFINITY WHICH SOUNDS LIKE A PRETTY UNCOMFORTABLE PLACE TO BE O K NOW THIS WAS A FAIRLY RAPID TRIP
10 | RO A NUMBER OF ISSUES IN PARTICULAR SOME OF THE ISSUES ASSOCIATED WITH THE BIOLINEAR TRANSFORMATION AND ALSO THIS ISSUE OF HOW YOU PICK THIS PEROMETER CAPITAL T AND HOW IT MIGHT BE
11 | TED WITH A SAMPLING FREQUENCY IF YOU'RE DOING DISCREET TIME PROCESSING OF CONTINUOUS TIME SIGNALS AND WE DON'T HAVE TIME TO EXPLORE SOME OF THOSE ISSUES MORE FULLY IN THIS LECTURE BUT I'D LIKE
12 | CONCLUDE BY MAKING A COUPLE OF COMMENTS ONE COMMENT IS THAT THE TWO TECHNIQUES THAT WE'VE TALKED ABOUT IMPULSE AND VARIANCE AND THE BIOLINEAR TRANSFORMATION ARE THE TWO TECHNIQUES THAT ARE PRINCIPALLY USED
13 | AND ONE THINKS OF MAPPING CONTINUOUS TIME FILTERS TO DISCREET TIME FILTERS FOR WHATEVER APPLICATION AND I STRESS AGAIN THAT YOU MAY WANT TO DO THAT MAPPING WHETHER OR NOT THE DISCREET TIME FILTER
14 | IS EVENTUALLY GOING TO BE USED FOR PROCESSING CONTINUOUS TIME SIGNALS NOW IMPULSE AND VARIANCE HAD THE CHARACTERISTIC THAT IT VERY NICE CHARACTERISTIC THAT THAT
15 | CORRESPONDS TO A LINEAR MAPPING BETWEEN THE TWO FREQUENCY AXES EXCEPT FOR THE ISSUE OF ALIASING AND THAT'S A PROBLEM WITH IT AND IN PARTICULAR LIMITS ITS USEFULNESS TO FILTER
16 | SIGNS OR FOR MAPPING CONTINUOUS TIME FILTERS THAT ARE BAND LIMITED ON THE OTHER HAND WE HAVE THE BILINEAR TRANSFORMATION AS A DESIGN PROCEDURE WHICH TOTALLY AVOIDS ALIOSING
17 | BUT HAS THE DISADVANTAGE OR DIFFICULTY THAT IT REPRESENTS A NON LINEAR MAPPING FROM THE CONTINUOUS TIME FILTER TO THE DISCREET TIME FILTER NOW THIS NON LINEAR DISTORTION IS PERFECTLY ACCEPT
18 | ABLE IF WE'RE DESIGNING OR ATTEMPTING TO DESIGN FILTERS THAT HAVE FLAT FREQUENCY CHARACTERISTICS IT'S NOT ACCEPTABLE IF FOR EXAMPLE WE HAD A LINEAR FREQUENCY CHARACTERISTIC THAT WE WANTED TO MAP TO A DISCREET TIME
19 | TER AND END UP WITH A LINEAR FREQUENCY CHARACTERISTIC IT WON'T COME OUT TO BE LINEAR BECAUSE OF THIS NON LINEAR MAPPING OF THE FREQUENCY AXES NOW THERE ARE ALSO A NUMBER OF OTHER DESIGN
20 | PROCEDURES WHICH WE WON'T GO INTO FOR DESIGNING DISCREET TIME FILTERS AND AMONG THEM ARE A VARIETY OF TECHNIQUES INCLUDING FOR EXAMPLE COMPUTERATED DESIGNED PROCEDURES AND I INVITE YOU
21 | IF YOU'RE INTERESTED AND WANT TO DIG INTO THAT IN MORE DETAIL AND MORE DEEPLY TO EXPLORE THAT TOPIC BY MAKING REFERENCE TO VARIOUS OF THE BOOKS LISTED IN THE BIBLIOGRAPHY
22 | IN THE TEXT THANK YOU
23 | ",3672,639
24 |
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/examples/TEST_folder_edition/wav2vec2-large-v2clntxt_transc_metadata/mit_vibrations_and_waves_002_vid2txt_Dec-18-2021_-22_metadata.csv:
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1 | orig_file,num_audio_chunks,chunk_len_sec,input_dur_mins,date_of_transc,full_text,num_chars,word_count
2 | MIT_VibrationsAndWaves002.mp4,80,15,20.0,Dec-18-2021_-22,"LANDS VERY VERY SIMILAR BETWEEN THE TWO WAVES RIGHT SO THEREFORE WHAT I AM GOING TO DO IS THAT I AM GOING TO ASSOON K ONE IS VERY CLOSE TO K TWO
3 | IS ROUGHLY K OK AND I M GOTO END BECAUSE OF THIS SINCE I HAVE A CONTINUOUS FUNCTION IF K Y IS RELLY CLOSE TO K TOO THAT MEANS O MAGA ONE IS GOING TO
4 | EALSO VERY CUSE TO OMEGA TOO RIGHT SO WHAT I AM GOING TO GET IS OMEGA ONE IS GOING TO BE ALSO VERY SIMILAR TO OMEGA TOO AND I WILL CALL IT OMEGA OK
5 | SO IF I DO THIS WHEN I HAVE VERY SIMILAR K ONE ANDE K TWO WHAT IS GOING TO HAPPEN WHAT IS GOING TO HAPPEN IS THAT K ONE MINUS K TWO WILL BE
6 | RYSMALL SOTA MEANS A THIS VERY SMALL K MEANS LARGE WAVE LANDS THEREFORE THIS COSINTEN WILD BECOME THEENVE
7 | BECAUSE THE SAY SE ARE SLOWLY BARITING A EMPERTU AS A FUNCTION OF POSITION BECAUSE A CASE VERY SMALL CASE CASE MALMEANS LAND ARE LARGE THEREFORE THEM
8 | DU IS GOING TO BE HAVING THIS MODULATION WHICH IS SATA LIKE A ENVELOPE HE TE THE SPEED OF THIS ENVELOPE THE OSCILLATION OF THIS ENVELOPE IS AS YO CONTRO BY THEK OK
9 | LAT LOOK AT THE LAPAN SITEN K ONE PROS K TWO OVER TWO IT'S KIND OF LIKE THE CALCULATING THE AVRAGE OF THE FIRST AND SECOND OF THE WAVE NUMBER OF THE FIRST AND SECOND WAVES RIGHT SO YOU WILL
10 | CLAT AVERAGE IT CAN BE STILL PETY LARGE THEREFORE YOU HAVE SMALL LONDE RIGHT COMPARED TO THE DIFFERENCE THEREFORE YOU SEE THAT TA I SHOUL CONTRIBUTE TO THOSE LITTLE STRUCTURES IN
11 | IN INDISCREPENT CALLED CARRIER YES TATAS
12 | SO THEY CAN BE DIFFERENTI THOUGHT Y SOSO YOU ARE ABSOLUTELY RIGHT IHT SO YOU CAN YOU CAN PRODUCEA SOME SOMETHING LIKE A CARRIER AA EVEN WHEN KINE IS NOT EQUAL TO K TWO RIS IS JUST AT EVERY RIT YOUARE RIGHT
13 | BUT THE THEN THETE ON THE OTHER HAND THE DIFFERENCE KAWY AND KA TOO WILL BE ALSO LARGE THEREFORE YU I'S NOT AS EASY AS WHAT WE HAVE BEEN DOING HERE TO IDENTIFY WHO IS THE
14 | EAR AND WHO IS THE ENVELOPE BUTE YOU DO YOU DO GET SOME KIND OF GRAF WHICH IS ICILLATING REALLY FAST BUT THE ENVELOPE IS GOING TO APPER ALSO ICILLATING REALLY FAST THAT IS HARDER TOO TO SEE AL THE STRUCTURE BUT
15 | YOUR ABSOLUTELY RIGHT YES VERY GOOD QUESTION SO NOW I HAVE THIS SET UP I ASSUME THAT THEY ARE VERY CLOSE TO EACH OTHER SO NOW I CAN DEFINE FACE VELOCITY FINALLY
16 | WITH DEFINE WHAT IS I U THE FACE OF VELOCITY THE FACE O VELOCITY I CALL IT V P YOU CAN SEE THAT BEFORE I ALREADY HAVE BEEN USING FACE VELOCITY V P FOR THE PREVIOUS
17 | ASTIONS THAT IN THE CASE OF NON DISPERSIVE MEDIUM THE FACE VELOCITY IS JUST A B P WHICH IS THE VELOCITY IN THE EQUATION AND IN THIS CASE B P WOLD BE EQUAL TO OR MAGA O
18 | AS WE DISCUSS EFOR LAS AT THE DEFINITION OF THIS FACE VELACITY O K AND I CAN NOW ALSO DEFINE THE GOVELOCITY OK
19 | GROUP VELOCITY E SAY SHOULDBE THE VELOCITY OF THE ENVELOPE OK I CAN CALCULATE THE VELOCITY OF THE ENVELOPE RIGHT IN THE CASE OF FACE VELOCITY I ANT CALCULATING
20 | THE VELOCITY OF THE CARRIER OK AM TAKING A RATIO OF THE AVERAGE AND THE I TE AVERAGE IS SO CLOSE TO K AND OBEGA THEREFORE THE FACE VELOCITY V P WOULD TEACH US THE SPEED OF THE PROBLICATION
21 | OF THE CARIE WHICH IS A OMEGAB K I CALL IT B P AND IN CASE OF GROUP VELOCITY I CALL IT B G B G IS DESCRIBING THE SPEED OF PROPAGATION OF THE ENVELOPE THEREFORE
22 | WHAT I'M GETTING IS OMEGA ONE MINUS OMEGA TWO OK TVI DEPI ONE MINUS K TWO POS OP AND HAVE A EFFECT OF ONE OVER TWO LIKE WHICHA
23 | CEN SOT RI AND WHEN THEY ARE REALLY SO CLOSE TO EACH OTHER THIS IS A SEL ROUGHLY LIKE THE OMEGA AND THE QUESTION SO FAR
24 | SO WE HAVE DERIVED TWO DIFFERENT KINDS OF SPEED ONE IS ACT RELATED TO THE FACE OF ALACITY WHICH ONE IS A ONE IS ATLY CALLED
25 | VELOCITY IS RELATED TO THE SPEED OF THE CARRIER OK THE OTHER ONE IS CRO VELOCITY WHICH ISENTLLY RELATED TO THEE SPEED OF THE ENVELOPE OK SO DA ME DISQUIDE YOU
26 | ARE INTERESTING INTERESTING EXAMPLES AND THE S WAKI WALT WE CAN NELY LEARN FROM THIS IN THE FIRST EXAMPLE I AM WALKING ON A NON DISPERSIVE MEDIAM OK IF I HAVE
27 | NON DISPERSIVE MEDIAN O K THEN PASTE WHAT IAM GOING TO GETIA OMEGA WILL BE PROPORTIONALE TO
28 | K IF I PRAT OMEGA VERSUS K IS A STRAIGHT LINE OK NOW IF I HAVE OMEGA I CHOOSE THE OMEGA OF THE TWO OMEGA WAN OMEGA TO
29 | THE TWO WAVES TO BE ROFTY EQUAL TO OMECA DIRO OK I CAN NOW EVALUATE THE V P THE V P WILL BE ER THE SLOPE RIGHT OF THE
30 | OF THIS POINT THE SLOPE OF A LINE CONNECTING THE TERO TO THAT POINT RIGHT WHICH SAY TO THE OMEGA OF BE CARI SO THAT ISU THE DEFINITION OF THE FASE VELOCITY IGET THIS SLOPE
31 | THIS IS THE SLOPE OF THIS THIS LINE ESSENTIALLY CALLEDEREATED TO THE FACE VELOCITY OK I CAN ALSO CALCULATE THE SLOPE OF A LINE CUT TO THIS POINT
32 | BUT I SHOULD CUT THROUGH TIS DESET TIS CURVE AND IN THIS CASE I AM ALSO GOING TO GET A LINE OVERLAPPING WITH FACE VELOCITY BECAUSE IN THIS CASE OMAGA OVER
33 | IS THE CONSTENT WHICH IS V THEREFORE IF NO MATTER WHAT YOU CALCULATE IF YOU CALCULATE V P AS A RATIO OF OMEGA AND HE K WOR YOU CALCULATE V G WHICH IS AS THE SLOW
34 | E LINE CUTTING THROUGH THAT POINT YOU ALWAYS GET GET AS YE BE OK THEREFORE WHAT WE LEARN FROM HERE IS THAT FOR A NON DISPERSIVE MEDIAN V P WILL BE EQUAL TO
35 | G OK NOW MEANS POST OF THIS A TWO CURVES POST OF THE CURVE OF A ENVELOPE DESCRIBING THE ENVELOPE AND DESCRIBING THE CARRIER
36 | IS GOING TO BE PROPAGATING AT E SANE SPEED ANY QUESTIONS SO THE WHOLE THING IS GOING TO BE MOVING AT A CONSTANT SPEED FOR THAT I CAN NOW SHOW YOU
37 | SOME EXAMPLE WHICH I PREPARED A SIN SIMULATION WHICH I PREPARED
38 | K SEE SO WHAT HE DOES IS THAT IT REALLYO WITH A SECOND DIS IS
39 | BIDZIRO OK SO THIS IS THE CASE WHEN I HAVE A NON DISPERSIVE MEDIUM OK IF I HAVE A NON DISPERSIVE MEDIUM WHAT IS GOING TO HAPPEN IS THAT BOS THAT IS A POSTER LA CARRIER
40 | WHICH IS THE SPEED OF THE AUDO'S LITTLE STRUCTURE AND THE ENVELOPE IS GOING TO BE PROPAGATING AT TE SENT SPEED SO YOU CAN SEE THE HIG IS LIKE A FIXED PATTERN IS PROPAGATING TOWARD THE RIGHT HAND SIDE AND TH THE RELATIVE MOTION
41 | BETWEEN THE FINE STRUCTURE AND THE ENVELOPE I SAT DERO SOPESI YOU HAVE EXACTLY THE SAME PATTERN AS A FUNCTION OF TIME OK SO NOW I AMT GOING TO MOVE FROM AWAY FROM THE NON DISPERSIVE MEDIUM
42 | HOW ABOUT WE DISCUSS WHAT WILL HAPPEN IF WE HAVE CONSIDER THE STIFFNESS OF THE STRING AND SEE WHAT WE GET FROM THERE SO IF I BROUGHT OMEGA
43 | AS A FUNCTION OF K O K AND THE CONSIDER AFA TO BE NON ZERO IS A POSITIVE VALUE SO IF I HAVE AFA TO BE A POSITIVE VALUE NON ZERO O K
44 | IN THIS CASE IAM GOING TO GET A CURVE LIKE THIS OK THE SLOPE IS SENTIALLY A CHANGING AND BECAUSE IT'S A CURVING DOWN IT'S CUVING UP BECAUSE IF YOU HAVE K LARGE
45 | THEN YOU WIL SEE THAT THE E RATIO OF OMEGA AND K AS TO INCREASE SO TOT ISSENTIALLY THE KIND OF CURV WHICH WE WOULD GET IF I SET THE OMEGA OF THE FIRST AND SECOND
46 | A WAF IN THE OF OF INCREST IN THIS STUDY TO BE OMEGADIRO NEBESITY WHAT YOU AREGOING TO GET IS THAT O K NOW I HAVE THIS POINT HERE UNDER CUFF OK IF I
47 | CALCULATE THE FACE VELOCITY THE FACE O VELOCITY HOW DO I CALCULATE THAT I CAN NOW CONNECT ZERO AND THAT POINT BY A LINE OK AND I CAN NOW CALCULATE
48 | LOPE OF THIS LINE AND I CAN GET THE AFACE VELOCITY VP OK ON THE OTHER HAND I CAN ALSO CALCULATE A THE SLOPE OF A LINE CUTTING
49 | THROGH TANGENTIAL TO TE THE POINT OF INTEREST OK AND THAT IS GOING TO GIVE ME A GOOD VELACITY O K AS YOU CAN SEE FROM HERE WHICH SLOPE IS AS YOU LARGER
50 | ANYBODY KNOW KENAAND POINTED OUT GROP VELOCITY IS LARGER RIGHT SO IN THIS CASE IF I TURN ON A FAR GREATER THAN ZERO WHAT IS GOING TO HAPPEN IS THAT SINCE THE CRUP VELOCITY IS LARGER THAN
51 | THE FACE VELOCITY THAT MEANS IF I GO BACK TO THAT PICTURE OK THE ENVELOPE IS GOING TO BE MOVING FASTER THEN THE FINE STRUCTURE INSIDE THE ENVELOPE HOW ABOUT WE TAKE A FIVE
52 | BREAK OM FROM HERE AND WE CONTINUE DISCUSSION AFTER BREAK WECAS A GOOD TIME TO TAKE AFREGHTO WELCOME BACK EVERYBODY SO WE WILL CONTINUE THE DISCUS
53 | ON OF THE PIT PHENOMENA SO WHAT WE HAVE SHOWN YOU IS THAT A PACE ON THOSE CURVES AS WE CANNESWIT DETERMINING WHAT WILL BE THE RELATIVE VELOCITY OF THE A OF THE
54 | WHAT WHAT WOULD BE THE VELOCITY OF TE THE CARRIER WHICH I SAY SOULD BE DENOTED BY AM T P AND THE WHAT WOULD BE THE VELOCITY OF THE ENVELOPE WHICH I SAY SULLY DENOTED
55 | BY A LAGRUPLOSITY O IM ENDING IN THE IN THIS CASE WHAT ITO BE PARTING HERE IS THAT IN THIS CASE BECAUSE ARFAISETALY GREATER THAN ZERO
56 | THEREFORE THIS A CUFISASOE A CURVING UP THEREFORE YOU HAVE LARGER A GROVELOCITY COMPARED TO THE FACE VELOCITY SO WHAT YOU WOULD EXPECT IS THAT THE EMB
57 | LOP IS GOING TO BE ACTUALLY PROGRESSING AT A SPEED HIGHER THAN THE SPEED OF A THE LA CARRIER OK ON THE OTHER HAND IF MANGICODE OK I CAN
58 | CONSTRUCT SOME KIND OF A MEDIAN WHICH CAN BE HISQUIVE IN WHICHI THE SITUATION ARE FAR SMALLER THAN DERON WHAT IS GOING TO HAPPEN SO IF I PROT THAT IF I PROT
59 | ATION WICH AFA SMALLER THAN TERO SO AND THE NOW I PROT OMEGA WAS THE FUNCTION OF K WHAT IS GOING TO HAPPEN JUST LIKE THIS TOPACITY YOU HAVE SOMETHING WHICH ISH IS RECURVIG
60 | DAN O K SO IF I NOW AGAIN WALK ON SOME POINT OF INTEREST HERE O K YOU CAN SEE THAT THESLO
61 | POF THE FACE VELOCITY IS NOW IT SHOULD BE AH THE SLOPE OF THE THE FACE VELOCITY IS NOW AT SHOULD BE LARGER THAN THE SLOPE WHICH IS ASUALLY A
62 | LINE CUTTING THROUGH THEE TANGENT TO THE THE CUF WHICH SAE ARE GETTING YOU THE GRUPLASY SO IN THE CASE OF AFAS MOR THEN ZERO
63 | WHICH IS SON STRANGEA AMEDIUM WHICH I CAN CREATE FROM WHAEVER PASMA OR SOME REATY A STRANGE A KIND NEW KIND OF MATERIAL OF INTEREST IF THAT HAPPENS THEN THAT MEANS YOU WERE A GRUP
64 | CITY WILL BE SMALLER THAN DUG THE FACEELACETY OK AND IF YOU LOOK AT THIS POINT HERE YOU CAN SEE THAT THIS CURVE ATO THE
65 | A MEXIMMAN HERE ANDE IF YOU ESUDY ARE OPERATING AT THIS POINT WHAT IS GOING TO HAPPEN WHAT IS GOING TO HAPPEN IS THAT IF YOU CALCULATE THE GROUP
66 | CITY WOL BET ABOUT O YOU'LL BE TERON WHAT DOES THAT MEAN THAT MEANS THE ENVELOPE WILL NOT BE MOVING ALONG OK BUT THE THE THE CARRIERS ARE STILL MOVINGO
67 | SINDEED AT THIS POINT YOU ARE GAY GOING TO GET GOD VOLOCITY EQUAL TO ZER OK AND FINALLY IF YOU ASHOD
68 | GOING TO A VERY LARGE CA VALUE IN THIS SCENEREO AFA SMALLER THAN ZERO YOU SEE THAT EVEN YOU CAN HAVE FACE VELOCITY B P
69 | POSITIVE BECAUSE HE SAYS Y A POSITIVE SLOPE AND ADUT VELOCITY AE IS NEGATIVE WHY WHAT DOES THAT MEAN NAI MEANS YOUA
70 | GOIN TO SEE A SITUATION THAT THE CARIERS ARE PROGRESSING IN A POSITIVE DIRECTION AND THE A THE THE ENVELOPE IS GOING TO BE A
71 | PROGRESSING IN THE NEGATIVE DIRECTION PROBIC FOQUESSING TO THE NEX LAPPING SIDE OF THE PORT SO WHAT DOES THAT MEAN THAT MIANS THIS WAVE IS DOING
72 | WHAT MICHAEL JESSON IS DOING LIES ESENTIALLY TWEN EH SO THIS ISSENTIALLY THE KIND OF THING WHICH COULD HAVE HAPPENED THAT IT LOOKS LIKE THAT
73 | ARE YOU ARE DOING YOARE GOING FORWARD BECAUSE ALL THE AR CARRIERS ARE MOVING IN A POSITIVE DIRECTION BUT THE BODY E SAYSOY GOING TO EARTH
74 | NEGATIVE DIRECTION OK MAYBE I CAN ALSO LEARN MOON WORK AT SOME POINT OK SO THAT'S GO BACK TO THE DEMONSTRATION WHICH I GOT STARTED AND SOMEHOW I GOT MEED UP A
75 | SO LETS TAKE A LOOK AT THE DETEMO AGAIN SO TAS LOOK AT ALL THE DIFFERENT SITUATION AT ONCE SO IN THIS CASEF US WE DISCUSSED BEFORE THIS ISSENTIALLY HAPPENING IN THE
76 | NON DISPERSIVE SITUATION TAT IN THIS SITUATION YOU HAVE A STRAIGHT LINE NON DISPERSIVE MEDIAN AS WE GIVE YOU ALWAYS THE GROP VELOCITY EQUAL TO A FACE VELOCITY OK SO
77 | IMEANS THE CARRIER AND THE A THE ENVELOPE IS GOING TO BE MOVING IN THE SAME DIRECTION AT THE SAME AS A SPEED OK ON THE
78 | HEHAND IN THIS CASE WE CAN ACTUALLY HAVE A SITUATION THAT THE THE FACEO VELOCITY ESSENTIALLY FASTER THAN THE GROUP VELOCITY O SO WHAT I MEAN IS THAT SILA SITUATION HERE
79 | FACE VELOCITY CALCULATED FROM A LINE CONNECTING FROM ZERO TO THAT POINT O IS ACTUALLY HAVING A LARGER SLOPE COMPARED TO THE TENGENTRA LINE AND YOU YOULL SEE THIS SITUATION SO BESY DO YOU SEE THAT
80 | INSIDE THE ENVELOPE ALL THOSE CARRIERS ARE ACTUALLY MOVING FASTER THAN THE ENVELOPE NOW I CAN HAVE A DISPERSIVE MEDIUM WHERE
81 | LACO VELOCITY IS SEQUEL TO TERO SO WHAT IS GOING TO HAPPEN IS THAT REALLY THE ENVELOPE ESSETALLY NOT MOVING IS NOT LIKE LAKE THIS EH BUT THA THE PARTY IS NOT MOVING RIGHT SO YOU HAVE SUNG
82 | ",11852,2399
83 |
--------------------------------------------------------------------------------
/examples/TEST_folder_edition/wav2vec2-large-v2clntxt_transc_metadata/mit_vibrations_and_waves_003_vid2txt_Dec-18-2021_-22_metadata.csv:
--------------------------------------------------------------------------------
1 | orig_file,num_audio_chunks,chunk_len_sec,input_dur_mins,date_of_transc,full_text,num_chars,word_count
2 | MIT_VibrationsAndWaves003.mp4,54,15,13.5,Dec-18-2021_-22,"CARRIESINSI THIS IN THIS IN THE STRUCTURE ESENTIALLY MOVING FORWARD BUT THE ENVELOPE ESSENTIALLY NOT MOVING
3 | SO FINALLY THE LAST SITUATION IS REALLY INTERESTING SO TAMIN IN THIS SITUATION THIS ISSANTIAL TE A HEAVY LACUBELOCITY A
4 | THE GROP VELOCITY IS ACTUALLY HAVING DIFFERENT SIGN COMPARED TO THE FACE VELOCITY SO YOU CAN SEE THAT THA THE WHOLE STRUCTURE OF THE ENVELOPE IS SANTIALLY MOVING BACKWARD BUT THAT THECAR
5 | ESPENCIALLY MOVING IN THE POSITIVE DIRECTION IN THIS EXAMPLE OK SO THIS ESPENTIALLY WHAT WE HAVE LEARNED FROM TE FROMTIS
6 | BIT PHENOMENA AND WE HAVE COVERED UP THE IDEA OF FACE VELOCITY AND HE GROUP VELOCITY SO HOW ABOUT FOUNDE CYSTEM HOW DO WE UNDERSTAND WHEN WE HAVE ABOUNDE SYSTEM
7 | HOW DOES THAT INVOLVE EVOLVE AS A FUNCTIONAL TIE SO IF I HAVE A SISTEN OF TWO WALLS AND THE ONE STRING AND OF COURSE I GIVE YOU THE DENSITY FOR DEINY LANDS AND
8 | THE TENT STRING TENSION AND ALSO THE AFA WHICH S AS WE TELL YOU ABOUT THE STEEPNESS OF THI SISTER OK AGAIN I CAN WRIDE DOWN SISTE TO BE
9 | SONG OF ORDER NO MORE MO FROM ONE TO INFINITY A M SIN K M X PAS AFM SIN
10 | ANT APAT AND THEN WHAT WE CAN DO IS THAT WE CAN FIRST GET THE INITIAL CONDITIONS OF THIS SYSTEM AND
11 | O THE BOUNDARY CONDITIONS OF THIS SYSTEM THEN WE AS JUST FOLLOW EXACTLY THE SAME PROCEDURE TO OBTAIN ALL THE UNKNOWN COEFFICIENTS THEN WE'LL BE ABLE TO EVOLVE THIS SYSTEM AS A FUNCTIONAL TIME AS I HAVE DEMONSTRATED YOU IN THE BEGINNING
12 | LECTURE SO IN THIS CASE YOU CAN HAVE TWO BOUNDARY CONDITIONS ONE ESESALLY AT X EQUAL TWO ZERO AND THE OTHER ONE IS ATE AT X EQUAL TO L O IN THOSE BOUNDARIES
13 | WE AS YE LEARNED BEFORE BECAUSE THE END POINTS ARE FIXED ON THE WALL THEREFORE SI OFTERO AT THE AT THE TIME T WILL BE ALWAYS
14 | EQUAL TO ZERO FOR THE LAFAND SI A PONDARY CONDITION AND THE VERY SIMILARDY AS WE DISCUSSED BEFORE SF L T WILL BE EQUAL TO ZERO IF YOU LOOK AT THE RIGHTAD SIDE OF THE WALL
15 | OF THE SISTER O SO I DON'T WANT TO REPEAT THIS BECAUSE THIS IS ATO EXACTLY THE SAME CALCULATION WHICH WE HAVE DONE BEFORE IGHT SO WITH THIS CONOND TIS TWO PONDARY CONDITIONS WE CAN ETU CONCRUDE AT
16 | M WILL BE EQUAL TO M PI OVER L AND THE F N WILL BE EQUAL TO ZERO OK SO YOU CAN ISSU GO BACK AND THE CHECK THIS
17 | A RESULT SO WHAT I WANT TO SAY IS THAT UNTIR NOW WHAT WE HAVE BEEN DOING IS IDENTICAL TO WHAT WE HAVE BEEN DOING FOR THE NON DISPRESSIVE MEDIUM O K WHAT I'M TO SAY IS THAT THE
18 | P THE NOMA MO IS ATESET BY THE BOUNDARY CONDITION IS DETERMINED BY THE BOUNDARY CONDITION AND IT HAS ACTUALLY SO FAR NOTHING TO DO WITH THE THE DISPERS
19 | RELATION O MAGA IS A FUNCTIONO OK SO SO IN SHORT BOUNDARY CONDITION CAN GIVE YOU THE SHAPE OF THENORMAL MOTE AND WE KNOW THAT THE FIRST NORMAL MO SECOND NORMAL MO ET CETERA ET CETERA
