├── .devcontainer
├── Dockerfile
├── devcontainer.json
└── noop.txt
├── .github
└── workflows
│ └── tests.yml
├── .gitignore
├── Makefile
├── README.md
├── _config.yml
├── book
├── Makefile
├── back.png
├── book.tex
├── diagram.tex
├── diagram2.tex
├── figs
│ ├── MP86F77F.pdf
│ ├── aliasing-3.eps
│ ├── aliasing-3.pdf
│ ├── aliasing1.eps
│ ├── aliasing1.pdf
│ ├── autocorr1.eps
│ ├── autocorr1.pdf
│ ├── autocorr2.eps
│ ├── autocorr2.pdf
│ ├── autocorr3.eps
│ ├── autocorr3.pdf
│ ├── autocorr4.eps
│ ├── autocorr4.pdf
│ ├── autocorr5.eps
│ ├── autocorr5.pdf
│ ├── autocorr6.eps
│ ├── autocorr6.pdf
│ ├── autocorr7.eps
│ ├── autocorr7.pdf
│ ├── autocorr8.eps
│ ├── autocorr8.pdf
│ ├── autocorr9.eps
│ ├── autocorr9.pdf
│ ├── brfss_weight_log.eps
│ ├── brfss_weight_log.pdf
│ ├── chirp1.eps
│ ├── chirp1.pdf
│ ├── chirp2.eps
│ ├── chirp2.pdf
│ ├── chirp3.eps
│ ├── chirp3.pdf
│ ├── convolution1.eps
│ ├── convolution1.pdf
│ ├── convolution10.eps
│ ├── convolution10.pdf
│ ├── convolution2.eps
│ ├── convolution2.pdf
│ ├── convolution4.eps
│ ├── convolution4.pdf
│ ├── convolution5.eps
│ ├── convolution5.pdf
│ ├── convolution6.eps
│ ├── convolution6.pdf
│ ├── convolution7.eps
│ ├── convolution7.pdf
│ ├── convolution8.eps
│ ├── convolution8.pdf
│ ├── convolution9.eps
│ ├── convolution9.pdf
│ ├── dct1.eps
│ ├── dct1.pdf
│ ├── dft1.eps
│ ├── dft1.pdf
│ ├── dft2.eps
│ ├── dft2.pdf
│ ├── dft3.eps
│ ├── dft3.pdf
│ ├── diagram.pdf
│ ├── diagram1.eps
│ ├── diagram1.pdf
│ ├── diagram2.eps
│ ├── diagram2.pdf
│ ├── diff_int1.eps
│ ├── diff_int1.pdf
│ ├── diff_int2.eps
│ ├── diff_int2.pdf
│ ├── diff_int3.eps
│ ├── diff_int3.pdf
│ ├── diff_int4.eps
│ ├── diff_int4.pdf
│ ├── diff_int5.eps
│ ├── diff_int5.pdf
│ ├── diff_int6.eps
│ ├── diff_int6.pdf
│ ├── diff_int7.eps
│ ├── diff_int7.pdf
│ ├── diff_int8.eps
│ ├── diff_int8.pdf
│ ├── diff_int9.eps
│ ├── diff_int9.pdf
│ ├── example1.eps
│ ├── example1.pdf
│ ├── example_cdf.eps
│ ├── example_cdf.pdf
│ ├── expo_cdf.eps
│ ├── expo_cdf.pdf
│ ├── interarrivals.eps
│ ├── interarrivals.pdf
│ ├── interarrivals_logy.eps
│ ├── interarrivals_logy.pdf
│ ├── noise-triple.eps
│ ├── noise-triple.pdf
│ ├── noise0.eps
│ ├── noise0.pdf
│ ├── noise1.eps
│ ├── noise1.pdf
│ ├── noise2.eps
│ ├── noise2.pdf
│ ├── noise3.eps
│ ├── noise3.pdf
│ ├── normal_cdf.eps
│ ├── normal_cdf.pdf
│ ├── nsfg_birthwgt_model.eps
│ ├── nsfg_birthwgt_model.pdf
│ ├── nsfg_birthwgt_normal.eps
│ ├── nsfg_birthwgt_normal.pdf
│ ├── pareto_cdf.eps
│ ├── pareto_cdf.pdf
│ ├── pinknoise0.eps
│ ├── pinknoise0.pdf
│ ├── pinknoise1.eps
│ ├── pinknoise1.pdf
│ ├── pinknoise2.eps
│ ├── pinknoise2.pdf
│ ├── pinknoise3.eps
│ ├── pinknoise3.pdf
│ ├── pinknoise4.eps
│ ├── pinknoise4.pdf
│ ├── pinknoise5.eps
│ ├── pinknoise5.pdf
│ ├── rednoise0.eps
│ ├── rednoise0.pdf
│ ├── rednoise1.eps
│ ├── rednoise1.pdf
│ ├── rednoise2.eps
│ ├── rednoise2.pdf
│ ├── rednoise3.eps
│ ├── rednoise3.pdf
│ ├── rednoise4.eps
│ ├── rednoise4.pdf
│ ├── rednoise5.eps
│ ├── rednoise5.pdf