20 | ESAYIALLY AA GOING TO BE IDENTICAL TO THE CASE OF NON DISPERSIVE MEDIUM O K SO THAT AS BE THE FIRST THING WHICH WE LEARN THE SECOND THING WE LEARN IS THE O K NOW
21 | WHAT WE SEE IS THAT ONCE THE BOUNDARY CONDITION IS GIVEN THEN THE KN IS SA TO BE ALSO GIVEN THEREFORE SINCE I HAVE THE DISPERSION RELATION OMEGA AS A FUNCTIONAL K
22 | ASJON THER RIGHT OMEGA IS EQUAL TO OMEGA BOQS EQUAL TO V TIMES SQUARED TO THE ONE PROS OFA SQUARE RIGT THEREFORE HENCE K N IS GIVEN OMEGA
23 | IS ALSO GIBEN SO YOU CAN SEE THAT THAT'S AS SE WER THE DISPERSION RELATION COMING TO PRAY THE OMEGA AN
24 | BET DIFFERENT IF YOU COMPARE THE DISPERSIVE CASE AND NOT DISPERSIVE CASE OK SO THAT IS A TO BE ER WHAT I WANT TO SAY THE K N WHICH IS THE SHAPE OF THE NORMAL MOLE DOESN'T DEPEND
25 | ON THE DISPERSION RELATION ON THE OTHER HAND THE SPEED OF THE OSCILLATION THE ANGURAR FREQUENCY O MEGA DEPENDS ON THE DISPERSIAN RELATION WHICH ESPECIALLY WHILE WE ABTAINED IT FROM
26 | IF I START TO PROT OMEGA AND AS THE FUNCTION OF
27 | SO IN THE CASE OF NON DISPERSIVE MEDIUM SO WHAT I AM GOING TO GET IS I SHOULDBE DISCRETE POINT ALONG A STRAIGHT LINE OK TISSOE K ONE
28 | TOFOUR ETCETERA THERE I SOUE THERE ISHOULD BE ALL SITTING ON A COMMON STRAIGHT LINE OK IF YOU DO GETTE LOK TEOO
29 | TIVE AS A DIFFERENCE BETWEEN K ONE K TWO AND K THREE THEY ARE CONSTANT ACCORDING TO THIS FORMULA THE DIFFERENCE BETWEEN K Y AND K TWO IS PI OVER TWO K TWO AND K THREES ALSO POVER TWO
30 | ERL IS ALWAYS A FIXED NUMBER AND THE SING OMEGA ESSENTIALLY PROPORTIONAL TO K THEREFORE THE SPACING BETWEEN OMEGA ONE OMEGA TWO OMEGA
31 | THREE IS ALSO CONSTANT OK IN SHORT OMEGA TO OMICA TRE AND OMIGA FOUR ET CETERA IS ALWAYS A MULTIPLE TINES OF VAE
32 | GET FROM OMAKA ONE RIGHT ACCORDING TO A DISE QUAR AND IN THE CASE OF NONE DISPERSIVE MEDIUN OK SO WHAT DOES THAT MEAN NO MEANS O K NOW IF I HAVE
33 | A VERY COMPLICATED INITIAL CONDITION OK THIS ESETALLY WHAT I HAVE AN INITIAL CONDITION VERY COMPLICATED OK I JUST NEED TO WAIT IF THIS IS ASURE NON DISPERSIVE MED
34 | THAT I JUST HAVE TO WAIT UNTIL T EQUAL TO TWO PI OBE OMEGA ONE THEN THIS SYSTEM WOULD RESTORED TO ITS ORIGINAL SHAPE O CASE A SAY TOB WHAT I CAN LEARN FROM HERE
35 | BECAUSE O MAKE OUT TWO OR MAKE OUT THREE AND ANY HIGHER OTHER A NO MORE MODES THE ANGR FREQUENCY SAY SHE MULTIPLY TIMES OF WHAT I GET FROM OR MAKE OUT ONE O K
36 | ON THE OTHER HAND IF I CONSIDER THE SITUATION OF THISPERSIVE MEDIUM OK YOU CAN SEE THAT NOW NOW THE DIFFERENCE BETWEEN
37 | O MEGA N IS NOW THE CONSTANT OK SO WHILE YOU WERE PRODIGOUS THAT IT WOULD TAKE MUCH MUCH LONGER FOR THIS SYSTEM TO GO BACK TO THE ORIGINAL SHAPE COMPARED TO ER ER
38 | NON DISPERSIVE MEDIUM O CAS OR NOT IS WHETHER YOU CAN AS YOU SEE IN INA REAL LIFE A EXPERIMENT I CAN DISTORT THIS IT THIS EQUIPMENT IN THIS BOUNDS AS A SISTEN AND IS
39 | GOING TO TAKE FOREVER WOR IMPOSSIBLE TO COME BACK TO THE ORIGINAL SHAPE BECAUSE OF THE DISPERSIONO ON THE OTHER HAND IF I HAVE T REALLY HIGHLY IDEALIZED THE SITUATION IF I HAVE BOS AND BOUND AND I JUST HAVE
40 | WAIT UNTIL T EQUAL TO TWO PI OVER OR MAKE OT ONE THEN THIS SYSTEM WILL GO BACK TO THE ORIGINAL SHAPE BEFORE I END THE THE LECTURE TO DAY K
41 | I WOULD LIKE TO DISCUSS WITH YOU TOO INTERESTING ISSUE SO MANY OF YOU HAVE SEEN WATER WAVES EH AND FIRMANT AS YOU TOLD US IN
42 | LECTURE THAT WATER WAVES ARE THE ARE REALLY EASILY SEEN BY EVERYBODY BUT I SAYS SOUE THE WORST POSSIBLE EXAMPLE THAT'S THE BAD NEWS THE WORST POSSIBLE EXAMPLE BECAUSE IT HAS ALL THE POSSIBLE
43 | ER THAT WAVES CAN HAVE THAT'S THE BAD NEWS THE GOOD NEWS IS THAT YOU ARE GOING TO DO THAT IN YOUR PIAED SO WE WERE BIBL TO UNDERSTAND THE BEHAVIOUR OF THE WATER WAVESSAID
44 | THA GOOD NEWS THE SECOND THING WHICH I WOULD LIKE TO TALK ABOUT IS FACE VELOCITY OK YOU CAN SEE THAT THIS OK YOU CAN SAY O K YOU SAY THAT FACE VELOCITY OR HARMONICA WAVES DONTSEND
45 | INFORMATION RIGHT AND AND TE HOW DO I A SO KNOW THAT RIGHT SO WHAT DOES THAT MEAN O K SO LET'S TAKE THIS HORRIBLE EXAMPLE OF WATE WAVE OK S SOTELE THE BLACK LINE IS ASU E
46 | BEACH AND TEYOU THERE'S A WATER WAVE PON THE OCEAN APPROACHING THE BEACH AND YOU CAN SEE THAT YOU CAN HAVE SOME KIND OF ANGLE BETWEEN THE INCERTANT WATER WAVE AND THE LINE OF THE BEACH OK
47 | AH WHAT I CAN NEASELY DO IS THAT I CAN NOW MEASURE THE SHAPE OF THEWATER WATER WAVE AT AT THE EDGE OF BEACH AND THE WERY
48 | SEE THAT HA NOW THE LEFACE VELOCITY WHICH I OBSERVE THERE ESENTIALLY FASTER THAN THE SPEED OF A PROPAGATION OF THE WATERWAY BECAUSE OF THIS THIS
49 | INSIDE THE ANGLE OK I CAN ASLY MAKE IT VERY VERY FAST I CAN MAKE THIS SPEED ISHAB EVEN FASTER THAN THE SPEED OF LIGHT RIGHT
50 | I CAN I CAN I CAN NOW DECREASE THE THE SITA TO ZERO THEN YOU HAVE YOU HAVE A FACE VELOCITY WHICH IS FASTER THAN THE SPEED OF LIGHT IT GO TO INFINITY
51 | BUT DOES THAT MEAN ANYTHING ISE THAT DOEDNOT MEAN ANYTHING BECAUSE THATI DON'T REALLY MOVE WITH WATER FROM A SPECIFIC POINT TO ANOTHER POINT INFINITELY FAST
52 | THEREFORE WHAT I WANT TO SAY IS THAT OK YOU CAN DO WHATEVER YOU WANT TO MAKE A FANCY FACE VELOCITY BUT THAT WILL NOT HELP YOU WITH SENDING THINGS COSE TO THE SPEED OF LIGHT OR GREATE SPEED OF
53 | OK SO AS YOU CAN SEE FROM THE EXAMPLE I CAN EASILY CONSTRUT A SIMPLE EXAMPLE WHICH YOU SEE THAT IS THAT SE IS REALLY NOT SENDING ANYTHING FROM ONE PRESS TO THE OTHER BUT YOU STILL HAVE A READIRLLY FAST F
54 | I OKI THANK YOU VERY MUCH EVERYBODY FOR THE ATTENTION AND THE WHOOF YOU ENJOY THA LECTURE AND IF YOU HAVE ANY QUESTIONS A ESTAME
55 |
56 | ",8044,1605
57 |
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/examples/TEST_folder_edition/wav2vec2-large-v2clntxt_transcriptions/YAKE - all keys for batch Dec-18-2021_-22.csv:
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13 | 11,modern day machine,0.014573979732179382,3,1,size,0.015650101368589048,1,9,practical challenges people,0.00016946279260305976,3,1,general setting simply,0.0003101769398658128,3,1,unit circle,0.0002201883470500182,2,8,jeomega axis,0.002345373382224024,2,2,offer high quality,0.004192112939266108,3,1,add,0.020456505694053204,1,11,group city,0.0015385580860965697,2,0,pas afm sin,0.003156604431343206,3,1
14 | 12,step size,0.018366854677310283,2,6,thing,0.0168253631746969,1,16,called back propagation,0.0001721289999991233,3,1,order differential equation,0.0003469059456899496,3,1,essentially pass banan,0.000276043108110422,3,1,reason aliasing,0.0046749623461530615,2,1,quality educational resources,0.004192112939266108,3,1,equal,0.021751690994279746,1,6,constant speed,0.0023556259674819852,2,1,equal,0.0036368346205325306,1,10
15 | 13,pretty big sum,0.018482257398784452,3,1,individual component,0.01978044639432752,2,3,uniform random feels,0.00020208101905188982,3,1,time,0.0003653519170654539,1,53,time,0.00036731892297985465,1,47,fact falls,0.0048610366677681325,2,1,consent era constantly,0.004192112939266108,3,1,clear evidence,0.022389393828548942,2,1,speed higher,0.0026027294837730214,2,1,system,0.0038623498737068397,1,10
16 | 14,ensuring the open,0.023048775779473406,3,1,make,0.021271220460623914,1,13,averaging things reduces,0.00020477189115692846,3,1,easily related back,0.00037410248808180584,3,1,impulse and variant,0.0003673558327425392,3,6,variant design,0.005188176217403321,2,1,knit infinite number,0.004581689401199865,3,1,part,0.023121379644650615,1,10,point,0.0026090427740095064,1,14,water water wave,0.004066807938462359,3,1
17 | 15,sum,0.023662087853672294,1,12,full,0.021594564826421664,1,10,big top performance,0.0002129783486861703,3,1,high quality educational,0.0005066837079168329,3,1,band cut,0.0007768365333073601,2,3,biological transformation,0.005188176217403321,2,1,kind,0.005100913652631202,1,10,good,0.025131643023440654,1,6,dispersive situation,0.0027700966785162966,2,1,depressed medium,0.009077323640906089,2,1
18 | 16,neural network,0.024910313956235886,2,5,optimum,0.02350979600373258,1,6,thousand cores great,0.00021899558112433467,3,1,view additional materials,0.0005066837079168329,3,1,left half,0.0014109471458458535,2,3,techniques including,0.005216359634633296,2,1,wave number kick,0.00579226819636664,3,1,time,0.02880241855950012,1,9,essentially faster,0.002826495771085642,2,1,time,0.009367328825826655,1,8
19 | 17,cost function,0.02615234036800766,2,3,problem,0.02374962898697658,1,9,compute ten thousand,0.000239904208426883,3,1,public of minus,0.0005855233144532426,3,6,jomega axis,0.0016143428071139954,2,2,unit circle,0.006303497609633871,2,1,discuss strategy,0.008573659202022485,2,0,question,0.02974297176484661,1,7,slope,0.0029458329414220118,1,12,speed of light,0.013470622197051583,3,3
20 | 18,end stuff reduces,0.02871193003918764,3,1,unbiased estimate,0.024572153443163353,2,3,major open problem,0.00024332139954204445,3,1,digital butterworth,0.0007511855020959167,2,2,point,0.002252926692507642,1,16,limits its usefulness,0.006303497609633871,3,1,speed,0.009636433482493423,1,14,components,0.0351576846682952,1,6,wave lands,0.0032358996128106186,2,1,normal mole,0.014723966664293963,2,1
21 | 19,big,0.030171766626357743,1,11,close,0.02726123868754761,1,7,multi gap system,0.0003774400457133255,3,1,system function,0.0009448150971547045,2,3,mapping represented,0.0029129438842063803,2,1,totally avoids,0.006303497609633871,2,1,time,0.011419541166508382,1,6,age make,0.03693478342015046,2,1,Michael lesson,0.003256509417001785,2,1,back,0.01811985594674038,1,5
22 | 20,idea,0.031680105943001906,1,10,key property,0.0289984691907239,2,3,envy dear yoga,0.0004224882234269176,3,1,omegus of sea,0.0014066558459028921,3,3,corresponds to mapping,0.003013227952165506,3,3,wanted to map,0.006303497609633871,3,1,question,0.013300196895870899,1,11,wider and wider,0.04842963138622234,3,3,kind of grade,0.003271161078391081,3,1,make,0.018370760509938605,1,7
23 | 21,common license,0.031969025728663586,2,1,making solid progress,0.031087340260910857,3,1,replacement version,0.0011261765209906352,2,1,filter amusing,0.0015018459589183923,2,1,equal to unity,0.0030139541002288653,3,1,higher and higher,0.0065483305257474,3,1,omega,0.013432917326656189,1,10,back,0.05327857650988372,1,6,curves post,0.003340750768503685,2,1,deiny lands,0.018911340835808824,2,1
24 | 22,start to withdraw,0.031969025728663586,3,1,sarcastic,0.045731485507574395,1,6,region of uncertainty,0.0019081145320031894,3,2,stop end,0.001547793119122118,2,2,design,0.0032347973516557386,1,20,procedure which totally,0.009772882968137187,3,1,hand side,0.015173854596605663,2,3,effect,0.05327857650988372,1,5,pretty equal,0.0037425576478092824,2,1,angurar frequency,0.018911340835808824,2,1
25 | 23,graciously agree,0.031969025728663586,2,1,key,0.04827164724473377,1,6,batch,0.0024172388919312497,1,19,response magnitude,0.002084058860685148,2,1,determine public,0.0032675946966469267,2,1,impulse,0.011523782458147969,1,5,don,0.015319285571674472,1,10,number coupled isolated,0.05724719294432417,3,1,equal to women,0.0037425576478092824,3,1,fixed number,0.018911340835808824,2,1
26 | 24,end,0.032131550079559285,1,9,idea,0.05069304390150877,1,5,method starts,0.002680290523876444,2,1,specific case,0.002200462380627036,2,2,approximately meets,0.003870315159983751,2,1,couple of comments,0.015594372166887853,3,1,produce,0.015553454400568895,1,5,originally,0.06940281835430026,1,3,carrier,0.00471327213055525,1,11,moving,0.019234605802892386,1,4
27 |
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/examples/TEST_folder_edition/wav2vec2-large-v2clntxt_transcriptions/mit_matrices_sgd_002_vid2txt_Dec-18-2021_-21_full.txt:
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1 | WELL LET'S LET ME ACTUALLY TELL YOU THEN ABOUT RATHER THAN THE THE PROOF I THINK I'LL SHARE THE PROOF WITH GILL BECAUSE THE PROOF THAT I WANT WANTED TO ACTUALLY SHOW YOU GIVES A PROOF OF
2 | THE STOCASTIC GRADIENT IS WELL BEHAVED ON BOTH CONVEX AND NON CONVEX PROBLEMS AND THE PROOF I WANTED TO SHOW WAS FOR THE NON CONVEX CASE BECAUSE IT APPLIES TO NEURAL NETWORK SO YOU MAY BE CURIOUS ABOUT THAT PROOF AND REMARKABLY THAT PROOF IS MUCH SIMPLER THAN THE CASE OF CONVEX
3 | PROBLEMS SO LET ME JUST MENTION SOME VERY IMPORTANT POINTS ABOUT SARCASTIC RADIENT SO EVEN THOUGH THIS METHOD HAS BEEN AROUND SINCE NINETEEN FIFTY ONE EVERY DEEP LEARNING TOOLKIT HAS IT AND WE ARE STUDYING IT IN CLASS THERE ARE STILL GAPSBET
4 | IN WHAT WE CAN SAY THEORETICALLY AND WHAT HAPPENS IN PRACTICE AND I'LL SHOW YOU THOSE GAPS ALREADY AND ENCOURAGE YOU TO THINK ABOUT THOSE IF YOU WISH SO LET'S LOOK BACK AT OUR PROBLEM AND TELL YOU ABOUT TWO VARIANTS SO HERE ARE THE TWO VARIANTS I'M GOING
5 | ASK IF ANY OF YOU IS FAMILIAR WITH THESE VARIANTS IN SOME WAY OR OTHER SO LET'S I JUST CALLED IT FEASIBLE HERE THERE ARE NO CONSTRAINTS SO YOU START WITH ANY RANDOM FACTOR OF YOUR CHOICE IN DEEP NETWORK TRAIN
6 | YOU HAVE TO WORK HARDER AND THEN THIS IS THE ITERATION YOU RUN RIGHT OPTION ONE AND OPTION TWO SO OPTION ONE SAYS THAT WAS THE IDEA WE HAD IN CLASS RANDOM LY PICK SOME TRAINING DATA POINT USE ITS DORCASTIC GRADIENT
7 | WELL WHAT DO WE MEAN BY RANDOM LY PICK THE MOMENT YOU USE THE WORD RANDOM YOU HAVE TO DEFINE WHAT'S THE RANDOM NESS SO ONE RANDOM NESS IS UNIFORM PROBABILITY
8 | AND TRAINING DATA POINTS THAT IS ONE'S RANDOMNESS THE OTHER VERSION IS YOU PICK A TRAINING DATA POINT WITHOUT REPLACEMENT SO SO WITH REPLACEMENT MEANS YOU KNOW JUST UNIFORMLY AT RANDOM EACH TIME
9 | DRAW A NUMBER FROM ONE THROUGH N USE THAT SARCASTIC RADIENT MOVE ON WHICH MEANS THE SAME POINT CAN EASILY BE PICKED TWICE ALSO AND WITHOUT REPLACEMENT MEANS IF YOU'VE PICKED U POINT NUMBER THREE YOU'RE NOT GOING TO PICK IT AGAIN UNTIL YOU'VE
10 | THROUGH THE ENTIRE TRAINING DATA SET THOSE ARE TWO TYPES OF RANDOMNESS WHICH VERSION WOULD YOU USE THERE IS NO RIGHT OR WRONG ANSWER TO THIS I'M JUST TAKING A POLE
11 | WHAT WOULD YOU USE THINK THAT YOU'RE WRITING A PROGRAMME FOR THIS AND MAYBE THINK REALLY PRAGMATICALLY PRACTICALLY THAT'S ENOUGH OF AN HIN WHICH VERSION WOULD YOU USE I'M JUST CURIOUS
12 | WHO WOULD USE ONE PLEASE RAISE HANDS O WHO AND THE THE EXCLUSION THE COMPLIMENT THEREOF OR I DON'T KNOW MAYBE SOME PEOPLE ARE UNDECIDED WHO WOULD USE TOO VERY FEW PEOPLE WO
13 | OK HOW MANY OF YOU USE THE NEURAL NETWORK TRAINING TOOL KITS LIKE DENSE FLO PIT TORCH WHAT NOT WHICH VERSION ARE THEY USING
14 | ACTUALLY EVERY PERSON IN THE REAL WORLD IS USING VERSION TOO ARE YOU REALLY GOING TO RANDOMLY GO THROUGH YOUR RAM EACH TIME TO PICK RANDOM POINTS THEY'LL KILL YOUR G P PERFORMANCE LIKE ANYTHING
15 | WHAT PEOPLE DO IS TAKE A DATA SET USE A PRE SHUFFLE OPERATION AND THEN JUST WHOOP STREAM THROUGH THE DATA WHAT DOES STREAMING THROUGH THE DATA MEAN WITHOUT REPLACEMENT SO ALL THE TOOLKITS ACTUALLY ARE USING THE WITHOUT REPLACEMENT ER
16 | EVEN THOUGH INTUITIVELY THE RE JUS UNIFORM RANDOM FEELS MUCH NICER AND THAT FEELING IS NOT ILL FOUNDED BECAUSE THAT'S THE ONLY VERSION WE KNOW HOW TO ANALYZE MATHEMATICALLY SO EVEN FOR THIS METHOD EVERYBODY STUDIES IT THERE
17 | AN PAPERS ON IT THE VERSION THAT IS USED IN PRACTICE IS NOT THE VERSION WE KNOW HOW TO ANALYZE IT'S A MAJOR OPEN PROBLEM IN THE FIELD OF STOCASTIC GRADIENT TO ACTUALLY ANALYZE THE VERSION THAT WE USE IN PRACTICE THIS KIND OF
18 | RISING BUT IT'S WITHOUT REPLACEMENT MEANS NON IID PROBABILITY THEORY AND NON IIDE PROBABILITY THEORY IS NOT SO EASY THAT'S THE ANSWER O K SO THE OTHER VERSION IS THIS MINE BATCH IDEA WHICH
19 | MENTIONED REALLY EARLY ON IS THAT RATHER THAN PICK ONE RANDOM POINT I'LL PICK A MINNIE BATCH SO I HAD A MILLION POINTS EACH TIME INSTEAD OF PICKING ONE MAYBE I'LL PICK
20 | TEN OR HUNDRED OR THOUSAND OR WHAT HAVE YOU SO THIS AVERAGES THINGS AVERAGING THINGS REDUCES THE VARIANTS SO THIS IS ACTUALLY A GOOD THING CAUSE THE MORE QUANTITIES YOU AVERAGE THE LESS NOISE YOU HAVE THATS
21 | KIND OF WHAT HAPPENS IN PROBABILITY RIGHT SO WE PICK A MINNIE BATCH AND THE SARCASTIC ESTIMATE NOW IS THIS YOU KNOW NOT JUST A SINGLE GRADIENT BUT AVERAGED OVER A MINNIE BATCH
22 | SO MINI BATCH OF SIZE ONE IS THE PURE VANILLA S G D MINNI BATCH OF SIZE N IS NOTHING OTHER THAN PURE GRADIENT DESCENT SOMETHING IN BETWEEN IS WHAT PEOPLE ACTUALLY USE AND AGAIN THE THEORETICAL ANALYSIS ONLY EX
23 | IF THE MINNIE BATCH IS PICKED WITH REPLACEMENT NOT WITHOUT REPLACEMENT SO ONE OF THE REASONS ACTUALLY A VERY IMPORTANT THING IN THEORY YOU DON'T GAIN TOO MUCH IN TERMS OF COMPUTATIONAL GAINS ON CONVERGENCE
24 | PEED BY USING MANY MATCHES BUT MINY BATCHES ARE REALLY CRUCIAL SPECIALLY IN YOUR DEEP LEARNING GPU STYLE TRAINING BECAUSE THEY ALLOW YOU TO DO THINGS IN PARALLEL EACH THREAD OR EACH CORE OR SUB
25 | OR OR SMALL CHIP OR WHAT HAVE YOU DEPENDING ON YOUR HARDWARE CAN BE WORKING WITH ONE SORCASTIC RADIANT SO MINNI BATCHES THE LARGER THE MINNIE BATCH THE MORE THINGS YOU CAN DO IN PARALLEL SO MINNI BATCHES ARE GREATLYEXPLOT
26 | BY PEOPLE TO ER GIVE YOU A CHEAP VERSION OF PARALELISM AND WHERE DOES THE PARALLELISM HAPPEN YOU CAN THINK THAT EACH CORE COMPUTES A SARCASTIC GRADIENT SO THE HARD PART IS NOT
27 | ADDING THESE THINGS UP AND MAKING THE UPDATE TO X THE HARD PART IS COMPUTING A SARCASTIC GRADIENT SO IF YOU CAN COMPUTE TEN THOUSAND OF THOSE IN PARALLEL BECAUSE YOU HAVE TEN THOUSAND CORES GREAT FOR YOU AND THAT'S THE REASON PEOPLE LOVE USING MANE
28 | ACHES BUT A NICE SIDE REMARK HERE THIS IS ALSO THIS BRINGS US CLOSE TO THE RESEARCH EDGE OF THINGS AGAIN THAT WELL YOU'D LOVE TO USE VERY LARGE MINNIE BADGES SO THAT YOU CAN FULLY MAX OUT ON THE PARA
29 | ISM AVAILABLE TO YOU RIGHT MAYBE YOU HAVE A MULTI GEP SYSTEM IF YOUARNO FRIENDS WITH ENVY DEAR GOGA I ONLY HAVE LIKE TWO GPS BUT DEPENDS ON HOW MANY GPS YOU HAVE YOU'D LIKE TO REALLY MAX OT ON PARALLELISM SO THAT YOU CAN REALLY
30 | UNCH THROUGH BIG DATA SETS AS FAST AS POSSIBLE BUT YOU KNOW WHAT HAPPENS WITH VERY LARGE MINNY BATCHES SIFYO HAVE VERY LARGE MINNI BATCHES STARCASTIC GRADIENT STARTS LOOKING MORE LIKE
31 | FULL GRADIENT DESCENT WHICH IS ALSO CALLED BACH GRADIENT DESCENTTHAT'S NOT A BAD THING THAT'S AWESOME FOR OPTIMIZATION BUT IT IS A WEIRD CONUNDRUM THAT HAPPENS IN TRAINING DEEP NERAL NETWORKS
32 | THIS TYPE OF PROBLEM WE WOULDN'T HAVE FOR CONVEX OPTIMIZATION BUT IN DEEP NURALET WECAUS THIS REALLY DISTURBING THING HAPPENS THAT IF YOU USE THESE VERY LARGE MANY BATCHES YOUR METHOD STARTS RESEMBLING RADIANT DESCENT THAT MEANS IT DECREASES NOISE
33 | MUCH SO THAT THIS REGION OF CONFUSION SHRINKS SO MUCH WHICH ALL SOUNDS GOOD BUT IT ENDS UP BEING REALLY BAD FOR MACHINE LEARNING THAT'S WHAT I SAID THAT IN MACHINE LEARNING YOU WANT SOME REGION OF UNCERTAINTY AND WHAT IT
34 | MEANS ACTUALLY IS A LOT OF PEOPLE HAVE BEEN WORKING ON THIS INCLUDING AT BIG COMPANIES THAT IF YOU REDUCE THAT REGION OF UNCERTAINTY TOO MUCH YOU END UP OVER FITTING YOUR NEURAL NETWORK
35 | AND THEN IT STARTS SUCKING IN ITS TEST DATA UNSEEN DATA PERFORMANCE SO EVEN THOUGH FOR PARALLELISM PROGRAMMING OPTIMIZATION THEORY BIG MINNI BATCH IS AWESOME
36 | TUNATELY THERE PRICE TO BE PAID THAT IT HURTS YOUR TEST ERROR PERFORMANCE AND THEY'RE ALL SORTS OF METHODS PEOPLE ARE TRYING TO COOK UP INCLUDING A SHRINKING ETA
37 | INGLY OR CHANGING NEURA NETWORK ARCHITECTURE AND ALL SORTS OF IDEAS YOU CAN COOK UP YOUR IDEAS FOR YOUR FAVOURITE ARCHITECTURE HOW TO MAKE A LARGE MINNIE BATCH WITHOUT HURTING THE FINAL PERFORMANCE BUT IT'S STILL SOMEWHAT OF AN OPEN QUESTION ON HOW TO OPTIMIL
38 | ECT WHICH MENI HOW LARGE YOUR MANY BATS SHOULD BE SO EVEN THOUGH THESE IDEAS ARE SIMPLE YOU SEE THAT EVERY SIMPLE IDEA LEADS TO AN ENTIRE SUB AREA OF S G D
39 | HERE ARE PRACTICAL CHALLENGES PEOPLE HAVE VARIOUS HERISTICS FOR SOLVING THESE CHALLENGES YOU CAN COOK UP YOUR OWN BUT IT'S NOT THAT ONE IDEA ALWAYS WORKS SO IF YOU LOOK AT S G D WHAT ARE THE
40 | IN PARTS THE MOVING PARTS IN GD THE GRADIENTS STACASTIC GRADIENTS THE STEP SIZE THE MINNI BATCH SO HOW SHOULD I PICK STEP SIZES VERY NON TRIVIAL PROBLEM DIFFERENT DEEP LEARNING TO
41 | S MAY HAVE DIFFERENT WAYS OF AUTOMATING THAT TUNING BUT IT'S ONE OF THE PAINFUL THINGS WHICH MINNY BATCH TO USE WITH REPLACEMENT WITHOUT REPLACEMENT I ALREADY SHOWED YOU BUT WHICH MINNY BATCH SHOULD I USE HOW LARGE THAT SHOULD BE AGAIN NOT
42 | EASY QUESTION TO ANSWER HOW TO COMPUTE STARCASTIC GRADIENTS DOES ANYBODY KNOW HOW STARCASTIC GRADIENTS ARE COMPUTED FOR DEEP NETWORK TRAINING ANYBODY KNOW THERE ISA
43 | FAMOUS ELGARITHM CALLED BACK PROPAGATION THAT BACK PROPAGATION ELGRITHM IS USED TO COMPUTE A SINGLE STARCASTIC GRADIENT SOME PEOPLE USE THE WORD BACK PROP TO MEAN ASJIDDY BUT WHAT BACK PROP REALLY MEANS IS SOME
44 | SOME KIND OF ALGORISM WHICH COMPUTES FOR YOU A SINGLE SARCASTIC GRADIENT AND HENCE YOUKNOW THIS R TENSER FLUED CETRA THESE TOOLKISS THEY COME UP WITH ALL SORTS OF WAST AUTOMATE THE COMPUTATION OF A GRADIENT BECAUSE REALLY THAT'S THE MAIN THING
45 | AND THEN OTHER IDEAS LIKE RADIENT CLIPPING AND MOMENTUM ET CETERA THE BUNCH OF OTHER IDEAS AND THE THEORETICAL CHALLENGES I MENTIONED TO YOU ALREADY PROVING THAT IT WORKS THAT IT ACTUALLY SOLVES WHAT IT SET OUT TO DO UNFORTUNATELY I WAS TOO SLOW
46 | COULDN'T SHOW YOU THE AWESOME FIVE LINE PROOF THAT I HAVE THAT S GD WORKS FOR NEWRAL NETWORKS AND THEORETICAL ANALYSIS AS I SAID IS REALLY LAGGING MY PROOF ALSO USES THE WID
47 | CEMENT AND THE WITHOUT REPLACEMENT VERSION WHICH IS THE ONE THAT IS ACTUALLY IMPLEMENTED O THERE'S VERY LITTLE PROGRESS ON THAT THERE IS SOME PROGRESS THERE'S A BUNCH OF PAPERS INCLUDING FROM OUR COLLEAGUES THAT IMIGHTY BUT IT'S QUITE
48 | AND THE BIGGEST QUESTION WHICH MOST OF THE PEOPLE IN MACHINE LEARNING ARE CURRENTLY EXCITED ABOUT THESE DAYS IS STUFF LIKE WHY DOES S GD WORK SO WELL FOR NEURAL NETWORKS WE
49 | THIS SCRAPPY OPTIMIZATION METHOD IT VERY RAPIDLY DOES SOME FITTING DATA IS LARGE NEURO NETWORK IS LARGE AND THEN THIS NEURO NETWORK ENDS UP HAVING GREAT CLASSIFICATION PERFORMANCE WHY IS THAT HAPPENING THAT'S CALLED TRYING TO EXPLAIN
50 | BUILD A THEORY OF GENERALIZATION WHY DOES AN S G D TRAINED NEURA NETWORK WORK BETTER THAN NEURAL NETWORKS TRAIN WITH MORE FANCY OPTIMIZATION METHODS IT'S A MYSTERY AND MOST OF THE PEOPLE WHO TAKE INTEREST IN THEORETICAL MACHINE LEARNING AND STATISTICS
51 | THAT IS ONE OF THE MYSTERIES THEY ARE TRYING TO UNDERSTAND SO I THINK THAT'S MY STORY OF S JIDDY AND THIS IS THE PART WE SCAP BUT ITS SOKE THE THE INTUITION BEHIND US JDDYS MUCH MORE IMPORTANT THAN THIS
52 | SO I THINK WE CAN THANK YOU CLOSE MAYBEWER THE ROOF OR MONDAYS EXACTLY I THINK SO THAT
53 | HEY'LL BE GREAT
54 |
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/examples/TEST_folder_edition/wav2vec2-large-v2clntxt_transcriptions/mit_signals_002_vid2txt_Dec-18-2021_-21_full.txt:
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1 | THE FILTHE FILTER THAT WE OBTAINED BY MAPPING THE BUTTERWORTH FILTER TO A DIGITAL FILTER THROUGH THE BIOLINEAL TRANSFORMATION IN FACT FALLS OFF IN FREQUENCY
2 | MUCH MORE RAPIDLY THAN THE ONE THAT WE GOT THROUGH IMPULSE AND VARIANCE A QUESTION IS WHY NOW ONE THOUGHT THAT MIGHT COME TO MIND AS WELL IMPULSE AND VARIANCE AS ALIASING THE BIOLINEAR TRANSFORM
3 | AN DOESN'T HAVE ALIASING THAT MUST BE A CONSEQUENCE OF ALIASING IN FACT THAT'S NOT THE REASON ALIASING AS IT TURNS OUT IN THIS PARTICULAR DESIGN IS WA WAS RELATIVELY MINIMAL IN THE IMPULSE AND VARIANT DESIGN
4 | THE REASON HAS TO DO WITH THIS NON LINEAR MAPPING IN THE BILINEAR TRANSFORMATION FROM THE CONTINUOUS TIME FREQUENCY TO THE DISCREET TIME FREQUENCY KEEP IN MIND THAT
5 | THROUGH THAT MAPPING AS YOU START WALKING AROUND THE UNIT CIRCLE AND MOVING UP THE JEOMEGA AXIS AS YOU MOVE UP THE JEOMEGA AXIS YOU HAVE TO MOVE FASTER AND FASTER AND FASTER AND FASTER AND WHAT'S IN
6 | NOUS TIME FREQUENCY AND INFINITY IS WHAT YOU GET TO IN THE DISCREET TIME FREQUENCY BY THE TIME YOU GET AROUND TO PI SO IN FACT WHAT WE'RE LOOKING AT IS AS AS WE LOOK OUT ALONG THIS
7 | QUENCY AXIS IS WE'RE SEEING HIGHER AND HIGHER AND HIGHER FREQUENCIES IN THE CONTINUOUS TIME FILTER BY THE TIME WE GET TO PI WE SHOULD IN FACT BE IN THE CONTINUOUS
8 | TIME FILTER EQUIVALENTLY OFF TO INFINITY WHICH SOUNDS LIKE A PRETTY UNCOMFORTABLE PLACE TO BE O K NOW THIS WAS A FAIRLY RAPID TRIP
9 | RO A NUMBER OF ISSUES IN PARTICULAR SOME OF THE ISSUES ASSOCIATED WITH THE BIOLINEAR TRANSFORMATION AND ALSO THIS ISSUE OF HOW YOU PICK THIS PEROMETER CAPITAL T AND HOW IT MIGHT BE
10 | TED WITH A SAMPLING FREQUENCY IF YOU'RE DOING DISCREET TIME PROCESSING OF CONTINUOUS TIME SIGNALS AND WE DON'T HAVE TIME TO EXPLORE SOME OF THOSE ISSUES MORE FULLY IN THIS LECTURE BUT I'D LIKE
11 | CONCLUDE BY MAKING A COUPLE OF COMMENTS ONE COMMENT IS THAT THE TWO TECHNIQUES THAT WE'VE TALKED ABOUT IMPULSE AND VARIANCE AND THE BIOLINEAR TRANSFORMATION ARE THE TWO TECHNIQUES THAT ARE PRINCIPALLY USED
12 | AND ONE THINKS OF MAPPING CONTINUOUS TIME FILTERS TO DISCREET TIME FILTERS FOR WHATEVER APPLICATION AND I STRESS AGAIN THAT YOU MAY WANT TO DO THAT MAPPING WHETHER OR NOT THE DISCREET TIME FILTER
13 | IS EVENTUALLY GOING TO BE USED FOR PROCESSING CONTINUOUS TIME SIGNALS NOW IMPULSE AND VARIANCE HAD THE CHARACTERISTIC THAT IT VERY NICE CHARACTERISTIC THAT THAT
14 | CORRESPONDS TO A LINEAR MAPPING BETWEEN THE TWO FREQUENCY AXES EXCEPT FOR THE ISSUE OF ALIASING AND THAT'S A PROBLEM WITH IT AND IN PARTICULAR LIMITS ITS USEFULNESS TO FILTER
15 | SIGNS OR FOR MAPPING CONTINUOUS TIME FILTERS THAT ARE BAND LIMITED ON THE OTHER HAND WE HAVE THE BILINEAR TRANSFORMATION AS A DESIGN PROCEDURE WHICH TOTALLY AVOIDS ALIOSING
16 | BUT HAS THE DISADVANTAGE OR DIFFICULTY THAT IT REPRESENTS A NON LINEAR MAPPING FROM THE CONTINUOUS TIME FILTER TO THE DISCREET TIME FILTER NOW THIS NON LINEAR DISTORTION IS PERFECTLY ACCEPT
17 | ABLE IF WE'RE DESIGNING OR ATTEMPTING TO DESIGN FILTERS THAT HAVE FLAT FREQUENCY CHARACTERISTICS IT'S NOT ACCEPTABLE IF FOR EXAMPLE WE HAD A LINEAR FREQUENCY CHARACTERISTIC THAT WE WANTED TO MAP TO A DISCREET TIME
18 | TER AND END UP WITH A LINEAR FREQUENCY CHARACTERISTIC IT WON'T COME OUT TO BE LINEAR BECAUSE OF THIS NON LINEAR MAPPING OF THE FREQUENCY AXES NOW THERE ARE ALSO A NUMBER OF OTHER DESIGN
19 | PROCEDURES WHICH WE WON'T GO INTO FOR DESIGNING DISCREET TIME FILTERS AND AMONG THEM ARE A VARIETY OF TECHNIQUES INCLUDING FOR EXAMPLE COMPUTERATED DESIGNED PROCEDURES AND I INVITE YOU
20 | IF YOU'RE INTERESTED AND WANT TO DIG INTO THAT IN MORE DETAIL AND MORE DEEPLY TO EXPLORE THAT TOPIC BY MAKING REFERENCE TO VARIOUS OF THE BOOKS LISTED IN THE BIBLIOGRAPHY
21 | IN THE TEXT THANK YOU
22 |
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/examples/TEST_folder_edition/wav2vec2-large-v2clntxt_transcriptions/mit_vibrations_and_waves_000_vid2txt_Dec-18-2021_-21_full.txt:
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1 | THE FOLLOWING CONTENT IS PROVIDED UNDER A CREATIVE COMMONS LICENSE YOUR SUPPORT WILL HELP M I T OPEN CORSE WARE CONTINUE TO OFFER HIGH QUALITY EDUCATIONAL RESOURCES FOR FREE TO MAKE A DONATION OR TO VIEW ADDITIONAL MATERIALS FROM HUNDREDS OF M I
2 | COURSES VISIT M I T OPEN COURSE WEARE AT O C W DOT M I T DOT E D U HALLO EVERYBODY WE'LL COME BACK TO A O THREE A TO DAY WE ARE GOING TO CONTINUE DISCUSSION OF WAVS A
3 | WE WOULD DISCUSS A VERY INTERESTING PHENOMENO TO DAY WHICH IS DISPERSION AND BEFORE DARK WE WOULD DISCUSS A BIT JUST O GIVE YOU SOME REMINDER ABOUT WHAT WE HAVE LEARNED SO FAR SO WE DISCOVERED THIS EFIQUATION
4 | WHICH IS SHOWN HERE IN THE CLASS AND WE ALSO SHOW YOU THAT IT DESQRIBED THREE DIFFERENT KINDS OF SISTENCE WHICH WE INCLUDED IN THE LECTURE THE MASSIVE STRINGS WHICH THE STRINGO CANAR
5 | THE ASSILATE UP AND DOWN IN THE RIGHT DIRECTION AND ALSO WE DISCUSSED ABOUT SON WAVES E THIS IS ALSO DISCUSSED INAPERIOUS LECTURE AND THE SOND WAVES CAN BE DESCRIBED BY
6 | WAVY QUESTION AND FINALLY LAS TINE WITH THIS TA ER ELETO MAGNETIC WAVES ISA SPECIAL KIND OF WAVES INVOLVING TWO OSCELLATING FER ONE ESENTIALLY THE ELECTRIC FER THE OTHER
7 | NIS MAGNETIFIL I SO THAT'S KIND OF INTERESTING BECAUSE THIS IS AT SLIGHTELY DIFFERENT FROM WHAT WE DISCUSSED BEFORE IN THE PREVIOUS TWO CASES THIS ISSENTUALLY A THREE DIMENSIONAL A WAVE AND ALSO INVOLVING TWO
8 | DIFFERENT COMPONENTS AND WE ALSO DISCUSS THE THE SOLUTION THE TRAVELLING WAVE SOLUTION OF THE ELECTROMAGNETIC WAVES AS YOUS YOU CAN SEE FROM HERE HE ELECTRIC FERE IS SHOWN AS THE RAT AND THE MAGNETIC FI
9 | JOINES TE TROW AND YOU CAN SEE THAT IN CASE OF TRAVELLING WAVE THEY ARE IN FACE AND THAT THE MAGNETUDE REACH MAXIMA SIMULTANEOUSLY FOR THE ELECTRIC ELECTRIC FIR AND THE MAGNETIC FIR AND WHILE IN THE CASE OF STANDING WAVE
10 | THERE'S A FACE DIFFERENCE RIGHT SO THEY DON'T REACH MAXIMA SIMULTANEOUSLY IN UNDERSTANDING ELECTROMAGNETI CASE OK SO WHAT ARE WE GOING TO DISCUSS TO DAY WE WOULD LIKE TO DISCUSS
11 | HESTRATOGY TO SEND INFORMATION ARE USING WAVES OK HOW DO WE AS YO SEND INFORMATION ARE USING WAVES SO YOU CAN SAY O K YOU JUST DO MAYBE I CAN JUST SEND THE HARMONIC
12 | OSCILLATION RISE OCCUPI TO THIS HARMONIC OSCELLATION I CAN VATL PRODUCE HARMONICAL WAVES I THEY MOVING UP AND DOWN AND TE ESPETILTE WITH A CONSTANT
13 | GAA MOMENTON AND ANGAA A FREQUENCY AND THE MAYBE THAT'S A WAY TO SEND THE INFORMATION BUT BUT THIS KIND OF A WAVE IS NOT IN IALITY NOT SUPERHEALFUL BECAUSE IF YOU
14 | THE WHOLE SPACE WITH HARMONIC WAVES THEN YOU DON'T KNOW WHEN DID YOU ACTUALLY SEND THE SIGNAL IGHT BECAUSE IT'S ALWAYS ASOLATING UP AND DOWN SO YOU DON'T KNOW THE STARTING KIND OF THE SIGNAL I SO SO IN REALITY THIS
15 | OF SIMPLE HARMONIC OSCILATING TROUBLING WAVE IS NOT SUPER HELPFUL SO WHAT IS IT TO HEALPFUL THAT'S THE QUESTION SO WHAT IS ACTUALLY HELPFUL IS TO PRODUCE SQUARE POUS FOR EXAMPLE LAT WE
16 | CREATE SQUARE POWS FOR EXAMPLE IN THIS IN THIS CASE I CAN CREATE A SQUARE POUS HERE AND IN THE NEXT TIME INTERVAL I DON'T CREATE SQUARE POWS IN THE NEXT TIME INTERVAL I DON'T DO ANYTHING AND I CREATE ANOTHER SQUARE POWS
17 | ET CETERA ETCETERA IF YOU USE THIS KIND OF STRATOGY WHAT WE CAN DO IS TO HAVE SOME KIND OF RECEIVER HERE TO ASSUTY MEASURE THE MAGNITUDE OF THE
18 | MAGNITUDE OF THE POWERS O AND THEN WE CAN NATRL INTERPRETE THIS DATA SO SO THIS OR THIS THIS WAYVE IS GOING TO WERE THE POSITIVE X DIRECTION OR GOING TO THE RIGHT HAND SIDE OF THE BOARD AND THE RECEIVER WILL BE ABLE TO INTERPRET
19 | WI HIS DATA BY PRASING IS RACIO UNDER ENERGY OR UNDER MATRDE MPUTO THEN I CAN CAN SAY OH NOW I'D RECEIVE A ZERO AND TH THE NEXT A SIGNAL AND RECEIVING IS ONE AND THIS ONE IS ZERO
20 | ZERO AND ONE AND ZERO IN THIS WAY I CAN ESE THE SCENT INFORMATION AND H THIS INFORMATION CAN BE BARITING AS A FUNCTIONAL TAO SO IN SHORT WHAT WIULL BE USEFUL IS PROBABLY TO USE A NARROW
21 | SQUARE PIS AND NOW WE BE VERY HELPFUL IN TRANSMITTING O INFORMATION OK SO AH IF WE CONSIDER A IDEAL STRING CASE OK IF I HAVE
22 | DEAL STRING AS WE LEARNED BEFORE AA THE BEHAVIOR OF THIS STRING IS DESCRIBED BY A A THE WAVE EQUATION I PASSE SQUARE
23 | PATO T SQUARE AND THIS IS EQUAL TO B SQUARE PAT SQUARE SI PAT T SQUARE OK AND THE DIS V IS ACTUALLY RELATED TO THE THAT THE SPEED OF THE PROGRESSING WAY
24 | AS WE DISCUSS BEFORE THE PROGRESSING WAVE SOLUTION O AND THATII IF I HAVE THIS IDEALIZED STRING AND OBEY THE WAVE EQUATION THE SIMPLE VERSION OF WAVE EQUATION THEN I WILL BE ABLE
25 | TO DERIVE THE DISPERSION RELATION RIGHT SO I CAN NOW WRITE DOWN MY HARMONIC ASPOASING WAVE IN THE FORM OF SIGN K X MINUS OMEGA T IF I HAVE A HARMONIC ISCELLATING WAVE
26 | ATING TOWARD THE POSITIVE EX DIRECTION AT SPEED OF V I CAN WRITE IT DOWN IN THIS FUNCTIONAL FORM WHERE K AS A REMINDER IS THE WAVE NUMBER AND THE OMEGA IS A DESCRIBED
27 | HOWISOE TEA ANGER FREQUENCY AND THEREFORE IF I PRAKING THIS SOLUTION AND OF COURSE I CAN HAVE ARBITRARY AMPITU IF I PRAKING THIS SOLUTION TO THIS QUESTION THEN WHAT I
28 | CON TO GETTIS AS WE ADID IN THE LAST FEW LECTURES THERE WILL BE A FIXED RELATION BETWEEN K WHICH IS TEWAY A NUMBER AND OMEGA THE ANGA FREQUENCY SO THE FIXED RELATION IS SAY TO THE OMEGA
29 | OBER K WILL BE EQUAL TO V WHICH WIS ATUAI THE VELOCITY IN THIS WAV EQUATION AND THAT FROM THE PREVIOUS DISCUSSION WE KNOW THIS SET EQUAL TO A SQUARE DOT OF T OFE ROW
30 | L WHERE T IS SATA ATTENTION THE CONSTANT TENTION WHICH WE APPRY ON THE STRING AND THE ROLL L ESSENTIALLY THE MASPER ONI LENDS US A REMINDER OK SO WHAT DOES THIS
31 | WHAT DOES THIS EQUATION MEAN WE CALL IT TIS PERSION RELATION A A TINE RIGHT BUT WE ACTUALLY DIDN'T EXPLAIN WHY DO I DO THAT RIGHT SO WE ARE GOING TO LEARN WHY THIS IS A YOU CALL THIS PERSION RELATION OR MAKE OUT AS
32 | NO K AND IN THIS CASE IN THIS VERY SIMPLE FIGHT IDEALIZE THE CASE OMEGA OVER K THIS RATIO O K WE KNOW THIS IS RELATED TO THE PROPAGATION OFTHE
33 | SPEEDABLHE PROPAGATION OF THE HARMONICAL WAVE OK IS EQUAL TO V B IS A CONSTANT IS INDEPENDENT OF K THIS RATIO IS INDEPENDENT OF K WHAT DOES THAT MEAN THAT MEANS
34 | IF I PREPARE WAVES OK WITH DIFFERENT WAVE NUMBER OR IN THE OTHER WORDS WAVES WITH DIFFERENT WAVE LANDS THEY ARE GOING TO PROPARGATE AT THE
35 | SPEED RIGHT SO THE SPEED OF THE HARMONIC PROGRESSING WAVE IS ITS INDEPENDENT OF THE WAVELETSOK THAT SAYS YO VERY
36 | BECAUSE IN THIS CASE IF I PREPARE THE SQUARE HOUSE AS WE LEARNED BEFORE THI SQUARE POUSE ESSENTIAL TE ER A VERY COMPLICATED OBJECT E SQUARE POUSE IS REALLY VERY COMPLICATED YOU CAN DO
37 | PUDIA DECOMPOSITION AS WE DID BEFORE AND WE KNIT INFINITE NUMBER OF TURNS OF HARMONIC OSCILLATING WAVES WITH WHICH WE ADD THEM TOGETHER SO THAT I CAN PRODUCE A SQUARE
38 | OK AND AS I MENTION HERE IF THE DISPERSION RELATION IS OMECA OBA K IS A CONSEN ESA CONSTANTLY THAT MEANS ALL THE WHATEVER
39 | OF WAVE LANDS POWS WHICH I SHOULD BE ADDED TOGETHER AND PRODUCE THES SQUARE POWS ARE GOING TO BE TROUBLEDING AT THE SAME SPEED THEREFORE A IF I HAVE THIS SQUARE
40 | OSE IN THE BEGINNING AFTER SOME TIME TE WHAT I AM GOING TO GET IS THAT OGE THIS IS THE ORIGINAL POSITION OF THE SQUARE POWS AND AFTER SOME TIME T THIS SQUARE POW
41 | WERE MOVED BY THE TINT IN THE HORENTAL DIRECTION AND THE SHAPE OF THE POWS IS NOT GOING TO BE CHANGED CA PICS NO MATTER WHAT KIND OF WAVE LANDS WHICH PRODUCE THE SQUARE POWS
42 | ALL THE COMPONENTS IN THE SQUARE POS ARE PROPAGATING AT THE SAME A SPEED BE SO THIS KIND OF SYSTEM THIS KIND OF A SYSTEM WHICH AS YOU SAI SATISFIED A THIS
43 | OF A LIS A DISPERSION RELATION IS CALLED NON DISPERSIVE MEDIAM RIGHT NO DISPERSION WAS HAPPENING IN THIS IN THIS CASE IN THIS HIGHLY IDEALIZED CASE OK
44 | WE ALSO KNOW THAT IN CASE OF THE STRING WE ARE ACTUALLY MAKING IT TOO IDEALIZED RIGHT SO IF WE CONSIDER A MORE REALISTIC STRING THEN
45 | I HAVE TO CONSIDER AN IMPORTANTAA PHENOMENA WHICH ISTH OR SAY IMPORTANT PROPERTY OF THE STRING FOR EXAMPLE STEEPNESS I WHAT DO I MEAN BY STEEPNESS FOREMP
46 | IF I CAN IF I TAKE A STRING FROM THE PIANO A PIANO STRING OK EVEN IF I DON'T APPLY ANY ATTENTION TO THE STRING IF I BEND THIS STRING OU DON'T LIKE IT
47 | IT'S GOING TO BOUNCE BACK AND RESTORE TO ITS ORIGINAL SHAPE RIGHT SO THATS I WHAT I CALL STEEPNESS IT'S A DIFFERENT CONTRIBUTION COMPARED TO THE STRIN TENSION RIT SO WHAT WE HAVE BEEN DISCS
48 | SING SO FAR THAT THIS RESTORTING FORCE ESSENTIALLY COMING FROM THE STRING TENSION TA OK WHAT WILL HAPPEN IF I INTRODUCE ADDITIONAL A CONTRIBUTION FROMTHE
49 | STEEPNESS OK THIS STEEPNESS ESSENTIALLY NOT COMPLETELY RELATED TO THE STRING TENSION AND HE ALSO WANTS TO RESTORE THE SHAPE OF THE STRING OK BEFORE WE GO TO THE MATODING
50 | I WOULD LIKE TO TAKE SOME VOTE TO PREDICT WHAT IS GOING TO HAPPEN HOW MANY OF YOU WILL PREDICT THAT IF I INTRODUCE INCRUDE THE STIEFNESS OF THE STRING OR GET INTO MY EQUATION WHEREE
51 | SPEED OF PROPAGATION INCREASE HOW MANY OF YOU THINK WHAT IS GOING TO HAPPEN ONE TWO THREE FOUR FIVE SO SO SOME OF YOU
52 | PREDICT THE SPEED OF PROPAGATION WERE INCREASED HOW MANY OF YOU PREDICT THAT THE SPEED OF PROPAGATION OF THE HARMONIC WAVE WILL STAY THE SAND HOW MANY OF YOU ONE
53 | OK ONLY ONE OK HOW MANY OF YOU A SOULD PREDICT THAT THE SPEED OF PROPAGATION WOULD DECREASE
54 | OK TO ALL THE OTHER STUDENTS DON'T HAVE OPINION OK WANT TO WAIT FOR THE ANSWER
55 | ALL RIGHT SO YOU CAN SEE THAT IT IS SAS YOUIDNOT COMPRETY OBIOUS BEFORE WE SOLVE THIS QUESTION ANDE WE ARE GOING TO SOLVE IT WITH A SIMPLE MOTTO WHICH WE SHOULD SLIGHTLY MODIFY
56 | THE A THE IDEALIZE CASE WE IDEALIZE THE WAVY QUESTION OK SO NOW ONE SEMI REALISTIC MOTO WHICH I CAN INTRODUCE IS TO ADD A TURN ADDITION
57 | TURN TO THE WAFY QUESTION SO I CAN NOW RE WRITE MY WAYQUESTION TO INCRUDE ISIFI DISEFECT TO DESCRIBE A REALISTIC STRING AND NOW DISET PATO SQUARSA PATOTIS
58 | SQUARE THIS WILL BE EQUAL TO B SQUARE PART SQUARE SI PATTSQUARE AND THE ADDITIONAL TERM WHICH I HAVE PUT INTO THIS GAN IS MINUS AFA PARTTEFOR
59 | SI PARTIA X TO FOR AND THIS ESSENTIALLY THE CONTRIBUTION WHICH FROM THE STIPNESSTIFNESS OK
60 | SO YOU CAN SEE THAT THE THE WAFY QUESTION IS NOW MODIFIED AND WHAT I COULD DO IN ORDER TO GET THE RELATION BETWEEN OMEGA AND THE K WHAT I COULD DO IS THAT I CAN NOW START
61 | WITH THIS A HARMONIC WAVE SOLUTION A PUBLIC OQUASING WAVE SOLUTION PRACK THAT INTO THIS EQUATION THIS MODIFI THE EQUATION AND SEE WHAT WILL HAPPEN OK IF I PRACTHISE EQUATION
62 | INTO THAT MODIFIED WAVY QUESTION WHAT I AM GOING TO GET IS THE BOWING SOPACITY THE LAUGHAND SIGH YOU ARE GOING TO GET OR MAKE A SQUARE O K MINUS MAKE A SQUARE AND THE THE RIGHT HAND SIHE
63 | GET B SQUARE MINUSA K SQUARE ANPRAS AFAA K TO THE FOUR IN THE RIGHT HAND SI OK SO OF COURSE I CAN
64 | CANSEL THIS A MINUS SIGN THIS WILL BECOME PRAS AND THIS WILL BECOME MINUS AND WE CAN SEE THAT THE RELATION BETWEEN OMEGA AND THE K IS NOW DIFFERENT OK AFTER I INTRODUCE
65 | THIS TERM WHICH IS PROPORTIONAL TO A AFI CETURY DESCRIBING HOW STIFF THISA STRAIN IS OK OF COURSE NOW I CAN CALCULATE OR MAKE AT OFA K
66 | SA TOLE AS WE ACTUALLY LEARNED BEFORE RIGHT IS THE SPEED OF THE PROPAGATION OF A HARMONIC AE A HARMONIC WAVE OK SUPASILY IF I CALCULATE OR MAKE A BOQE FOND IS
67 | THEN PASITE WHILE YOU GET IS V SQUARE DUD OF ONE PUS AFA SQUARE O K SO IF YOU LOOK AT THIS EQUATION OK THE FIRST REACTION IS
68 | NOW THIS OMEGA AND KRACO IS NOT A CONSTANT ANY MORE AS A FUNCTION O K WHAT DOES THAT MEAN THAT MEANS IF I
69 | AR PROGRESSING WAVES WITH DIFFERENT WAVE LENTS OR WAVE NUMBER KOK IT'S GOING TO BE PROPAGATING AT DIFFERENT SPEED OK BEFORE WE INTRODUCE
70 | ING INTO THE ARMAND INTO THE MOTO THE RATIO OMACA AN K IS A CONSTANT V INDEPENDENT OF K NOW ONCE YOU INTRODUCE THIS MODO INTO THE EQUATION
71 | AND YOU PRAGIN THUS A PROGRESSING WAVE SOLUTION TOO ASECHECK THE DISPERSION RELATION OBTAINEDID FROM THIS EQUATION YOU FIND THAT THE PROGRESSING WAVE AE SPEEDO
72 | GRESSING WAVE DEPENDS ON HOW DISTORTED THIS PROGRESSING WAVE IS OK SO LET ME COMPARE THIS TWO SITUATION
73 | IN DIS GRAF OMEGA VERSUSK OK SO YOU SEE THIS DISPERSION RELATION GRAV PRETTY OFTEN IN THE IN THE CUST TO DAY THE Y XIS I SETLY THE OMEGAA ANGULAR
74 | QUENCY AND THE K IS THE WEIGHT NUMBER TWO PI OBE LONDON IN THE ORIGINAL CASE IN THE CASE I HAVE THIS IDEALIZED STRING OBEYED
75 | THE WAVQUATION WHICH I W INTRODUCE IN THE PREVIOUS LECTURES IF I PROT OR MAKE OUT AS A FUNCTIONA K WHAT I AM GETTING IS A STRAIGHT LINE O K QUESTION
76 | A NOT THIS INE RIHT OH MAYBE I HA MADE SOME MISTAKE HERE
77 | YOU SHOULD BE AR YOU SHOULD BE ALSO PROS HERE RIGHTTO NO SO YOU HAVE THIS OMEO SO THISIS O MAKASQUAR
78 | ANDE AS US HAVE THIS MINUS INT HERE I SOGHT SO THIS SHOULD BE MINUS AND THIS SHOULD BE O K LET'S GO BACK TO THE ORIGINAL EQUATION OK SO BASILY YOU
79 | SO IF I PROCKING THIS EQUESTION TO THIS EQUETION RIGHT SO BESILY I GET MINUS O MAKA SQUARE OUT OF IT AND I GET MINUS K SQUARE OUT OF THIS AND I'M GOING TO GET A PROSQE TO THE
80 | OR OUT OF THIS PART SQUARE TO THE FOUR SIE PARTO X FOUR EH OK THEREFORE THIS SHOULD BE MINUS O MAYBE I MADE A MISTE THINK THANK YOU MUCH FOR FOR SPORTING THAT
81 | A INTROCEO SI
82 |
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/examples/TEST_folder_edition/wav2vec2-large-v2clntxt_transcriptions/mit_vibrations_and_waves_002_vid2txt_Dec-18-2021_-22_full.txt:
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1 | LANDS VERY VERY SIMILAR BETWEEN THE TWO WAVES RIGHT SO THEREFORE WHAT I AM GOING TO DO IS THAT I AM GOING TO ASSOON K ONE IS VERY CLOSE TO K TWO
2 | IS ROUGHLY K OK AND I M GOTO END BECAUSE OF THIS SINCE I HAVE A CONTINUOUS FUNCTION IF K Y IS RELLY CLOSE TO K TOO THAT MEANS O MAGA ONE IS GOING TO
3 | EALSO VERY CUSE TO OMEGA TOO RIGHT SO WHAT I AM GOING TO GET IS OMEGA ONE IS GOING TO BE ALSO VERY SIMILAR TO OMEGA TOO AND I WILL CALL IT OMEGA OK
4 | SO IF I DO THIS WHEN I HAVE VERY SIMILAR K ONE ANDE K TWO WHAT IS GOING TO HAPPEN WHAT IS GOING TO HAPPEN IS THAT K ONE MINUS K TWO WILL BE
5 | RYSMALL SOTA MEANS A THIS VERY SMALL K MEANS LARGE WAVE LANDS THEREFORE THIS COSINTEN WILD BECOME THEENVE
6 | BECAUSE THE SAY SE ARE SLOWLY BARITING A EMPERTU AS A FUNCTION OF POSITION BECAUSE A CASE VERY SMALL CASE CASE MALMEANS LAND ARE LARGE THEREFORE THEM
7 | DU IS GOING TO BE HAVING THIS MODULATION WHICH IS SATA LIKE A ENVELOPE HE TE THE SPEED OF THIS ENVELOPE THE OSCILLATION OF THIS ENVELOPE IS AS YO CONTRO BY THEK OK
8 | LAT LOOK AT THE LAPAN SITEN K ONE PROS K TWO OVER TWO IT'S KIND OF LIKE THE CALCULATING THE AVRAGE OF THE FIRST AND SECOND OF THE WAVE NUMBER OF THE FIRST AND SECOND WAVES RIGHT SO YOU WILL
9 | CLAT AVERAGE IT CAN BE STILL PETY LARGE THEREFORE YOU HAVE SMALL LONDE RIGHT COMPARED TO THE DIFFERENCE THEREFORE YOU SEE THAT TA I SHOUL CONTRIBUTE TO THOSE LITTLE STRUCTURES IN
10 | IN INDISCREPENT CALLED CARRIER YES TATAS
11 | SO THEY CAN BE DIFFERENTI THOUGHT Y SOSO YOU ARE ABSOLUTELY RIGHT IHT SO YOU CAN YOU CAN PRODUCEA SOME SOMETHING LIKE A CARRIER AA EVEN WHEN KINE IS NOT EQUAL TO K TWO RIS IS JUST AT EVERY RIT YOUARE RIGHT
12 | BUT THE THEN THETE ON THE OTHER HAND THE DIFFERENCE KAWY AND KA TOO WILL BE ALSO LARGE THEREFORE YU I'S NOT AS EASY AS WHAT WE HAVE BEEN DOING HERE TO IDENTIFY WHO IS THE
13 | EAR AND WHO IS THE ENVELOPE BUTE YOU DO YOU DO GET SOME KIND OF GRAF WHICH IS ICILLATING REALLY FAST BUT THE ENVELOPE IS GOING TO APPER ALSO ICILLATING REALLY FAST THAT IS HARDER TOO TO SEE AL THE STRUCTURE BUT
14 | YOUR ABSOLUTELY RIGHT YES VERY GOOD QUESTION SO NOW I HAVE THIS SET UP I ASSUME THAT THEY ARE VERY CLOSE TO EACH OTHER SO NOW I CAN DEFINE FACE VELOCITY FINALLY
15 | WITH DEFINE WHAT IS I U THE FACE OF VELOCITY THE FACE O VELOCITY I CALL IT V P YOU CAN SEE THAT BEFORE I ALREADY HAVE BEEN USING FACE VELOCITY V P FOR THE PREVIOUS
16 | ASTIONS THAT IN THE CASE OF NON DISPERSIVE MEDIUM THE FACE VELOCITY IS JUST A B P WHICH IS THE VELOCITY IN THE EQUATION AND IN THIS CASE B P WOLD BE EQUAL TO OR MAGA O
17 | AS WE DISCUSS EFOR LAS AT THE DEFINITION OF THIS FACE VELACITY O K AND I CAN NOW ALSO DEFINE THE GOVELOCITY OK
18 | GROUP VELOCITY E SAY SHOULDBE THE VELOCITY OF THE ENVELOPE OK I CAN CALCULATE THE VELOCITY OF THE ENVELOPE RIGHT IN THE CASE OF FACE VELOCITY I ANT CALCULATING
19 | THE VELOCITY OF THE CARRIER OK AM TAKING A RATIO OF THE AVERAGE AND THE I TE AVERAGE IS SO CLOSE TO K AND OBEGA THEREFORE THE FACE VELOCITY V P WOULD TEACH US THE SPEED OF THE PROBLICATION
20 | OF THE CARIE WHICH IS A OMEGAB K I CALL IT B P AND IN CASE OF GROUP VELOCITY I CALL IT B G B G IS DESCRIBING THE SPEED OF PROPAGATION OF THE ENVELOPE THEREFORE
21 | WHAT I'M GETTING IS OMEGA ONE MINUS OMEGA TWO OK TVI DEPI ONE MINUS K TWO POS OP AND HAVE A EFFECT OF ONE OVER TWO LIKE WHICHA
22 | CEN SOT RI AND WHEN THEY ARE REALLY SO CLOSE TO EACH OTHER THIS IS A SEL ROUGHLY LIKE THE OMEGA AND THE QUESTION SO FAR
23 | SO WE HAVE DERIVED TWO DIFFERENT KINDS OF SPEED ONE IS ACT RELATED TO THE FACE OF ALACITY WHICH ONE IS A ONE IS ATLY CALLED
24 | VELOCITY IS RELATED TO THE SPEED OF THE CARRIER OK THE OTHER ONE IS CRO VELOCITY WHICH ISENTLLY RELATED TO THEE SPEED OF THE ENVELOPE OK SO DA ME DISQUIDE YOU
25 | ARE INTERESTING INTERESTING EXAMPLES AND THE S WAKI WALT WE CAN NELY LEARN FROM THIS IN THE FIRST EXAMPLE I AM WALKING ON A NON DISPERSIVE MEDIAM OK IF I HAVE
26 | NON DISPERSIVE MEDIAN O K THEN PASTE WHAT IAM GOING TO GETIA OMEGA WILL BE PROPORTIONALE TO
27 | K IF I PRAT OMEGA VERSUS K IS A STRAIGHT LINE OK NOW IF I HAVE OMEGA I CHOOSE THE OMEGA OF THE TWO OMEGA WAN OMEGA TO
28 | THE TWO WAVES TO BE ROFTY EQUAL TO OMECA DIRO OK I CAN NOW EVALUATE THE V P THE V P WILL BE ER THE SLOPE RIGHT OF THE
29 | OF THIS POINT THE SLOPE OF A LINE CONNECTING THE TERO TO THAT POINT RIGHT WHICH SAY TO THE OMEGA OF BE CARI SO THAT ISU THE DEFINITION OF THE FASE VELOCITY IGET THIS SLOPE
30 | THIS IS THE SLOPE OF THIS THIS LINE ESSENTIALLY CALLEDEREATED TO THE FACE VELOCITY OK I CAN ALSO CALCULATE THE SLOPE OF A LINE CUT TO THIS POINT
31 | BUT I SHOULD CUT THROUGH TIS DESET TIS CURVE AND IN THIS CASE I AM ALSO GOING TO GET A LINE OVERLAPPING WITH FACE VELOCITY BECAUSE IN THIS CASE OMAGA OVER
32 | IS THE CONSTENT WHICH IS V THEREFORE IF NO MATTER WHAT YOU CALCULATE IF YOU CALCULATE V P AS A RATIO OF OMEGA AND HE K WOR YOU CALCULATE V G WHICH IS AS THE SLOW
33 | E LINE CUTTING THROUGH THAT POINT YOU ALWAYS GET GET AS YE BE OK THEREFORE WHAT WE LEARN FROM HERE IS THAT FOR A NON DISPERSIVE MEDIAN V P WILL BE EQUAL TO
34 | G OK NOW MEANS POST OF THIS A TWO CURVES POST OF THE CURVE OF A ENVELOPE DESCRIBING THE ENVELOPE AND DESCRIBING THE CARRIER
35 | IS GOING TO BE PROPAGATING AT E SANE SPEED ANY QUESTIONS SO THE WHOLE THING IS GOING TO BE MOVING AT A CONSTANT SPEED FOR THAT I CAN NOW SHOW YOU
36 | SOME EXAMPLE WHICH I PREPARED A SIN SIMULATION WHICH I PREPARED
37 | K SEE SO WHAT HE DOES IS THAT IT REALLYO WITH A SECOND DIS IS
38 | BIDZIRO OK SO THIS IS THE CASE WHEN I HAVE A NON DISPERSIVE MEDIUM OK IF I HAVE A NON DISPERSIVE MEDIUM WHAT IS GOING TO HAPPEN IS THAT BOS THAT IS A POSTER LA CARRIER
39 | WHICH IS THE SPEED OF THE AUDO'S LITTLE STRUCTURE AND THE ENVELOPE IS GOING TO BE PROPAGATING AT TE SENT SPEED SO YOU CAN SEE THE HIG IS LIKE A FIXED PATTERN IS PROPAGATING TOWARD THE RIGHT HAND SIDE AND TH THE RELATIVE MOTION
40 | BETWEEN THE FINE STRUCTURE AND THE ENVELOPE I SAT DERO SOPESI YOU HAVE EXACTLY THE SAME PATTERN AS A FUNCTION OF TIME OK SO NOW I AMT GOING TO MOVE FROM AWAY FROM THE NON DISPERSIVE MEDIUM
41 | HOW ABOUT WE DISCUSS WHAT WILL HAPPEN IF WE HAVE CONSIDER THE STIFFNESS OF THE STRING AND SEE WHAT WE GET FROM THERE SO IF I BROUGHT OMEGA
42 | AS A FUNCTION OF K O K AND THE CONSIDER AFA TO BE NON ZERO IS A POSITIVE VALUE SO IF I HAVE AFA TO BE A POSITIVE VALUE NON ZERO O K
43 | IN THIS CASE IAM GOING TO GET A CURVE LIKE THIS OK THE SLOPE IS SENTIALLY A CHANGING AND BECAUSE IT'S A CURVING DOWN IT'S CUVING UP BECAUSE IF YOU HAVE K LARGE
44 | THEN YOU WIL SEE THAT THE E RATIO OF OMEGA AND K AS TO INCREASE SO TOT ISSENTIALLY THE KIND OF CURV WHICH WE WOULD GET IF I SET THE OMEGA OF THE FIRST AND SECOND
45 | A WAF IN THE OF OF INCREST IN THIS STUDY TO BE OMEGADIRO NEBESITY WHAT YOU AREGOING TO GET IS THAT O K NOW I HAVE THIS POINT HERE UNDER CUFF OK IF I
46 | CALCULATE THE FACE VELOCITY THE FACE O VELOCITY HOW DO I CALCULATE THAT I CAN NOW CONNECT ZERO AND THAT POINT BY A LINE OK AND I CAN NOW CALCULATE
47 | LOPE OF THIS LINE AND I CAN GET THE AFACE VELOCITY VP OK ON THE OTHER HAND I CAN ALSO CALCULATE A THE SLOPE OF A LINE CUTTING
48 | THROGH TANGENTIAL TO TE THE POINT OF INTEREST OK AND THAT IS GOING TO GIVE ME A GOOD VELACITY O K AS YOU CAN SEE FROM HERE WHICH SLOPE IS AS YOU LARGER
49 | ANYBODY KNOW KENAAND POINTED OUT GROP VELOCITY IS LARGER RIGHT SO IN THIS CASE IF I TURN ON A FAR GREATER THAN ZERO WHAT IS GOING TO HAPPEN IS THAT SINCE THE CRUP VELOCITY IS LARGER THAN
50 | THE FACE VELOCITY THAT MEANS IF I GO BACK TO THAT PICTURE OK THE ENVELOPE IS GOING TO BE MOVING FASTER THEN THE FINE STRUCTURE INSIDE THE ENVELOPE HOW ABOUT WE TAKE A FIVE
51 | BREAK OM FROM HERE AND WE CONTINUE DISCUSSION AFTER BREAK WECAS A GOOD TIME TO TAKE AFREGHTO WELCOME BACK EVERYBODY SO WE WILL CONTINUE THE DISCUS
52 | ON OF THE PIT PHENOMENA SO WHAT WE HAVE SHOWN YOU IS THAT A PACE ON THOSE CURVES AS WE CANNESWIT DETERMINING WHAT WILL BE THE RELATIVE VELOCITY OF THE A OF THE
53 | WHAT WHAT WOULD BE THE VELOCITY OF TE THE CARRIER WHICH I SAY SOULD BE DENOTED BY AM T P AND THE WHAT WOULD BE THE VELOCITY OF THE ENVELOPE WHICH I SAY SULLY DENOTED
54 | BY A LAGRUPLOSITY O IM ENDING IN THE IN THIS CASE WHAT ITO BE PARTING HERE IS THAT IN THIS CASE BECAUSE ARFAISETALY GREATER THAN ZERO
55 | THEREFORE THIS A CUFISASOE A CURVING UP THEREFORE YOU HAVE LARGER A GROVELOCITY COMPARED TO THE FACE VELOCITY SO WHAT YOU WOULD EXPECT IS THAT THE EMB
56 | LOP IS GOING TO BE ACTUALLY PROGRESSING AT A SPEED HIGHER THAN THE SPEED OF A THE LA CARRIER OK ON THE OTHER HAND IF MANGICODE OK I CAN
57 | CONSTRUCT SOME KIND OF A MEDIAN WHICH CAN BE HISQUIVE IN WHICHI THE SITUATION ARE FAR SMALLER THAN DERON WHAT IS GOING TO HAPPEN SO IF I PROT THAT IF I PROT
58 | ATION WICH AFA SMALLER THAN TERO SO AND THE NOW I PROT OMEGA WAS THE FUNCTION OF K WHAT IS GOING TO HAPPEN JUST LIKE THIS TOPACITY YOU HAVE SOMETHING WHICH ISH IS RECURVIG
59 | DAN O K SO IF I NOW AGAIN WALK ON SOME POINT OF INTEREST HERE O K YOU CAN SEE THAT THESLO
60 | POF THE FACE VELOCITY IS NOW IT SHOULD BE AH THE SLOPE OF THE THE FACE VELOCITY IS NOW AT SHOULD BE LARGER THAN THE SLOPE WHICH IS ASUALLY A
61 | LINE CUTTING THROUGH THEE TANGENT TO THE THE CUF WHICH SAE ARE GETTING YOU THE GRUPLASY SO IN THE CASE OF AFAS MOR THEN ZERO
62 | WHICH IS SON STRANGEA AMEDIUM WHICH I CAN CREATE FROM WHAEVER PASMA OR SOME REATY A STRANGE A KIND NEW KIND OF MATERIAL OF INTEREST IF THAT HAPPENS THEN THAT MEANS YOU WERE A GRUP
63 | CITY WILL BE SMALLER THAN DUG THE FACEELACETY OK AND IF YOU LOOK AT THIS POINT HERE YOU CAN SEE THAT THIS CURVE ATO THE
64 | A MEXIMMAN HERE ANDE IF YOU ESUDY ARE OPERATING AT THIS POINT WHAT IS GOING TO HAPPEN WHAT IS GOING TO HAPPEN IS THAT IF YOU CALCULATE THE GROUP
65 | CITY WOL BET ABOUT O YOU'LL BE TERON WHAT DOES THAT MEAN THAT MEANS THE ENVELOPE WILL NOT BE MOVING ALONG OK BUT THE THE THE CARRIERS ARE STILL MOVINGO
66 | SINDEED AT THIS POINT YOU ARE GAY GOING TO GET GOD VOLOCITY EQUAL TO ZER OK AND FINALLY IF YOU ASHOD
67 | GOING TO A VERY LARGE CA VALUE IN THIS SCENEREO AFA SMALLER THAN ZERO YOU SEE THAT EVEN YOU CAN HAVE FACE VELOCITY B P
68 | POSITIVE BECAUSE HE SAYS Y A POSITIVE SLOPE AND ADUT VELOCITY AE IS NEGATIVE WHY WHAT DOES THAT MEAN NAI MEANS YOUA
69 | GOIN TO SEE A SITUATION THAT THE CARIERS ARE PROGRESSING IN A POSITIVE DIRECTION AND THE A THE THE ENVELOPE IS GOING TO BE A
70 | PROGRESSING IN THE NEGATIVE DIRECTION PROBIC FOQUESSING TO THE NEX LAPPING SIDE OF THE PORT SO WHAT DOES THAT MEAN THAT MIANS THIS WAVE IS DOING
71 | WHAT MICHAEL JESSON IS DOING LIES ESENTIALLY TWEN EH SO THIS ISSENTIALLY THE KIND OF THING WHICH COULD HAVE HAPPENED THAT IT LOOKS LIKE THAT
72 | ARE YOU ARE DOING YOARE GOING FORWARD BECAUSE ALL THE AR CARRIERS ARE MOVING IN A POSITIVE DIRECTION BUT THE BODY E SAYSOY GOING TO EARTH
73 | NEGATIVE DIRECTION OK MAYBE I CAN ALSO LEARN MOON WORK AT SOME POINT OK SO THAT'S GO BACK TO THE DEMONSTRATION WHICH I GOT STARTED AND SOMEHOW I GOT MEED UP A
74 | SO LETS TAKE A LOOK AT THE DETEMO AGAIN SO TAS LOOK AT ALL THE DIFFERENT SITUATION AT ONCE SO IN THIS CASEF US WE DISCUSSED BEFORE THIS ISSENTIALLY HAPPENING IN THE
75 | NON DISPERSIVE SITUATION TAT IN THIS SITUATION YOU HAVE A STRAIGHT LINE NON DISPERSIVE MEDIAN AS WE GIVE YOU ALWAYS THE GROP VELOCITY EQUAL TO A FACE VELOCITY OK SO
76 | IMEANS THE CARRIER AND THE A THE ENVELOPE IS GOING TO BE MOVING IN THE SAME DIRECTION AT THE SAME AS A SPEED OK ON THE
77 | HEHAND IN THIS CASE WE CAN ACTUALLY HAVE A SITUATION THAT THE THE FACEO VELOCITY ESSENTIALLY FASTER THAN THE GROUP VELOCITY O SO WHAT I MEAN IS THAT SILA SITUATION HERE
78 | FACE VELOCITY CALCULATED FROM A LINE CONNECTING FROM ZERO TO THAT POINT O IS ACTUALLY HAVING A LARGER SLOPE COMPARED TO THE TENGENTRA LINE AND YOU YOULL SEE THIS SITUATION SO BESY DO YOU SEE THAT
79 | INSIDE THE ENVELOPE ALL THOSE CARRIERS ARE ACTUALLY MOVING FASTER THAN THE ENVELOPE NOW I CAN HAVE A DISPERSIVE MEDIUM WHERE
80 | LACO VELOCITY IS SEQUEL TO TERO SO WHAT IS GOING TO HAPPEN IS THAT REALLY THE ENVELOPE ESSETALLY NOT MOVING IS NOT LIKE LAKE THIS EH BUT THA THE PARTY IS NOT MOVING RIGHT SO YOU HAVE SUNG
81 |
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1 | CARRIESINSI THIS IN THIS IN THE STRUCTURE ESENTIALLY MOVING FORWARD BUT THE ENVELOPE ESSENTIALLY NOT MOVING
2 | SO FINALLY THE LAST SITUATION IS REALLY INTERESTING SO TAMIN IN THIS SITUATION THIS ISSANTIAL TE A HEAVY LACUBELOCITY A
3 | THE GROP VELOCITY IS ACTUALLY HAVING DIFFERENT SIGN COMPARED TO THE FACE VELOCITY SO YOU CAN SEE THAT THA THE WHOLE STRUCTURE OF THE ENVELOPE IS SANTIALLY MOVING BACKWARD BUT THAT THECAR
4 | ESPENCIALLY MOVING IN THE POSITIVE DIRECTION IN THIS EXAMPLE OK SO THIS ESPENTIALLY WHAT WE HAVE LEARNED FROM TE FROMTIS
5 | BIT PHENOMENA AND WE HAVE COVERED UP THE IDEA OF FACE VELOCITY AND HE GROUP VELOCITY SO HOW ABOUT FOUNDE CYSTEM HOW DO WE UNDERSTAND WHEN WE HAVE ABOUNDE SYSTEM
6 | HOW DOES THAT INVOLVE EVOLVE AS A FUNCTIONAL TIE SO IF I HAVE A SISTEN OF TWO WALLS AND THE ONE STRING AND OF COURSE I GIVE YOU THE DENSITY FOR DEINY LANDS AND
7 | THE TENT STRING TENSION AND ALSO THE AFA WHICH S AS WE TELL YOU ABOUT THE STEEPNESS OF THI SISTER OK AGAIN I CAN WRIDE DOWN SISTE TO BE
8 | SONG OF ORDER NO MORE MO FROM ONE TO INFINITY A M SIN K M X PAS AFM SIN
9 | ANT APAT AND THEN WHAT WE CAN DO IS THAT WE CAN FIRST GET THE INITIAL CONDITIONS OF THIS SYSTEM AND
10 | O THE BOUNDARY CONDITIONS OF THIS SYSTEM THEN WE AS JUST FOLLOW EXACTLY THE SAME PROCEDURE TO OBTAIN ALL THE UNKNOWN COEFFICIENTS THEN WE'LL BE ABLE TO EVOLVE THIS SYSTEM AS A FUNCTIONAL TIME AS I HAVE DEMONSTRATED YOU IN THE BEGINNING
11 | LECTURE SO IN THIS CASE YOU CAN HAVE TWO BOUNDARY CONDITIONS ONE ESESALLY AT X EQUAL TWO ZERO AND THE OTHER ONE IS ATE AT X EQUAL TO L O IN THOSE BOUNDARIES
12 | WE AS YE LEARNED BEFORE BECAUSE THE END POINTS ARE FIXED ON THE WALL THEREFORE SI OFTERO AT THE AT THE TIME T WILL BE ALWAYS
13 | EQUAL TO ZERO FOR THE LAFAND SI A PONDARY CONDITION AND THE VERY SIMILARDY AS WE DISCUSSED BEFORE SF L T WILL BE EQUAL TO ZERO IF YOU LOOK AT THE RIGHTAD SIDE OF THE WALL
14 | OF THE SISTER O SO I DON'T WANT TO REPEAT THIS BECAUSE THIS IS ATO EXACTLY THE SAME CALCULATION WHICH WE HAVE DONE BEFORE IGHT SO WITH THIS CONOND TIS TWO PONDARY CONDITIONS WE CAN ETU CONCRUDE AT
15 | M WILL BE EQUAL TO M PI OVER L AND THE F N WILL BE EQUAL TO ZERO OK SO YOU CAN ISSU GO BACK AND THE CHECK THIS
16 | A RESULT SO WHAT I WANT TO SAY IS THAT UNTIR NOW WHAT WE HAVE BEEN DOING IS IDENTICAL TO WHAT WE HAVE BEEN DOING FOR THE NON DISPRESSIVE MEDIUM O K WHAT I'M TO SAY IS THAT THE
17 | P THE NOMA MO IS ATESET BY THE BOUNDARY CONDITION IS DETERMINED BY THE BOUNDARY CONDITION AND IT HAS ACTUALLY SO FAR NOTHING TO DO WITH THE THE DISPERS
18 | RELATION O MAGA IS A FUNCTIONO OK SO SO IN SHORT BOUNDARY CONDITION CAN GIVE YOU THE SHAPE OF THENORMAL MOTE AND WE KNOW THAT THE FIRST NORMAL MO SECOND NORMAL MO ET CETERA ET CETERA
19 | ESAYIALLY AA GOING TO BE IDENTICAL TO THE CASE OF NON DISPERSIVE MEDIUM O K SO THAT AS BE THE FIRST THING WHICH WE LEARN THE SECOND THING WE LEARN IS THE O K NOW
20 | WHAT WE SEE IS THAT ONCE THE BOUNDARY CONDITION IS GIVEN THEN THE KN IS SA TO BE ALSO GIVEN THEREFORE SINCE I HAVE THE DISPERSION RELATION OMEGA AS A FUNCTIONAL K
21 | ASJON THER RIGHT OMEGA IS EQUAL TO OMEGA BOQS EQUAL TO V TIMES SQUARED TO THE ONE PROS OFA SQUARE RIGT THEREFORE HENCE K N IS GIVEN OMEGA
22 | IS ALSO GIBEN SO YOU CAN SEE THAT THAT'S AS SE WER THE DISPERSION RELATION COMING TO PRAY THE OMEGA AN
23 | BET DIFFERENT IF YOU COMPARE THE DISPERSIVE CASE AND NOT DISPERSIVE CASE OK SO THAT IS A TO BE ER WHAT I WANT TO SAY THE K N WHICH IS THE SHAPE OF THE NORMAL MOLE DOESN'T DEPEND
24 | ON THE DISPERSION RELATION ON THE OTHER HAND THE SPEED OF THE OSCILLATION THE ANGURAR FREQUENCY O MEGA DEPENDS ON THE DISPERSIAN RELATION WHICH ESPECIALLY WHILE WE ABTAINED IT FROM
25 | IF I START TO PROT OMEGA AND AS THE FUNCTION OF
26 | SO IN THE CASE OF NON DISPERSIVE MEDIUM SO WHAT I AM GOING TO GET IS I SHOULDBE DISCRETE POINT ALONG A STRAIGHT LINE OK TISSOE K ONE
27 | TOFOUR ETCETERA THERE I SOUE THERE ISHOULD BE ALL SITTING ON A COMMON STRAIGHT LINE OK IF YOU DO GETTE LOK TEOO
28 | TIVE AS A DIFFERENCE BETWEEN K ONE K TWO AND K THREE THEY ARE CONSTANT ACCORDING TO THIS FORMULA THE DIFFERENCE BETWEEN K Y AND K TWO IS PI OVER TWO K TWO AND K THREES ALSO POVER TWO
29 | ERL IS ALWAYS A FIXED NUMBER AND THE SING OMEGA ESSENTIALLY PROPORTIONAL TO K THEREFORE THE SPACING BETWEEN OMEGA ONE OMEGA TWO OMEGA
30 | THREE IS ALSO CONSTANT OK IN SHORT OMEGA TO OMICA TRE AND OMIGA FOUR ET CETERA IS ALWAYS A MULTIPLE TINES OF VAE
31 | GET FROM OMAKA ONE RIGHT ACCORDING TO A DISE QUAR AND IN THE CASE OF NONE DISPERSIVE MEDIUN OK SO WHAT DOES THAT MEAN NO MEANS O K NOW IF I HAVE
32 | A VERY COMPLICATED INITIAL CONDITION OK THIS ESETALLY WHAT I HAVE AN INITIAL CONDITION VERY COMPLICATED OK I JUST NEED TO WAIT IF THIS IS ASURE NON DISPERSIVE MED
33 | THAT I JUST HAVE TO WAIT UNTIL T EQUAL TO TWO PI OBE OMEGA ONE THEN THIS SYSTEM WOULD RESTORED TO ITS ORIGINAL SHAPE O CASE A SAY TOB WHAT I CAN LEARN FROM HERE
34 | BECAUSE O MAKE OUT TWO OR MAKE OUT THREE AND ANY HIGHER OTHER A NO MORE MODES THE ANGR FREQUENCY SAY SHE MULTIPLY TIMES OF WHAT I GET FROM OR MAKE OUT ONE O K
35 | ON THE OTHER HAND IF I CONSIDER THE SITUATION OF THISPERSIVE MEDIUM OK YOU CAN SEE THAT NOW NOW THE DIFFERENCE BETWEEN
36 | O MEGA N IS NOW THE CONSTANT OK SO WHILE YOU WERE PRODIGOUS THAT IT WOULD TAKE MUCH MUCH LONGER FOR THIS SYSTEM TO GO BACK TO THE ORIGINAL SHAPE COMPARED TO ER ER
37 | NON DISPERSIVE MEDIUM O CAS OR NOT IS WHETHER YOU CAN AS YOU SEE IN INA REAL LIFE A EXPERIMENT I CAN DISTORT THIS IT THIS EQUIPMENT IN THIS BOUNDS AS A SISTEN AND IS
38 | GOING TO TAKE FOREVER WOR IMPOSSIBLE TO COME BACK TO THE ORIGINAL SHAPE BECAUSE OF THE DISPERSIONO ON THE OTHER HAND IF I HAVE T REALLY HIGHLY IDEALIZED THE SITUATION IF I HAVE BOS AND BOUND AND I JUST HAVE
39 | WAIT UNTIL T EQUAL TO TWO PI OVER OR MAKE OT ONE THEN THIS SYSTEM WILL GO BACK TO THE ORIGINAL SHAPE BEFORE I END THE THE LECTURE TO DAY K
40 | I WOULD LIKE TO DISCUSS WITH YOU TOO INTERESTING ISSUE SO MANY OF YOU HAVE SEEN WATER WAVES EH AND FIRMANT AS YOU TOLD US IN
41 | LECTURE THAT WATER WAVES ARE THE ARE REALLY EASILY SEEN BY EVERYBODY BUT I SAYS SOUE THE WORST POSSIBLE EXAMPLE THAT'S THE BAD NEWS THE WORST POSSIBLE EXAMPLE BECAUSE IT HAS ALL THE POSSIBLE
42 | ER THAT WAVES CAN HAVE THAT'S THE BAD NEWS THE GOOD NEWS IS THAT YOU ARE GOING TO DO THAT IN YOUR PIAED SO WE WERE BIBL TO UNDERSTAND THE BEHAVIOUR OF THE WATER WAVESSAID
43 | THA GOOD NEWS THE SECOND THING WHICH I WOULD LIKE TO TALK ABOUT IS FACE VELOCITY OK YOU CAN SEE THAT THIS OK YOU CAN SAY O K YOU SAY THAT FACE VELOCITY OR HARMONICA WAVES DONTSEND
44 | INFORMATION RIGHT AND AND TE HOW DO I A SO KNOW THAT RIGHT SO WHAT DOES THAT MEAN O K SO LET'S TAKE THIS HORRIBLE EXAMPLE OF WATE WAVE OK S SOTELE THE BLACK LINE IS ASU E
45 | BEACH AND TEYOU THERE'S A WATER WAVE PON THE OCEAN APPROACHING THE BEACH AND YOU CAN SEE THAT YOU CAN HAVE SOME KIND OF ANGLE BETWEEN THE INCERTANT WATER WAVE AND THE LINE OF THE BEACH OK
46 | AH WHAT I CAN NEASELY DO IS THAT I CAN NOW MEASURE THE SHAPE OF THEWATER WATER WAVE AT AT THE EDGE OF BEACH AND THE WERY
47 | SEE THAT HA NOW THE LEFACE VELOCITY WHICH I OBSERVE THERE ESENTIALLY FASTER THAN THE SPEED OF A PROPAGATION OF THE WATERWAY BECAUSE OF THIS THIS
48 | INSIDE THE ANGLE OK I CAN ASLY MAKE IT VERY VERY FAST I CAN MAKE THIS SPEED ISHAB EVEN FASTER THAN THE SPEED OF LIGHT RIGHT
49 | I CAN I CAN I CAN NOW DECREASE THE THE SITA TO ZERO THEN YOU HAVE YOU HAVE A FACE VELOCITY WHICH IS FASTER THAN THE SPEED OF LIGHT IT GO TO INFINITY
50 | BUT DOES THAT MEAN ANYTHING ISE THAT DOEDNOT MEAN ANYTHING BECAUSE THATI DON'T REALLY MOVE WITH WATER FROM A SPECIFIC POINT TO ANOTHER POINT INFINITELY FAST
51 | THEREFORE WHAT I WANT TO SAY IS THAT OK YOU CAN DO WHATEVER YOU WANT TO MAKE A FANCY FACE VELOCITY BUT THAT WILL NOT HELP YOU WITH SENDING THINGS COSE TO THE SPEED OF LIGHT OR GREATE SPEED OF
52 | OK SO AS YOU CAN SEE FROM THE EXAMPLE I CAN EASILY CONSTRUT A SIMPLE EXAMPLE WHICH YOU SEE THAT IS THAT SE IS REALLY NOT SENDING ANYTHING FROM ONE PRESS TO THE OTHER BUT YOU STILL HAVE A READIRLLY FAST F
53 | I OKI THANK YOU VERY MUCH EVERYBODY FOR THE ATTENTION AND THE WHOOF YOU ENJOY THA LECTURE AND IF YOU HAVE ANY QUESTIONS A ESTAME
54 |
55 |
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1 | well let ' s let me actually tell you then about rather than the the proof I think I ' ll share the proof with kill because the proof that I want wanted to actually show you gives a proof of
2 | the stocastic gradient is well behaved on both convex and non convex problems and the proof it wanted to show was for the non convex case because it applies to neural network so you may be curious about that proof and remarkably that proof is much simpler than the case of convex
3 | problems so let me just mention some very important points about sarcastic radiant so even though this method has been around since nineteen fifty one every deep learning toolkit has it and we are studying it in class there are still gapsbet
4 | in what we can say theoretically and what happens in practice and I ' ll show you those gaps already and encourage you to think about those if you wish so let ' s look back at our problem and tell you about two variants so here are the two variants I ' m going
5 | ask if any of you is familiar with these variants in some way or other so let ' s is just called it feasible here there are no constraints so you start with any random factor of your choice in deep network train
6 | you have to work harder and then this is the iteration you run right option one and option to so option one says that was the idea we had in class random by pick some training data point use its futuristic gradient
7 | well what do we mean by random by pick the moment you use the word random you have to define what ' s the random news so the random news is uniform probability
8 | and training data points that is one ' s randomness the other version is you pick a training data point without replacement so so with replacement means you know just uniformly at random each time
9 | draw a number from one through a use that sarcastic radiant move on which means the same point can easily be picked twice also and without replacement means if you ' ve picked up point number three you ' re not going to pick it again until you ' ve
10 | through the entire training data set those are two types of randomness which version would you use there is no right or wrong answer to this I ' m just taking a pole
11 | what would you use think that you ' re writing a programme for this and maybe think really pragmatically practically that ' s enough of an in which version would you use I ' m just curious
12 | who would use one please raise hands on who and the the exclusion the complement thereof or I don ' t know maybe some people are undecided who would use too very few people to
13 | of how many of you use the neural network training tool kits like dense flu pit torch what not which versions are they using
14 | actually every person in the real world is using versions too are you really going to randomly go through your ram each time to pick random points they ' ll kill your big top performance like anything
15 | what people do is take a data set use a pre shuffle operation and then just whoop stream through the data what does streaming through the data mean without replacement so all the toolkits actually are using the without replacement or
16 | even though intuitively the re as uniform random feels much nicer and that feeling is not ill founded because that ' s the only version we know how to analyze mathematically so even for this method everybody studies it there
17 | and papers on it the version that is used in practice is not the version we know how to analyze it ' s a major open problem in the field of stocastic gradient to actually analyze the version that we use in practice this kind of
18 | rising but it ' s without replacement means non big probability theory and non side probability theory is not so easy that ' s the answer to it so the other version is this main batch idea which
19 | mentioned really early on is that rather than pick one random point I ' ll pick a minnie batch so I had a million points each time instead of picking one maybe I ' ll pick
20 | ten or hundred or thousand or what have you so this averages things averaging things reduces the variants so this is actually a good thing because the more quantities you average the less noise you have that
21 | kind of what happens in probability right so we pick a minnie batch and the sarcastic estimate now is that you know not just a single gradient but averaged over a minnie batch
22 | so mini batch of size one is the pure vanilla s s d mini batch of size and is nothing other than pure gradient descent something in between is what people actually use and again the theoretical analysis only adds
23 | if the minnie batch is picked with replacement not without replacement is one of the reasons actually a very important thing in theory you don ' t gain too much in terms of computational gains on convergence
24 | speed by using many matches but many batches are really crucial especially in your deep learning your style training because they allow you to do things in parallel each thread or each core or sub
25 | or your small chip or what have you depending on your hardware can be working with one sorcastic radiant so mini batches the larger the minnie batch the more things you can do in parallel so mini batches are greatlyexplot
26 | by people to air give you a cheap version of paralelism and where does the parallelism happen you can think that each core customer a sarcastic gradient so the hard part is not
27 | adding these things up and making the update to x the hard part is computing a sarcastic gradient so if you can compute ten thousand of those in parallel because you have ten thousand cores great for you and that ' s the reason people love using many
28 | aches but a nice side remark here this is also this brings us close to the research edge of things again that well you ' d love to use very large minnie badges so that you can fully max out on the parade
29 | is available to you right maybe you have a multi gap system if younger friends with envy dear yoga i only have like two gps but depends on how many ups you have you ' d like to really mix it on parallelism so that you can really
30 | inch through big data sets as fast as possible but you know what happens with very large many batches sifyo have very large mini batches starcastic gradient starts looking more like
31 | full gradient descent which is also called back gradient descentthat ' s not a bad thing that ' s awesome for optimization but it is a weird conundrum that happens in training deep metal networks
32 | this type of problem we wouldn ' t have for convex optimization but in deep nuralet because this really disturbing thing happens that if you use these very large many batches your method starts resembling radiant dissent that means it decreases noise
33 | much so that this region of confusion shrinks so much which all sounds good but it ends up being really bad for machine learning that ' s what I said that in machine learning you want some region of uncertainty and what it
34 | means actually is a lot of people have been working on this including at big companies that if you reduce that region of uncertainty too much you end up over fitting your neural network
35 | and then it starts sucking in its test data unseen data performance so even though for parallelism programming optimization theory big mini batch is awesome
36 | tunately their price to be paid that it hurts your test error performance and they ' re all sorts of methods people are trying to cook up including a shrinking data
37 | only or changing natural network architecture and all sorts of ideas you can cook up your ideas for your favourite architecture how to make a large minnie batch without hurting the final performance but it ' s still somewhat of an open question on how to optimal
38 | etc which means how large your many bats should be so even though these ideas are simple you see that every simple idea leads to an entire sub area of s g d
39 | here are practical challenges people have various heristics for solving these challenges you can cook up your own but it ' s not that one idea always works so if you look at s go do what are the
40 | in parts the moving parts to go the gradients stacastic gradients the step size the mini batch so how should it pick step sizes very non trivial problem different deep learning to
41 | s may have different ways of automating that tuning but it ' s one of the painful things which many batch to use with replacement without replacement is already showed you but which many batch should it use how large that should be again not
42 | easy question to answer how to computer starcastic gradients does anybody know how starcastic gradients are computed for deep network training anybody know there is
43 | famous elgarithm called back propagation that back propagation elgrithm is used to compute a single starcastic gradient some people use the word back prop to mean asjiddy but what back prop really means is some
44 | some kind of algorism which computer for you a single sarcastic gradient and hence youknow this are tenser filled central these toolkiss they come up with all sorts of waste automate the computation of a gradient because really that ' s the main thing
45 | and then other ideas like radiant clipping and momentum and veteran the bunch of other ideas and the theoretical challenges is mentioned to you already proving that it works that it actually solves what it set out to do unfortunately it was too slow
46 | couldn ' t show you the awesome five line proof that I have that s s works for several networks and theoretical analysis as i said is really lagging my proof also uses the wind
47 | cement and the without replacement version which is the one that is actually implemented so there ' s very little progress on that there is some progress there ' s a bunch of papers including from our colleagues that insight but it ' s quite
48 | and the biggest question which most of the people in machine learning are currently excited about these days is stuff like why does s go work so well for neural networks are
49 | this scrappy optimization method it very rapidly does some fitting data is large neuro network is large and then this neuro network ends up having great classification performance why is that happening that ' s called trying to explain
50 | build a theory of generalization why does so s go the trained natural network work better than neural networks train with more fancy optimization methods it ' s a mystery and most of the people who take interest in theoretical machine learning and statistics
51 | that is one of the mysteries they are trying to understand so I think that ' s my story of a jiddy and this is the part we shape but its take the the intuition behind us gods much more important than this
52 | so I think we can thank you close somewhere the roof or mondays exactly I think so that
53 | they ' ll be great
54 |
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1 | the filthy filter that is obtained by mapping the butterworth filter to a digital filter through the biolineal transformation in fact falls off in frequency
2 | much more rapidly than the one that we got through impulse and variance a question is why no one thought that might come to mind as well impulse and variance as aliasing the biolinear transform
3 | it doesn ' t have aliasing that must be a consequence of aliasing in fact that ' s not the reason aliasing as it turns out in this particular design is he was relatively minimal in the impulse and variant design
4 | the reason has to do with this non linear mapping in the bilinear transformation from the continuous time frequency to the discreet time frequency keeps in mind that
5 | through that mapping as you start walking around the unit circle and moving up the jeomega axis as you move up the jeomega axis you have to move faster and faster and faster and faster and what ' s in
6 | this time frequency and infinity is what you get to in the discreet time frequency by the time you get around to do so in fact what we ' re looking at is as as we look out along this
7 | currency axis is we ' re seeing higher and higher and higher frequencies in the continuous time filter by the time we get to go we should in fact be in the continuous
8 | time filter equivalently off to infinity which sounds like a pretty uncomfortable place to be to k now this was a fairly rapid trip
9 | to a number of issues in particular some of the issues associated with the biological transformation and also this issue of how you pick this permanent capital it and how it might be
10 | met with a sampling frequency if you ' re doing discreet time processing of continuous time signals and we don ' t have time to explore some of those issues more fully in this lecture but I ' d like
11 | conclude by making a couple of comments one comment is that the two techniques that we ' ve talked about impulse and variance and the biolinear transformation are the two techniques that are principally used
12 | and one thinks of mapping continuous time filters to discreet time filters for whatever application and the stress again that you may want to do that mapping whether or not the discreet time filter
13 | is eventually going to be used for processing continuous time signals now impulse and variance had the characteristic that it very nice characteristic that that
14 | corresponds to a linear mapping between the two frequency axes except for the issue of aliasing and that ' s a problem with it and in particular limits its usefulness to filter
15 | signs or for mapping continuous time filters that are banned limited on the other hand we have the bilinear transformation as a design procedure which totally avoids allowing
16 | but has the disadvantage or difficulty that it represents a non linear mapping from the continuous time filter to the discreet time filter now this non linear distortion is perfectly accepted
17 | able if we ' re designing or attempting to design filters that have flat frequency characteristics it ' s not acceptable if for example we had a linear frequency characteristic that we wanted to map to a discreet time
18 | tear and end up with a linear frequency characteristic it won ' t come out to be linear because of this non linear mapping of the frequency axes now there are also a number of other design
19 | procedures which we won ' t go into for designing discreet time filters and among them are a variety of techniques including for example computerised designed procedures and I invite you
20 | if you ' re interested and want to dig into that in more detail and more deeply to explore that topic by making reference to various of the books listed in the bibliography
21 | in the text thank you
22 |
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1 | lands very very similar between the two waves right so therefore what I am going to do is that I am going to assume me one is very close to go two
2 | is roughly k ok and I am got end because of this since I have a continuous function if k why is really close to key too that means no maga one is going to
3 | also very cause to omega too right so what I am going to get is omega one is going to be also very similar to omega too and I will call it omega or
4 | so if I do this when I have very similar a one and key to what is going to happen what is going to happen is that no one minus a two will be
5 | rysmall data means a this very small k means large wave lands therefore this cosinten will become twelve
6 | because they say we are slowly bariting a empty as a function of position because a case very small case case malmeans land are large therefore them
7 | do is going to be having this modulation which is stay like an envelope he is the speed of this envelope the oscillation of this envelope is as to control by the of
8 | last look at the lap site a one pros a two over two it ' s kind of like the calculating the average of the first and second of the wave number of the first and second waves right so you will
9 | flat average it can be still very large therefore you have small life right compared to the difference therefore you see that that i should contribute to those little structures in
10 | an indiscrepent called carrier yes tatas
11 | so they can be different thought why so you are absolutely right that so you can you can produce some something like a carrier as even when line is not equal to key to this is just at every bit your right
12 | but the then there on the other hand the difference may and my too will be also large therefore you it ' s not as easy as what we have been doing here to identify who is the
13 | ear and who is the envelope but you do you do get some kind of grade which is icillating really fast but the envelope is going to appear also icillating really fast that is harder to to see all the structure but
14 | your absolutely right yes very good question so now I have this set up I assume that they are very close to each other so now I can define face velocity finally
15 | will define what is I you the face of velocity the face of velocity i call it v but you can see that before I already have been using face velocity v up for the previous
16 | astions that in the case of non dispersal medium the face velocity is just a b p which is the velocity in the equation and in this case be up will be equal to your image of
17 | as we discuss for law at the definition of this face velacity of k and I can now also define the govelocity of
18 | group velocity we say should the velocity of the envelope or i can calculate the velocity of the envelope right in the case of face velocity i and calculating
19 | the velocity of the carrier on and taking a ratio of the average and the time the average is so close to k and omega therefore the face velocity v but would teach us the speed of the publication
20 | of the carrier which is a omega k i call it be up and in case of group velocity I call it be g b g is describing the speed of propagation of the envelope therefore
21 | what I ' m getting is omega one minus omega two or ten despite one minus k two post of and have an effect of one over two like whicha
22 | can sit run and when they are really so close to each other this is a sell roughly like the omega and the question so far
23 | so we have derived two different kinds of speed one is act related to the face of quality which one is a one is actually called
24 | velocity is related to the speed of the carrier or the other one is cro velocity which essentially related to the speed of the envelope or so do me disguise you
25 | are interesting interesting examples and the s like what we can really learn from this in the first example I am walking on a non dispersive medium or if I have
26 | non dispersal median of k then paste what is going to get omega will be proportional to
27 | k if the part omega versus k is a straight line or now if I have omega I choose the omega of the two omega was omega to
28 | the two waves to be pretty equal to women do or I can now evaluate the v but the v but will be near the slope right of the
29 | of this point the slope of a line connecting the euro to that point right which say to the omega to be care so that is the definition of the face velocity get this slope
30 | this is the slope of this this line essentially calledereated to the face velocity or I can also calculate the slope of a line cut to this point
31 | but I should cut through his desert this curve and in this case I am also going to get a line overlapping with face velocity because in this case image over
32 | is the constant which is v therefore if no matter what you calculate if you calculate v p as a ratio of omega and the k for you calculate v g which is as the slow
33 | the line cutting through that point you always get get as you be or therefore what we learn from here is that for a non disservice median v but will be equal to
34 | g ok not means most of this a two curves post of the curve of the envelope describing the envelope and describing the carrier
35 | is going to be propagating at the same speed any questions so the whole thing is going to be moving at a constant speed for that I can not show you
36 | some example which is prepared a sun simulation which is prepared
37 | ok see so what he does is that it really with a second did is
38 | bidziro or so this is the case when I have a non dispersive medium or if I have a non dispersal medium what is going to happen is that boys that is a poster la carries
39 | which is the speed of the audio ' s little structure and the envelope is going to be propagating at the sent speed so you can see the wig is like a fixed pattern is propagating toward the right hand side and in the relative motion
40 | between the fine structure and the envelope I sat dero sopesi you have exactly the same pattern as a function of time or so now I am going to move from away from the non disservice medium
41 | how about we discuss what will happen if we have considered the stiffness of the string and see what we get from there so if I brought omega
42 | as a function of k o k and the consider advantage to be non zero is a positive value so if I have had to be a positive value on zero to k
43 | in this case him going to get a curve like this on the slope is sentially a changing and because it ' s a curling down it ' s covering up because if you have a large
44 | then you will see that the a ratio of omega and k as to increase so that essentially the kind of curve which we would get if I set the omega of the first and second
45 | a wag in the top of increase in this study to be omegadiro obesity what you going to get is that you k now i have this point here under cuff or if I
46 | calculate the face velocity the face of velocity how do I calculate that I can now connect zero and that point by a line of and I can now calculate
47 | love of this line and I can get the face velocity up ok on the other hand I can also calculate a the slope of a line cutting
48 | throw tangential to the the point of interest ok and that is going to give me a good velacity to k as you can see from here which slope is as your larger
49 | anybody no demand pointed out group velocity is larger right so in this case if I turn on a far greater than zero what is going to happen is that since the crop velocity is larger than
50 | the face velocity that means if I go back to that picture of the envelope is going to be moving faster than the fine structure inside the envelope how about we take a five
51 | break on from here and we continue discussion after break faces a good time to take afreghto welcome back everybody so we will continue the discuss
52 | one of the pit phenomena so what we have shown you is that a pace on those curves as we canneswit determining what will be the relative velocity of the day of the
53 | what what would be the velocity of to the carrier which I say would be debated by am the up and the what would be the velocity of the envelope which I say slowly debated
54 | by a lagruplosity of him ending in the in this case what to be parting here is that in this case because arfaisetaly greater than zero
55 | therefore this a cufisasoe a curling up therefore you have larger a grovelocity compared to the face velocity so what you would expect is that the empathy
56 | lot is going to be actually progressing at a speed higher than the speed of a time la carries or on the other hand if mangicode or i can
57 | construct some kind of a median which can be highest in which the situations are far smaller than deron what is going to happen so if it protest that if the protest
58 | action which as smaller than very so and the new the pro omega was the function of it what is going to happen just like this topacity you have something which is is receiving
59 | can to k so if I now again walk on some point of interest here to t you can see that theslo
60 | of the face velocity is now it should be and the slope of the the face velocity is now that should be larger than the slope which is usually a
61 | line cutting through the tangent to the the cuff which we are getting you the gruplasy so in the case of afas more than zero
62 | which is some strange amedium which I can create from whatever pasma or some reality a strange a kind of kind of material of interest if that happens then that means you were a group
63 | city will be smaller than dug the faceelacety on and if you look at this point here you can see that this curve to the
64 | a meximman here and if you truly are operating at this point what is going to happen what is going to happen is that if you calculate the group
65 | city will bet about you you ' ll be torn what does that mean that means the envelope will not be moving along or but the time the carriers are still moving
66 | sindeed at this point you are gay going to get good volocity equal to zero ok and finally if you should
67 | going to a very large car value in this scenery as smaller than zero you see that even you can have face velocity public place
68 | positive because he says why a positive slope and about velocity he is negative why what does that mean any means you
69 | going to see a situation that the careers are progressing in a positive direction and the as time the envelope is going to be a
70 | progressing in the negative direction produce foquessing to the new lapping side of the sport so what does that mean that means this wave is doing
71 | what Michael lesson is doing lies essentially twin eh so this essentially the kind of thing which could have happened that it looks like that
72 | are you are doing your going forward because all the air carriers are moving in a positive direction but the body are says going to earth
73 | negative direction or maybe I can also learn moon work at some point or so that ' s going back to the demonstration which I got started and somehow I got meet up and
74 | so lets take a look at the detemo again so has look at all the different situations at once so in this case us we discussed before this essentially happening in the
75 | non dispersive situation that in this situation you have a straight line non dispersal median as we give you always the group velocity equal to a face velocity or so
76 | means the carrier and the as the envelope is going to be moving in the same direction at the same as a speed ok on the
77 | hands in this case we can actually have a situation that the the face velocity essentially faster than the group velocity do so what I mean is that usual situation here
78 | face velocity calculated from a line connecting from zero to that point you is actually having a larger slope compared to the tengentra line and you will see this situation so easy do you see that
79 | inside the envelope all those carriers are actually moving faster than the envelope now I can have a disservice medium where
80 | local velocity is sequel to there so what is going to happen is that really the envelope essentially not moving is not like like this eh but that the party is not moving right so you have so
81 |
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1 | carries this in this in the structure essentially moving forward but the envelope essentially not moving
2 | so finally the last situation is really interesting to time in this situation this essential is a heavy lacubelocity and
3 | the group velocity is actually having different signs compared to the face velocity so you can see that that the whole structure of the envelope is constantly moving backward but that theater
4 | especially moving in the positive direction in this example or so this especially what we have learned from the fromtis
5 | bit phenomena and we have covered up the idea of face velocity and the group velocity is how about found system how do we understand when we have abounded system
6 | how does that involve evolve as a functional time so if I have a system of two walls and the one string and of course I give you the density for deiny lands and
7 | the tent strong tension and also the afa which is as we tell you about the steepness of the sister or again I can write down site to be
8 | song of order no more go from one to infinity a m sin k m x pas afm sin
9 | want apart and then what we can do is that we can first get the initial conditions of this system and
10 | on the boundary conditions of this system then we must just follow exactly the same procedure to obtain all the unknown coefficients that we ' ll be able to evolve this system as a functional time as I have demonstrated you in the beginning
11 | lecture so in this case you can have two boundary conditions one really at x equal to zero and the other one is are at a equal to l o in those boundaries
12 | we as he learned before because the end points are fixed on the wall therefore so often at the at the time it will be always
13 | equal to zero for the land is a pondary condition and the very similarity as we discussed before so l it will be equal to zero if you look at the right side of the wall
14 | of the sister so so I don ' t want to repeat this because this is not exactly the same calculation which we have done before right so with this second its two pondary conditions we can get conclude that
15 | it will be equal to the pie over l and then that it will be equal to zero or so you can issue go back and the check this
16 | a result so what I want to say is that until now what we have been doing is identical to what we have been doing for the non depressed medium of of what I ' m to say is that the
17 | but the name mo is ateset by the boundary condition is determined by the boundary condition and it has actually so far nothing to do with the the disorders
18 | relation to maga is a function or so so in short boundary condition can give you the shape of thenormal note and we know that the first normal to second normal to get cetera et cetera
19 | essentially as going to be identical to the case of non dispersive medium to k so that as be the first thing which we learn the second thing we learn is they o is now
20 | what we see is that once the boundary condition is given then the in is set to be also given therefore since I have the dispersion relation omega as a functional key
21 | asjon the right omega is equal to omega books equal to two times squared to the one pros of square right therefore hence k n is given omega
22 | is also given so you can see that that ' s as so were the dispersion relation coming to pray the omega .
23 | bit different if you compare the disservice case and not dispersive case or so that is a to be over what I want to say the k in which is the shape of the normal mole doesn ' t depend
24 | on the dispersion relation on the other hand the speed of the installation the angurar frequency of mega depends on the dispersian relations which especially while we obtained it from
25 | if I start to protect omega and as the function of
26 | so in the case of non dispersal medium so what I am going to get is I shoulder discreet point along a straight line of tissue k one
27 | tofour etcetera there is sure there should be all sitting on a common straight line or if you do get look too
28 | time as a difference between a one k two and k three they are constant according to this formula the difference between k y and k two is pie over two or two and a three also over two
29 | girl is always a fixed number and the song omega essentially proportional to be therefore the spacing between omega one omega two omega
30 | there is also constant or in short omega to omica tree and omega for et veteran is always a multiple times of vae
31 | get from omaka one right according to a dise quarter and in the case of none dispersal medium or so what does that mean no means to go now if I have
32 | a very complicated initial condition of this really what I have an initial condition very complicated or I just need to wait if this is ensure no dispersive me
33 | that I just have to wait until the equal to two pay one omega one then this system would restored to its original shape to case a day to what I can learn from here
34 | because you make out two or make out three and any higher other as no more modes the angry frequency say the multiple times of what I get from or make out one on k
35 | on the other hand if I consider the situation of thispersive medium or you can see that now now the difference between
36 | on mega n is now the constant or so while you were prodigious that it would take much much longer for this system to go back to the original shape compared to her her
37 | no dispersal medium of case or not is whether you can as you see in in real life a experiment i can distort this is this equipment in this bounds as a system and is
38 | going to take forever any impossible to come back to the original shape because of the dispersiono on the other hand if I have it really highly idolized the situation if I have boys and bound and I just have
39 | wait until the equal to two of over or make it one then this system will go back to the original shape before I end the the lecture to day a
40 | I would like to discuss with you to interesting issue so many of you have seen water waves eh and firmant as you told us in
41 | lecture that water waves are they are really easily seen by everybody but it says some the worst possible example that ' s the bad news the worst possible example because it has all the possible
42 | here that waves can have that ' s the bad news the good news is that you are going to do that in your place so we were able to understand the behaviour of the water wavessaid
43 | the good news the second thing which I would like to talk about is face velocity or you can see that this or you can say to if you say that face velocity or harmonica waves beyond
44 | information right and on to how do I and so know that right so what does that mean to k so let ' s take this horrible example of what wave of us sotele the black line is as e
45 | beach and you there ' s a water wave on the ocean approaching the beach and you can see that you can have some kind of angle between the incertant water wave and the line of the beach of
46 | and what I can easily do is that I can now measure the shape of water water wave at at the edge of beach and the very
47 | see that is now the surface velocity which I observe there essentially faster than the speed of a propagation of the waterway because of this this
48 | inside the angle or I can easily make it very very fast I can make this speed ishab even faster than the speed of light right
49 | I can I can I can now decrease the the site to zero then you have you have a face velocity which is faster than the speed of light it go to infinity
50 | but does that mean anything is that doesnt mean anything because that don ' t really move with water from a specific point to another point infinitely fast
51 | therefore what I want to say is that or you can do whatever you want to make a fancy face velocity but that will not help you with sending things close to the speed of light or greater speed of
52 | or so as you can see from the example I can easily construct a simple example which you see that is that he is really not sending anything from one press to the other but you still have a readily fast of
53 | I like thank you very much everybody for the attention and the whole you enjoy that lecture and if you have any questions a estimate
54 |
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1 | Well let's let me actually tell you then about rather than the the proof I think I'll share the proof with kill because the proof that I want wanted to actually show you gives a proof of. The stocastic gradient is well behaved on both convex and non convex problems and the proof it wanted to show was for the non convex case because it applies to neural network so you may be curious about that proof and remarkably that proof is much simpler than the case of convex. Problems so let me just mention some very important points about sarcastic radiant so even though this method has been around since nineteen fifty one every deep learning toolkit has it and we are studying it in class there are still gapsbet. In what we can say theoretically and what happens in practice and I'll show you those gaps already and encourage you to think about those if you wish so let's look back at our problem and tell you about two variants so here are the two variants I'm going. Ask if any of you is familiar with these variants in some way or other so let's is just called it feasible here there are no constraints so you start with any random factor of your choice in deep network train. You have to work harder and then this is the iteration you run right option one and option to so option one says that was the idea we had in class random by pick some training data point use its futuristic gradient. Well what do we mean by random by pick the moment you use the word random you have to define what's the random news so the random news is uniform probability. And training data points that is one's randomness the other version is you pick a training data point without replacement so so with replacement means you know just uniformly at random each time. Draw a number from one through a use that sarcastic radiant move on which means the same point can easily be picked twice also and without replacement means if you've picked up point number three you're not going to pick it again until you've. Through the entire training data set those are two types of randomness which version would you use there is no right or wrong answer to this I'm just taking a pole. What would you use think that you're writing a programme for this and maybe think really pragmatically practically that's enough of an in which version would you use I'm just curious. Who would use one please raise hands on who and the the exclusion the complement thereof or I don't know maybe some people are undecided who would use too very few people to. Of how many of you use the neural network training tool kits like dense flu pit torch what not which versions are they using. Actually every person in the real world is using versions too are you really going to randomly go through your ram each time to pick random points they'll kill your big top performance like anything. What people do is take a data set use a pre shuffle operation and then just whoop stream through the data what does streaming through the data mean without replacement so all the toolkits actually are using the without replacement or. Even though intuitively the re as uniform random feels much nicer and that feeling is not ill founded because that's the only version we know how to analyze mathematically so even for this method everybody studies it there. And papers on it the version that is used in practice is not the version we know how to analyze it's a major open problem in the field of stocastic gradient to actually analyze the version that we use in practice this kind of. Rising but it's without replacement means non big probability theory and non side probability theory is not so easy that's the answer to it so the other version is this main batch idea which. Mentioned really early on is that rather than pick one random point I'll pick a minnie batch so I had a million points each time instead of picking one maybe I'll pick. Ten or hundred or thousand or what have you so this averages things averaging things reduces the variants so this is actually a good thing because the more quantities you average the less noise you have that. Kind of what happens in probability right so we pick a minnie batch and the sarcastic estimate now is that you know not just a single gradient but averaged over a minnie batch. So mini batch of size one is the pure vanilla s s d mini batch of size and is nothing other than pure gradient descent something in between is what people actually use and again the theoretical analysis only adds. If the minnie batch is picked with replacement not without replacement is one of the reasons actually a very important thing in theory you don't gain too much in terms of computational gains on convergence. Speed by using many matches but many batches are really crucial especially in your deep learning your style training because they allow you to do things in parallel each thread or each core or sub. Or your small chip or what have you depending on your hardware can be working with one sorcastic radiant so mini batches the larger the minnie batch the more things you can do in parallel so mini batches are greatlyexplot. By people to air give you a cheap version of paralelism and where does the parallelism happen you can think that each core customer a sarcastic gradient so the hard part is not. Adding these things up and making the update to x the hard part is computing a sarcastic gradient so if you can compute ten thousand of those in parallel because you have ten thousand cores great for you and that's the reason people love using many. Aches but a nice side remark here this is also this brings us close to the research edge of things again that well you'd love to use very large minnie badges so that you can fully max out on the parade. Is available to you right maybe you have a multi gap system if younger friends with envy dear yoga i only have like two gps but depends on how many ups you have you'd like to really mix it on parallelism so that you can really. Inch through big data sets as fast as possible but you know what happens with very large many batches sifyo have very large mini batches starcastic gradient starts looking more like. Full gradient descent which is also called back gradient descentthat's not a bad thing that's awesome for optimization but it is a weird conundrum that happens in training deep metal networks. This type of problem we wouldn't have for convex optimization but in deep nuralet because this really disturbing thing happens that if you use these very large many batches your method starts resembling radiant dissent that means it decreases noise. Much so that this region of confusion shrinks so much which all sounds good but it ends up being really bad for machine learning that's what I said that in machine learning you want some region of uncertainty and what it. Means actually is a lot of people have been working on this including at big companies that if you reduce that region of uncertainty too much you end up over fitting your neural network. And then it starts sucking in its test data unseen data performance so even though for parallelism programming optimization theory big mini batch is awesome. Tunately their price to be paid that it hurts your test error performance and they're all sorts of methods people are trying to cook up including a shrinking data. Only or changing natural network architecture and all sorts of ideas you can cook up your ideas for your favourite architecture how to make a large minnie batch without hurting the final performance but it's still somewhat of an open question on how to optimal. Etc which means how large your many bats should be so even though these ideas are simple you see that every simple idea leads to an entire sub area of s g d. Here are practical challenges people have various heristics for solving these challenges you can cook up your own but it's not that one idea always works so if you look at s go do what are the. In parts the moving parts to go the gradients stacastic gradients the step size the mini batch so how should it pick step sizes very non trivial problem different deep learning to. S may have different ways of automating that tuning but it's one of the painful things which many batch to use with replacement without replacement is already showed you but which many batch should it use how large that should be again not. Easy question to answer how to computer starcastic gradients does anybody know how starcastic gradients are computed for deep network training anybody know there is. Famous elgarithm called back propagation that back propagation elgrithm is used to compute a single starcastic gradient some people use the word back prop to mean asjiddy but what back prop really means is some. Some kind of algorism which computer for you a single sarcastic gradient and hence youknow this are tenser filled central these toolkiss they come up with all sorts of waste automate the computation of a gradient because really that's the main thing. And then other ideas like radiant clipping and momentum and veteran the bunch of other ideas and the theoretical challenges is mentioned to you already proving that it works that it actually solves what it set out to do unfortunately it was too slow. Couldn't show you the awesome five line proof that I have that s s works for several networks and theoretical analysis as i said is really lagging my proof also uses the wind. Cement and the without replacement version which is the one that is actually implemented so there's very little progress on that there is some progress there's a bunch of papers including from our colleagues that insight but it's quite. And the biggest question which most of the people in machine learning are currently excited about these days is stuff like why does s go work so well for neural networks are. This scrappy optimization method it very rapidly does some fitting data is large neuro network is large and then this neuro network ends up having great classification performance why is that happening that's called trying to explain. Build a theory of generalization why does so s go the trained natural network work better than neural networks train with more fancy optimization methods it's a mystery and most of the people who take interest in theoretical machine learning and statistics. That is one of the mysteries they are trying to understand so I think that's my story of a jiddy and this is the part we shape but its take the the intuition behind us gods much more important than this. So I think we can thank you close somewhere the roof or mondays exactly I think so that. They'll be great
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1 | The filthy filter that is obtained by mapping the butterworth filter to a digital filter through the biolineal transformation in fact falls off in frequency. Much more rapidly than the one that we got through impulse and variance a question is why no one thought that might come to mind as well impulse and variance as aliasing the biolinear transform. It doesn't have aliasing that must be a consequence of aliasing in fact that's not the reason aliasing as it turns out in this particular design is he was relatively minimal in the impulse and variant design. The reason has to do with this non linear mapping in the bilinear transformation from the continuous time frequency to the discreet time frequency keeps in mind that. Through that mapping as you start walking around the unit circle and moving up the jeomega axis as you move up the jeomega axis you have to move faster and faster and faster and faster and what's in. This time frequency and infinity is what you get to in the discreet time frequency by the time you get around to do so in fact what we're looking at is as as we look out along this. Currency axis is we're seeing higher and higher and higher frequencies in the continuous time filter by the time we get to go we should in fact be in the continuous. Time filter equivalently off to infinity which sounds like a pretty uncomfortable place to be to k now this was a fairly rapid trip. To a number of issues in particular some of the issues associated with the biological transformation and also this issue of how you pick this permanent capital it and how it might be. Met with a sampling frequency if you're doing discreet time processing of continuous time signals and we don't have time to explore some of those issues more fully in this lecture but I'd like. Conclude by making a couple of comments one comment is that the two techniques that we've talked about impulse and variance and the biolinear transformation are the two techniques that are principally used. And one thinks of mapping continuous time filters to discreet time filters for whatever application and the stress again that you may want to do that mapping whether or not the discreet time filter. Is eventually going to be used for processing continuous time signals now impulse and variance had the characteristic that it very nice characteristic that that. Corresponds to a linear mapping between the two frequency axes except for the issue of aliasing and that's a problem with it and in particular limits its usefulness to filter. Signs or for mapping continuous time filters that are banned limited on the other hand we have the bilinear transformation as a design procedure which totally avoids allowing. But has the disadvantage or difficulty that it represents a non linear mapping from the continuous time filter to the discreet time filter now this non linear distortion is perfectly accepted. Able if we're designing or attempting to design filters that have flat frequency characteristics it's not acceptable if for example we had a linear frequency characteristic that we wanted to map to a discreet time. Tear and end up with a linear frequency characteristic it won't come out to be linear because of this non linear mapping of the frequency axes now there are also a number of other design. Procedures which we won't go into for designing discreet time filters and among them are a variety of techniques including for example computerised designed procedures and I invite you. If you're interested and want to dig into that in more detail and more deeply to explore that topic by making reference to various of the books listed in the bibliography. In the text thank you
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1 | The following content is provided under a creative common license your support will help be ensuring the open course was continue to offer high quality educational resources for free to make a donation or to view additional materials from hundreds of the and. Courses visit the ensuring the open course are at o see w dot up i t dot e d u hallo everybody we'll come back to a on three and to day we are going to continue discussion of waves and. We would discuss a very interesting phenomenon to say which is dispersion and before dark we would discuss a bit just to give you some reminder about what we have learned so far so we discovered this equation. Which is shown here in the class and we also show you that it described three different kinds of distance which we included in the lecture the massive strings which the stringo camera. The assilate up and down in the right direction and also we discussed about sun waves me this is also discussed inaperious lecture and the sound waves can be described by. Wavy question and finally last time with this to her eleto magnetic waves is special kind of waves involving two oscellating for one essentially the electric for the other. Is magnetic is so that's kind of interesting because this is at slightly different from what we discussed before in the previous two cases this essentially a three dimensional a wave and also involving two. Different components and we also discuss the the solution the travelling wave solution of the electromagnetic waves as you you can see from here the electric fire is shown as the rat and the magnetic of. Joined the true and you can see that in case of travelling have they are in fact and that the magnetude reach maximum simultaneously for the electric electric fire and the magnetic fire and while in the case of standing waves. There's a face difference right so they don't reach maxima simultaneously in understanding electromagneti cases or so what are we going to discuss to say we would like to discuss. Strategy to send information are using waves or how do we as you send information are using waves so you can say to t you just do maybe I can just send the harmonic. Oscillation rise occupy to this harmonic installation I can well produce harmonical waves if they moving up and down and the espetilte with a constant. Great momentum and again a frequency and then maybe that's a way to send the information but but this kind of a wave is not in reality not superhealful because if you. The whole space with harmonic waves that you don't know when did you actually send the signal right because it's always asolating up and down so you don't know the starting kind of the signal is so so in reality this. Of simple harmonic oscilating troubling wave is not super helpful so what is it to helpful that's the question so what is actually helpful is to produce square pounds for example that is. Create square pews for example in this in this case I can create a square post here and in the next time interval I don't create square pews in the next time interval I don't do anything and I create another square plows. Yet veteran etcetera if you use this kind of strategy what we can do is to have some kind of receiver here to actually measure the magnitude of the. Magnitude of the powers of and then we can natural interpret this data so so this or this this wave is going to wear the positive x direction or going to the right hand side of the board and the receiver will be able to interpret. Of his data by pressing is racial under energy or under matrde output then I can can say oh now I'd receive a zero and in the next a signal and receiving is one and this one is zero. Zero and one and zero in this way I can use the scent information and it this information can be bariting as a functional tap so in short what will be useful is probably to use a narrow. Square is and now we be very helpful in transmitting on information or so and if we consider an ideal strong case or if I have. Deal string as we learned before as the behavior of this string is described by a a top wave equation and passes square. Pato the square and this is equal to be square part square six part the square ok and the this v is actually related to the that the speed of the progressing way. As we discuss before the progressing have solution on and that if i have this idealized string and obey the wave equation the simple version of wave equation then it will be able. To derive the dispersion relation right so I can now write down my harmonic aspoasing wave in the form of sign k x minus omega it if I have a harmonic escalating wave. Acting toward the positive ex direction at speed of v I can write it down in this functional form where k as a reminder is the wave number and the omega is a described. However the anger frequency and therefore if i parking this solution and of course I can have arbitrary ampitu if i parking this solution to this question then what is. Come to get as we said in the last few lectures there will be a fixed relation between a which is really a number and omega the anga frequency so the fixed relation is said to the omega. Over it will be equal to v which is actually the velocity in this wave equation and that from the previous discussion we know this set equal to a square dose of the one row. Little where it is great attention the constant tension which we apply on the string and the roll is essentially the masper one lends us a reminder of so what does this. What does this equation mean we call it this person relation as a time right but we actually didn't explain why do I do that right so we are going to learn why this is as you call this person relation or make out as. No k and in this case in this very simple fight idealize the case omega over it this ratio to k we know this is related to the propagation of. Speedablhe propagation of the harmonical wave or is equal to v be is a constant is independent of why this ratio is independent of k what does that mean that means. If I prepare waves or with different wave number or in the other words waves with different wave lands they are going to propargate at the. Speed right to the speed of the harmonic progressing wave is its independent of the waveletsok that says no very. Because in this case if I prepare the square house as we learned before the square pause essential to her a very complicated object the square pause is really very complicated you can do. Media decomposition as we did before and we knit infinite number of turns of harmonic oscillating waves with which we add them together so that I can produce a square. On and as I mention here if the dispersion relation is omeca of k is a consent era constantly that means all the whatever. Of wave lands pows which I should be added together and produce the square pews are going to be troubling at the same speed therefore as if I have this square. Rose in the beginning after some time to what I am going to get is that age this is the original position of the square pows and after some time at this square pow. Were moved by the tent in the horizontal direction and the shape of the pews is not going to be changed as picks no matter what kind of wave lands which produce the square plows. All the components in the square post are propagating at the same a speed be so this kind of system this kind of a system which as you am satisfied at this. Of a lies a dispersion relation is called on dispersive media right no dispersion was happening in this in this case in this highly idealized case of. We also know that in case of the string we are actually making it too idealized right so if we consider a more realistic string then. I have to consider an important phenomena which is or say important property of the string for example steepness is what do I mean by steepness foremp. If I can if I take a string from the piano a piano string or even if I don't apply any attention to the string if I bend this string you don't like it. It's going to bounce back and restore to its original shape right so that is what I call steepness it's a different contribution compared to the strong tension it is what we have been discs. Using so far that this resorting force essentially coming from the strong tension is or what will happen if it introduce additional a contribution from. Steepness of this steepness essentially not completely related to the strong tension and he also wants to restore the shape of the string or before we go to the matoding. I would like to take some vote to predict what is going to happen how many of you will predict that if I introduce include the stiffness of the string or get into my equation where. Speed of propagation increases how many of you think what is going to happen one to three for five so so some of you. Predict the speed of propagation were increased how many of you predict that the speed of propagation of the harmonic wave will stay the sand how many of you won. Of only one of how many of you have would predict that the speed of propagation would decrease. Or to all the other students don't have opinion or what to wait for the answer. All right so you can see that it is as younger completely obvious before we solve this question and we are going to solve it with a simple motto which we should slightly modify. To as the idealize case we idolize the wavy question or so now one semi realistic motor which I can introduce is to add a turn addition. Turn to the wafy question so I can now to write my wayquestion to include isifi defects to describe a realistic string and now different pato squarsa potatoes. Square this will be equal to be square part square six pattsquare and the additional term which I have put into this fan is minus as platform. Is parties x to four and this essentially the contribution which from the stipnesstifness of. So you can see that the the way question is now modified and what I could do in order to get the relation between omega and the key what I could do is that I can now start. With this a harmonic wave solution a public oquasing wave solution practices that into this equation this modify the equation and see what will happen or if the practice equation. Into that modified wavy question what I am going to get is the bowing capacity the laughing sigh you are going to get or make a square o k minus make a square and the the right hand side. Get a square minus a square anpras away k to the four in the right hand side or so of course I can. Cansel this a minus sign this will become press and this will become minus and we can see that the relation between omega and the k is now different or after it introduce. This term which is proportional to a life century describing how stiff this strain is ok of course now I can calculate or make it of k. As toll as we actually learned before right is the speed of the propagation of a harmonic as a harmonic wave of supasily if I calculate or make a rough find is. Then pasite while you get to v square due of one bus age square to k so if you look at this equation or the first reaction is. Know this omega and kraco is not a constant any more as a function to k what does that mean that means if is. Of progressing waves with different wave length or wave number kick it's going to be propagating at different speed or before we introduced. Ing into the armand into the motto the ratio omaca an k is a constant v independent of it now once you introduce this modo into the equation. And you begin thus a progressing wave solution to asecheck the dispersion relationship obtained from this equation you find that the progressing have be speedo. Gressing wave depends on how distorted this progressing wave is ok to let me compare this two situations. In this grade omega versus or so you see this dispersion relation grab pretty often in the in the past to say the y is i certainly the omega angular. Currency and the k is the weight number two pie one london in the original case in the case I have this idealized string obeyed. The valuation which I w introduce in the previous lectures if I protest to make out as a function k what I am getting is a straight line of a question. And not this the right of maybe I had made some mistake here. You should be as you should be also pros here right is so you have this omen so this to makasquar. And as us have this minus it here I sight so this should be minus and this should be on k let's go back to the original equation or so basically you. So if I probing this question to this equation right so besily I get minus a make square out of it and I get minus a square out of this and I'm going to get a pressure to the. Or out of this part square to the four side party x for eh or therefore this should be minus or maybe i made a miste think thank you much for for sporting that. A introduce is
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1 | Oh ya i'm sorry and now make my best day to say you what what did i do i or I must be drunk to say. Thank you very much any more mistake to a fortunately not right or very good is so so a let me to this again so now I can modify. Wave equation right originally the wave equation is part square side part the square equal to v square parts square side par x square and now it add additional turn with safe the. Proportional to the as a plate square page to the four side part x to the fort so if I had this turn into again and now the drag in the wafy question the progressing waves. Solution into the second equation then I will get this formula do so now everything should be correct and I have clear evidence that everybody is following so that is very good and then. I can now cancel all the minor signs in then this become press and now I can a o calculus we be the the spedofa propagation for this specific harmonic processing wave and the. Make you k will be equal to v square to one pros all k square i thank you very much for the contribution and now we see that clearly this ratio depends on k. I see if I pray this month of the previous cup which I stay optainte franc from here or then what I am going to get is something like this. The beginning is very close to the non disservice case and then it goes up because because of this contribution of it a positive number in my mymado. And the key essatalbe at time at the weight number or so what is going to happen is that nasty after you increase the steepness the slope of this curve is caught. Did as a functional kit or a what will I learn from this exercise is that if I inquise kick or if I have a very large key. Ok that means I have a very small land because it as so be too pie over land or so that means ain't looking at something really really still distorted like this. Or bosring tension and the stiffness wants to restore or restore the string back to name therefore what is happening is that. Are going to get additional restored in force therefore as well as only and calculate here if age is also positive then the velocity so. Creased with respect to what would be over or what we have to get before we we actually add this into the mat or so I think that'll make sense right because the stiffness also wants to restore them. The distortion therefore you have larger and larger at a restoring force therefore the speed of proportion of this harmonic wave will increase or so that's pretty nice. But what does that mean to our project back our project is to send information from one place to the other place right so what we just discuss be is that. We can as we send a square house and a large prop of a square pause can be decomposed into many many pieces many many harmonic waves or before. The square post works because all the waves with different wave lands and pokea up a pogea astheo moving at this constant speed is independent of thewave. Less now we are in trouble as you can see here that now the speed which is omegabag depends on the wave number or wavelets the. For different components which lady are needed to create a square house are going to be propagating at different speed you can say or come on this is a mathematics why I don't believe. And you know a square post is for square pause and tax mathematics has mans department but we can really see that in the experiment to it so that's take a look at this demonstration maybe. Didn't notice that before but we have seen this effect from her previous lectures a case of it can now quit as a square not not really square pass but as of some kind of pounds I can quit a. Some kind of pows like this ok and me as we learned before it when these pows pass through as open and it's going to be bounced aback so therefore I can have a limit of I can that. Show you this damn in a dimity to be set up at this house is going to be going back and forth because I have opened and ok as we discussed before or what is going to happen is that since we have a reality. Realistic assistance what is going to happen is that this post will become wider and wider right that's the prediction coming from a thisequation different component with. Any wave lands is going to be propagating at different speed therefore this house is going to become wider and we can see that our so damn quickly produce a pause and see what will happen to be. Originally essentially really sharp and you can see that really these of the posts become wider and wider and at the same point it disappear or if I have a beer. Seat what you are going to see is that it's going to be propagating a toward the same decision and the whiz of the pews usually going to be increasing as a functional time dusyou take a look. This again now this time you have a negative powers you sort of see very similar thing and also you can see that there sounds strange vibration as show did lag behind that the man pops it. That means different to do harmonic ways with different it lands really we prove propagating at different speed and for that to the. Strategy this effect is also prepared some demonstrations which waste her a passed on your calculation or so you can say that or now i am convinced if i can see me. Dispersion in the experiment how do I know this calculation is to match with experimental data right how about we really are put a wrong assimilation and see what happens or so what this are what. Is expand how to do is in the other beginning of you would do immigration like crazy or in order to get all the components due calculated land is going to propagate all those parts. Although stiff apposite to his different component through the medium so and that there would be two different colors one essentially blue which is the original shape the other one is actually the one this steeple. Is turned out or so now in the beginning it can set the safe value to a point or two and see what will happen and it will produce a triangular pause or you can see that now the program. Really working very hard to calculate all components of from one to one ninety nine and equal to one ninety nine and now this individual components are propagating through. The medium and you can see that originally the shape is like as a label as a shape a triangular shape and you can see that is a functional time the pals become wider and wider. Now of course I can increase the age two point or two and see what a happen front or to two point to and see what happen you should expect a much larger dispersion and you can. See that now in the beginning thing the immigration and you can see that this time because it wife says you larger therefore you see that this effect sees this broadeningis. Happening earlier and that become broader and broader and that they are a lot of stranger structures as you can see also from the teams are produced because different components are as source propagated at different speed. Of so of course we are on it so in this course we have an it as it waves right so let's take a look at the bit wave and see what I happen now you see that led. Very sharp to which I should require really a lot of effort to reproduce that and you can see that and in its kind of distorted as a bunk in line you can kind of still identify the peak. Butsasoulde not distressed and in the end of the simulation you cannot see even recognize that to the origin of that signal which you sent from your source of. So what I want to say is that and this effect this dispersion if that is really enemy which is usually very dangerous and now the is will prevent us from. Scenting a high quality signals eh of any questions about olostemos. And do so this because of a a the steepness a you ssetia symetric it or if you if you open this thing if you pende the string then share. Soon from the positive and negative part of if you have a ten to the if you have a part to the three part to the x to the three components then this is going to be a symetric and suggestion against your physics intuition and also. In the inside matoding you also match with your experimental data pretty well very good question and on the other hand without considering the stiepness of you can also go back to the. Infinite number coupled isolated case if you instead a take an example which you say so not super small the displacement of pocimation you take the. Until next time to taking your turn then you see that the partial to the three pass your ax to the three turn as you can so because is symmetric so I argued and that you will be able to also obtain this turn. When you have slightly larger a displaisement with respect to the equilibrium position to k so I hope they'll answer your question any other question yes. Otapo when you pass through the medium and monacas you change the speed of a a different a wit lunch. She temperately the very good question to is so very good that when we got two questions and we can see that if I now turn on the age make the if about you large then you can see that. Information is distorted on and this involves infinite number of country of terms and that in this case in this new time which I show here I have half value equal to point to therefore the. Effect of a disperse and his dispersion it should be much larger than what you showed before and then you can see that is another wave quickdip you come to something like a cousin like wave of o k so very. Good so a so you can say you be as you are making an example which I o m maybe its slavery interesting example but you involve too many turns you have infinite number of. Progressing waves in in this example of it's very difficult to understand how about we go back to a much simpler example to see what well we can do. Is that instead of you know going through infinite number of harmonic waves now we just consider two waves and to overlap these two waves together and see. Happen ok and I see what we can learn from it because the the ear you know that required number of a haminka was to describe such poses to complicate so you can say that you is now. Lets just consider two waves and see what we can learn from this and this is exactly what I am going to do now so from poll's lecture I hope he covered the pit phenomena supposedly what is it even phenomena. Bit phenomena happens when you overlap two air waves two harmonic waves they have pretty close her her her wave lands on but don another set of. And now if you add two waves together that's at what you are going to get you are going to get a something which is isolating really really fast which you say she called a carrier on and also you can. That the magnitude of the installation is certainly changing as the function of position and that we call it envelope or so that issue tepet phenomena which we learn from period lectures soon. Example I am going to add a two waves together so the first wave as described by soka is center by six one. The functiono x and d and he has the function of form as is the most and the sign of one x minus omega to omaca on the hook to. A progressing wave propagating toward the right hand side of the board the positive direction of the x axis in my coordinate system and he has a wave number no one and the age. Quency is make out what ok and I can also write down my second wave which I would like to overlap with the first wave it so disability having exactly the same ampit which is have and it. Described by a silent function and you have a white number a two x minus omega to the age frequency omica to work with this. Two equations we can calculate at the speed of provocation for the individual waves right so the first one I can calculate the speed of propagation in one will be equal to omega one. Everyone very similarly you can also calculate the speed of propagation for the second wave which homage to over two or so now what I am going to do is to. What the son of these two waves is I have the total of wind o as i sq to see one as six or so what I am going to do is to overlap these two waves and see what happens. For that I need this formula which is a sign a plus sign b and this will be equal to two times sign a press public. Of two and sign become cossign here cousin a minus public two or so if I used that formullero. Pasily what I am going to get is we have two times for a formula so we have to a ok sign one point two. X minus omega one plus omega to two supposedly the first turn is the machine function the second function and the content. A problem therefore you add these two together right divided by two thenbesidy this is star you as ten of the second turn is a consign turn you get a consign here. But now you calculate a minus b which is this this term minus often divided by two then bet e it what you get is a one minus a two divided by two minus x minus or make. One man coming at two or two or so that to say you see what would happen if you add these two a waves together or. Until now everything is exact and I would like to add additional conditions or additional assumptions when I discuss this solution or so how about. In order to produce the bit phenomena I need to make the
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1 | Lands very very similar between the two waves right so therefore what I am going to do is that I am going to assume me one is very close to go two. Is roughly k ok and I am got end because of this since I have a continuous function if k why is really close to key too that means no maga one is going to. Also very cause to omega too right so what I am going to get is omega one is going to be also very similar to omega too and I will call it omega or. So if I do this when I have very similar a one and key to what is going to happen what is going to happen is that no one minus a two will be. Rysmall data means a this very small k means large wave lands therefore this cosinten will become twelve. Because they say we are slowly bariting a empty as a function of position because a case very small case case malmeans land are large therefore them. Do is going to be having this modulation which is stay like an envelope he is the speed of this envelope the oscillation of this envelope is as to control by the of. Last look at the lap site a one pros a two over two it's kind of like the calculating the average of the first and second of the wave number of the first and second waves right so you will. Flat average it can be still very large therefore you have small life right compared to the difference therefore you see that that i should contribute to those little structures in. An indiscrepent called carrier yes tatas. So they can be different thought why so you are absolutely right that so you can you can produce some something like a carrier as even when line is not equal to key to this is just at every bit your right. But the then there on the other hand the difference may and my too will be also large therefore you it's not as easy as what we have been doing here to identify who is the. Ear and who is the envelope but you do you do get some kind of grade which is icillating really fast but the envelope is going to appear also icillating really fast that is harder to to see all the structure but. Your absolutely right yes very good question so now I have this set up I assume that they are very close to each other so now I can define face velocity finally. Will define what is I you the face of velocity the face of velocity i call it v but you can see that before I already have been using face velocity v up for the previous. Astions that in the case of non dispersal medium the face velocity is just a b p which is the velocity in the equation and in this case be up will be equal to your image of. As we discuss for law at the definition of this face velacity of k and I can now also define the govelocity of. Group velocity we say should the velocity of the envelope or i can calculate the velocity of the envelope right in the case of face velocity i and calculating. The velocity of the carrier on and taking a ratio of the average and the time the average is so close to k and omega therefore the face velocity v but would teach us the speed of the publication. Of the carrier which is a omega k i call it be up and in case of group velocity I call it be g b g is describing the speed of propagation of the envelope therefore. What I'm getting is omega one minus omega two or ten despite one minus k two post of and have an effect of one over two like whicha. Can sit run and when they are really so close to each other this is a sell roughly like the omega and the question so far. So we have derived two different kinds of speed one is act related to the face of quality which one is a one is actually called. Velocity is related to the speed of the carrier or the other one is cro velocity which essentially related to the speed of the envelope or so do me disguise you. Are interesting interesting examples and the s like what we can really learn from this in the first example I am walking on a non dispersive medium or if I have. Non dispersal median of k then paste what is going to get omega will be proportional to. K if the part omega versus k is a straight line or now if I have omega I choose the omega of the two omega was omega to. The two waves to be pretty equal to women do or I can now evaluate the v but the v but will be near the slope right of the. Of this point the slope of a line connecting the euro to that point right which say to the omega to be care so that is the definition of the face velocity get this slope. This is the slope of this this line essentially calledereated to the face velocity or I can also calculate the slope of a line cut to this point. But I should cut through his desert this curve and in this case I am also going to get a line overlapping with face velocity because in this case image over. Is the constant which is v therefore if no matter what you calculate if you calculate v p as a ratio of omega and the k for you calculate v g which is as the slow. The line cutting through that point you always get get as you be or therefore what we learn from here is that for a non disservice median v but will be equal to. G ok not means most of this a two curves post of the curve of the envelope describing the envelope and describing the carrier. Is going to be propagating at the same speed any questions so the whole thing is going to be moving at a constant speed for that I can not show you. Some example which is prepared a sun simulation which is prepared. Ok see so what he does is that it really with a second did is. Bidziro or so this is the case when I have a non dispersive medium or if I have a non dispersal medium what is going to happen is that boys that is a poster la carries. Which is the speed of the audio's little structure and the envelope is going to be propagating at the sent speed so you can see the wig is like a fixed pattern is propagating toward the right hand side and in the relative motion. Between the fine structure and the envelope I sat dero sopesi you have exactly the same pattern as a function of time or so now I am going to move from away from the non disservice medium. How about we discuss what will happen if we have considered the stiffness of the string and see what we get from there so if I brought omega. As a function of k o k and the consider advantage to be non zero is a positive value so if I have had to be a positive value on zero to k. In this case him going to get a curve like this on the slope is sentially a changing and because it's a curling down it's covering up because if you have a large. Then you will see that the a ratio of omega and k as to increase so that essentially the kind of curve which we would get if I set the omega of the first and second. A wag in the top of increase in this study to be omegadiro obesity what you going to get is that you k now i have this point here under cuff or if I. Calculate the face velocity the face of velocity how do I calculate that I can now connect zero and that point by a line of and I can now calculate. Love of this line and I can get the face velocity up ok on the other hand I can also calculate a the slope of a line cutting. Throw tangential to the the point of interest ok and that is going to give me a good velacity to k as you can see from here which slope is as your larger. Anybody no demand pointed out group velocity is larger right so in this case if I turn on a far greater than zero what is going to happen is that since the crop velocity is larger than. The face velocity that means if I go back to that picture of the envelope is going to be moving faster than the fine structure inside the envelope how about we take a five. Break on from here and we continue discussion after break faces a good time to take afreghto welcome back everybody so we will continue the discuss. One of the pit phenomena so what we have shown you is that a pace on those curves as we canneswit determining what will be the relative velocity of the day of the. What what would be the velocity of to the carrier which I say would be debated by am the up and the what would be the velocity of the envelope which I say slowly debated. By a lagruplosity of him ending in the in this case what to be parting here is that in this case because arfaisetaly greater than zero. Therefore this a cufisasoe a curling up therefore you have larger a grovelocity compared to the face velocity so what you would expect is that the empathy. Lot is going to be actually progressing at a speed higher than the speed of a time la carries or on the other hand if mangicode or i can. Construct some kind of a median which can be highest in which the situations are far smaller than deron what is going to happen so if it protest that if the protest. Action which as smaller than very so and the new the pro omega was the function of it what is going to happen just like this topacity you have something which is is receiving. Can to k so if I now again walk on some point of interest here to t you can see that theslo. Of the face velocity is now it should be and the slope of the the face velocity is now that should be larger than the slope which is usually a. Line cutting through the tangent to the the cuff which we are getting you the gruplasy so in the case of afas more than zero. Which is some strange amedium which I can create from whatever pasma or some reality a strange a kind of kind of material of interest if that happens then that means you were a group. City will be smaller than dug the faceelacety on and if you look at this point here you can see that this curve to the. A meximman here and if you truly are operating at this point what is going to happen what is going to happen is that if you calculate the group. City will bet about you you'll be torn what does that mean that means the envelope will not be moving along or but the time the carriers are still moving. Sindeed at this point you are gay going to get good volocity equal to zero ok and finally if you should. Going to a very large car value in this scenery as smaller than zero you see that even you can have face velocity public place. Positive because he says why a positive slope and about velocity he is negative why what does that mean any means you. Going to see a situation that the careers are progressing in a positive direction and the as time the envelope is going to be a. Progressing in the negative direction produce foquessing to the new lapping side of the sport so what does that mean that means this wave is doing. What Michael lesson is doing lies essentially twin eh so this essentially the kind of thing which could have happened that it looks like that. Are you are doing your going forward because all the air carriers are moving in a positive direction but the body are says going to earth. Negative direction or maybe I can also learn moon work at some point or so that's going back to the demonstration which I got started and somehow I got meet up and. So lets take a look at the detemo again so has look at all the different situations at once so in this case us we discussed before this essentially happening in the. Non dispersive situation that in this situation you have a straight line non dispersal median as we give you always the group velocity equal to a face velocity or so. Means the carrier and the as the envelope is going to be moving in the same direction at the same as a speed ok on the. Hands in this case we can actually have a situation that the the face velocity essentially faster than the group velocity do so what I mean is that usual situation here. Face velocity calculated from a line connecting from zero to that point you is actually having a larger slope compared to the tengentra line and you will see this situation so easy do you see that. Inside the envelope all those carriers are actually moving faster than the envelope now I can have a disservice medium where. Local velocity is sequel to there so what is going to happen is that really the envelope essentially not moving is not like like this eh but that the party is not moving right so you have so
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1 | Carries this in this in the structure essentially moving forward but the envelope essentially not moving. So finally the last situation is really interesting to time in this situation this essential is a heavy lacubelocity and. The group velocity is actually having different signs compared to the face velocity so you can see that that the whole structure of the envelope is constantly moving backward but that theater. Especially moving in the positive direction in this example or so this especially what we have learned from the fromtis. Bit phenomena and we have covered up the idea of face velocity and the group velocity is how about found system how do we understand when we have abounded system. How does that involve evolve as a functional time so if I have a system of two walls and the one string and of course I give you the density for deiny lands and. The tent strong tension and also the afa which is as we tell you about the steepness of the sister or again I can write down site to be. Song of order no more go from one to infinity a m sin k m x pas afm sin. Want apart and then what we can do is that we can first get the initial conditions of this system and. On the boundary conditions of this system then we must just follow exactly the same procedure to obtain all the unknown coefficients that we'll be able to evolve this system as a functional time as I have demonstrated you in the beginning. Lecture so in this case you can have two boundary conditions one really at x equal to zero and the other one is are at a equal to l o in those boundaries. We as he learned before because the end points are fixed on the wall therefore so often at the at the time it will be always. Equal to zero for the land is a pondary condition and the very similarity as we discussed before so l it will be equal to zero if you look at the right side of the wall. Of the sister so so I don't want to repeat this because this is not exactly the same calculation which we have done before right so with this second its two pondary conditions we can get conclude that. It will be equal to the pie over l and then that it will be equal to zero or so you can issue go back and the check this. A result so what I want to say is that until now what we have been doing is identical to what we have been doing for the non depressed medium of of what I'm to say is that the. But the name mo is ateset by the boundary condition is determined by the boundary condition and it has actually so far nothing to do with the the disorders. Relation to maga is a function or so so in short boundary condition can give you the shape of thenormal note and we know that the first normal to second normal to get cetera et cetera. Essentially as going to be identical to the case of non dispersive medium to k so that as be the first thing which we learn the second thing we learn is they o is now. What we see is that once the boundary condition is given then the in is set to be also given therefore since I have the dispersion relation omega as a functional key. Asjon the right omega is equal to omega books equal to two times squared to the one pros of square right therefore hence k n is given omega. Is also given so you can see that that's as so were the dispersion relation coming to pray the omega.. Bit different if you compare the disservice case and not dispersive case or so that is a to be over what I want to say the k in which is the shape of the normal mole doesn't depend. On the dispersion relation on the other hand the speed of the installation the angurar frequency of mega depends on the dispersian relations which especially while we obtained it from. If I start to protect omega and as the function of. So in the case of non dispersal medium so what I am going to get is I shoulder discreet point along a straight line of tissue k one. Tofour etcetera there is sure there should be all sitting on a common straight line or if you do get look too. Time as a difference between a one k two and k three they are constant according to this formula the difference between k y and k two is pie over two or two and a three also over two. Girl is always a fixed number and the song omega essentially proportional to be therefore the spacing between omega one omega two omega. There is also constant or in short omega to omica tree and omega for et veteran is always a multiple times of vae. Get from omaka one right according to a dise quarter and in the case of none dispersal medium or so what does that mean no means to go now if I have. A very complicated initial condition of this really what I have an initial condition very complicated or I just need to wait if this is ensure no dispersive me. That I just have to wait until the equal to two pay one omega one then this system would restored to its original shape to case a day to what I can learn from here. Because you make out two or make out three and any higher other as no more modes the angry frequency say the multiple times of what I get from or make out one on k. On the other hand if I consider the situation of thispersive medium or you can see that now now the difference between. On mega n is now the constant or so while you were prodigious that it would take much much longer for this system to go back to the original shape compared to her her. No dispersal medium of case or not is whether you can as you see in in real life a experiment i can distort this is this equipment in this bounds as a system and is. Going to take forever any impossible to come back to the original shape because of the dispersiono on the other hand if I have it really highly idolized the situation if I have boys and bound and I just have. Wait until the equal to two of over or make it one then this system will go back to the original shape before I end the the lecture to day a. I would like to discuss with you to interesting issue so many of you have seen water waves eh and firmant as you told us in. Lecture that water waves are they are really easily seen by everybody but it says some the worst possible example that's the bad news the worst possible example because it has all the possible. Here that waves can have that's the bad news the good news is that you are going to do that in your place so we were able to understand the behaviour of the water wavessaid. The good news the second thing which I would like to talk about is face velocity or you can see that this or you can say to if you say that face velocity or harmonica waves beyond. Information right and on to how do I and so know that right so what does that mean to k so let's take this horrible example of what wave of us sotele the black line is as e. Beach and you there's a water wave on the ocean approaching the beach and you can see that you can have some kind of angle between the incertant water wave and the line of the beach of. And what I can easily do is that I can now measure the shape of water water wave at at the edge of beach and the very. See that is now the surface velocity which I observe there essentially faster than the speed of a propagation of the waterway because of this this. Inside the angle or I can easily make it very very fast I can make this speed ishab even faster than the speed of light right. I can I can I can now decrease the the site to zero then you have you have a face velocity which is faster than the speed of light it go to infinity. But does that mean anything is that doesnt mean anything because that don't really move with water from a specific point to another point infinitely fast. Therefore what I want to say is that or you can do whatever you want to make a fancy face velocity but that will not help you with sending things close to the speed of light or greater speed of. Or so as you can see from the example I can easily construct a simple example which you see that is that he is really not sending anything from one press to the other but you still have a readily fast of. I like thank you very much everybody for the attention and the whole you enjoy that lecture and if you have any questions a estimate
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/examples/TEST_singlefile/base_v2clntxt_transcriptions/YAKE - all keys for batch Dec-15-2021_-01.csv:
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1 | ,key_phrase,YAKE_score,word_count,phrase_freq
2 | 0,war total war,2.000546622553602e-05,3,1
3 | 1,powers genuine peace,2.4015724821835567e-05,3,1
4 | 2,genuine world security,4.0237933852717345e-05,3,1
5 | 3,good human interest,4.818329732703819e-05,3,0
6 | 4,soviet union adopt,5.978434680881089e-05,3,1
7 | 5,attainable peace based,6.882406412741375e-05,3,1
8 | 6,interest pupil powers,7.291220323092778e-05,3,1
9 | 7,nations closest allies,7.322452954143902e-05,3,1
10 | 8,cold war remembering,7.938747864660162e-05,3,1
11 | 9,single nuclear weapon,9.891298232192464e-05,3,1
12 | 10,american university responded,9.95607190543842e-05,3,1
13 | 11,hurt enlightened hope,0.00011594589354461669,3,1
14 | 12,spiraling arms race,0.00012150223731880824,3,1
15 | 13,keysthose treaty obligations,0.00015761822455520174,3,1
16 | 14,high level discussions,0.0001872422094609626,3,1
17 | 15,uncontrolled unpredictable arm,0.00019771745422585382,3,1
18 | 16,explosive force delivered,0.00020213890185472578,3,1
19 | 17,force chairman krushar,0.00020213890185472578,3,1
20 | 18,day graduating professor,0.00021490244467588931,3,1
21 | 19,Methodist church founded,0.00023263934539483654,3,1
22 | 20,inhuman ice institutions,0.00025349892597037324,3,0
23 | 21,bishop john fletcher,0.000280389586398236,3,1
24 | 22,president woodro wisdom,0.000280389586398236,3,1
25 | 23,find communism profoundly,0.000280389586398236,3,1
26 | 24,recent authoritative service,0.0002871397828002857,3,1
27 |
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/examples/TEST_singlefile/console_prinout_basemodel.md:
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1 | # Console output of the script: base Wav2Vec2 model
2 |
3 | The source video for the below is ~27 minutes long, and took about 7.5 minutes to finish running on my machine.
4 |
5 | ## The following is the output of the script:
6 |
7 | peter@Shem-ryePowerStation MINGW64 ~/Dropbox/programming*projects/vid2cleantxt (user-friendly)
8 | $ python vid2cleantxt/transcribe.py --input-dir "example_JFK_speech\TEST_singlefile"
9 | data folder is set to `C:\Users\peter\.conda\envs\v2ct\lib\site-packages\neuspell\../data` script
10 | Loading models @ Dec-15-2021*-00-55-45 - may take a while...
11 | If RT seems excessive, try --verbose flag or checking logfile
12 |
13 | Found 1 video files in C:\Users\peter\Dropbox\programming*projects\vid2cleantxt\example_JFK_speech\TEST_singlefile
14 | Creating .wav audio clips: 100%|█| 109/109 [00:00<00:00, 2
15 | Creating .wav audio clips: 66%|▋| 72/109 [00:00<00:00, 26
16 | created audio chunks for wav2vec2 - Dec-15-2021*-00
17 | No GPU being used by this machine :(
18 |
19 | No GPU being used :/ 0%| | 0/109 [00:00=7.1.1
8 | neuspell>=1.0.0
9 | numpy
10 | packaging
11 | pandas>=1.3.0
12 | psutil>=5.9.2
13 | pydub>=0.24.1
14 | pysbd>=0.3.4
15 | requests
16 | setuptools>=58.1.0
17 | spacy>=3.0.0,<4.0.0
18 | symspellpy~=6.7.0
19 | torch>=1.8.2
20 | tqdm
21 | transformers>=4.23.0
22 | wordninja==2.0.0
23 | wrapt
24 | yake>=0.4.8
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/setup.py:
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1 | import glob
2 | import os
3 | import setuptools
4 | from pathlib import Path
5 |
6 |
7 | def get_package_description():
8 | """Returns a description of this package from the markdown files."""
9 | _readme = Path("README.md")
10 | _history = Path("HISTORY.md")
11 | if _readme.exists() and _history.exists():
12 | with open(_readme.resolve(), "r", encoding="utf-8", errors="ignore") as f:
13 | readme = f.read()
14 | else:
15 | readme = "README"
16 | if _history.exists():
17 | with open(_history.resolve(), "r", encoding="utf-8", errors="ignore") as f:
18 | history = f.read()
19 | else:
20 | history = "No history yet."
21 | return f"{readme}\n\n{history}"
22 |
23 |
24 | def get_scripts_from_bin():
25 | """Get all local scripts from bin so they are included in the package."""
26 | return glob.glob("bin/*")
27 |
28 |
29 | def get_requirements():
30 | """Returns all requirements for this package."""
31 | with open("requirements.txt", "r", encoding="utf-8") as f:
32 | requirements = f.readlines()
33 | return list(requirements)
34 |
35 |
36 | def scour_for_file(file_name: str):
37 | """
38 | scour_for_file - search every possible location for a file name. Load each line from that filename into a list.
39 | """
40 | contents = []
41 | for root, dirs, files in os.walk("."):
42 | if file_name in files:
43 | with open(os.path.join(root, file_name), "r") as f:
44 | contents = f.readlines()
45 | assert len(contents) > 0, f"Could not find {file_name} in any of the locations"
46 | file_contents = [l for l in contents if l.strip()]
47 | return file_contents
48 |
49 |
50 | try:
51 | with open("README.md", "r", encoding="utf-8") as fh:
52 | long_description = fh.read()
53 | except FileNotFoundError as e:
54 | print(f"could not read README.md: {e}")
55 | long_description = get_package_description()
56 |
57 |
58 | setuptools.setup(
59 | name="vid2cleantxt",
60 | author="Peter Szemraj, Jonathan Lehner",
61 | author_email="szemraj.dev@gmail.com",
62 | description="A command-line tool to easily transcribe speech-based video files into clean text. also in Colab.",
63 | long_description=long_description,
64 | long_description_content_type="text/markdown",
65 | url="https://github.com/pszemraj/vid2cleantxt",
66 | include_package_data=True,
67 | include_dirs=["bin"],
68 | # package_dir={"": "confectionary"},
69 | data_files=[("", ["LICENSE"]), ("", ["requirements.txt"]), ("", ["README.md"])],
70 | packages=setuptools.find_packages(),
71 | install_requires=scour_for_file("requirements.txt"),
72 | classifiers=[
73 | "Programming Language :: Python :: 3",
74 | "License :: OSI Approved :: Apache Software License",
75 | "Development Status :: 3 - Alpha",
76 | "Operating System :: OS Independent",
77 | "Natural Language :: English",
78 | "Topic :: Text Processing",
79 | ],
80 | scripts=get_scripts_from_bin(),
81 | python_requires=">=3.7",
82 | setuptools_git_versioning={
83 | "enabled": True,
84 | },
85 | setup_requires=["setuptools-git-versioning"],
86 | )
87 |
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/vid2cleantxt/__init__.py:
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1 | from .v2ct_utils import load_spacy_models
2 |
3 | load_spacy_models()
4 | from . import audio2text_functions
5 | from . import transcribe
6 | from . import v2ct_utils
7 |
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