│ ├── sampling1.eps
│ ├── sampling1.pdf
│ ├── sampling2.eps
│ ├── sampling2.pdf
│ ├── sampling3.eps
│ ├── sampling3.pdf
│ ├── sampling4.eps
│ ├── sampling4.pdf
│ ├── sampling5.eps
│ ├── sampling5.pdf
│ ├── sampling6.eps
│ ├── sampling6.pdf
│ ├── sampling7.eps
│ ├── sampling7.pdf
│ ├── sampling8.eps
│ ├── sampling8.pdf
│ ├── sampling9.eps
│ ├── sampling9.pdf
│ ├── sinusoid1.eps
│ ├── sinusoid1.pdf
│ ├── sounds1.eps
│ ├── sounds1.pdf
│ ├── sounds2.eps
│ ├── sounds2.pdf
│ ├── sounds3.eps
│ ├── sounds3.pdf
│ ├── sounds4.eps
│ ├── sounds4.pdf
│ ├── square-100-1.eps
│ ├── square-100-1.pdf
│ ├── square-100-2.eps
│ ├── square-100-2.pdf
│ ├── systems1.eps
│ ├── systems1.pdf
│ ├── systems2.eps
│ ├── systems2.pdf
│ ├── systems3.eps
│ ├── systems3.pdf
│ ├── systems4.eps
│ ├── systems4.pdf
│ ├── systems5.eps
│ ├── systems5.pdf
│ ├── systems6.eps
│ ├── systems6.pdf
│ ├── systems7.eps
│ ├── systems7.pdf
│ ├── systems8.eps
│ ├── systems8.pdf
│ ├── triangle-1100-1.eps
│ ├── triangle-1100-1.pdf
│ ├── triangle-1100-2.eps
│ ├── triangle-1100-2.pdf
│ ├── triangle-200-1.eps
│ ├── triangle-200-1.pdf
│ ├── triangle-200-2.eps
│ ├── triangle-200-2.pdf
│ ├── tuning1.eps
│ ├── tuning1.pdf
│ ├── uml_diagram1.eps
│ ├── uml_diagram1.pdf
│ ├── violin1.eps
│ ├── violin1.pdf
│ ├── violin2.eps
│ ├── violin2.pdf
│ ├── whitenoise0.eps
│ ├── whitenoise0.pdf
│ ├── whitenoise1.eps
│ ├── whitenoise1.pdf
│ ├── whitenoise2.eps
│ ├── whitenoise2.pdf
│ ├── whitenoise3.eps
│ ├── whitenoise3.pdf
│ ├── whitenoise4.eps
│ ├── whitenoise4.pdf
│ ├── whitenoise5.eps
│ ├── whitenoise5.pdf
│ ├── windowing1.eps
│ ├── windowing1.pdf
│ ├── windowing2.eps
│ ├── windowing2.pdf
│ ├── windowing3.eps
│ └── windowing3.pdf
├── footer.html
├── header.html
├── hevea.sty
├── htmlonly
├── latexonly
├── localdef.py
├── next.png
└── up.png
├── code
├── 100475__iluppai__saxophone-weep.wav
├── 105977__wcfl10__favorite-station.wav
├── 120994__thirsk__120-oboe.wav
├── 132736__ciccarelli__ocean-waves.wav
├── 170255__dublie__trumpet.wav
├── 180929__docquesting__crowd-noise.wav
├── 180960__kleeb__gunshot.wav
├── 181934__landub__applause2.wav
├── 18871__zippi1__sound-bell-440hz.wav
├── 253887__themusicalnomad__positive-beeps.wav
├── 263868__kevcio__amen-break-a-160-bpm.wav
├── 28042__bcjordan__voicedownbew.wav
├── 328878__tzurkan__guitar-phrase-tzu.wav
├── 72475__rockwehrmann__glissup02.wav
├── 87778__marcgascon7__vocals.wav
├── 92002__jcveliz__violin-origional.wav
├── BTC_USD_2013-10-01_2020-03-26-CoinDesk.csv
├── FB_2.csv
├── GardnerFractalMusic.pdf
├── Makefile
├── aliasing.py
├── autocorr.py
├── cacophony.ipynb
├── chap01.ipynb
├── chap01preview.ipynb
├── chap01soln.ipynb
├── chap02.ipynb
├── chap02soln.ipynb
├── chap03.ipynb
├── chap03soln.ipynb
├── chap04.ipynb
├── chap04soln.ipynb
├── chap05.ipynb
├── chap05soln.ipynb
├── chap06.ipynb
├── chap06soln.ipynb
├── chap07.ipynb
├── chap07soln.ipynb
├── chap08.ipynb
├── chap08soln.ipynb
├── chap09.ipynb
├── chap09soln.ipynb
├── chap10.ipynb
├── chap10preview.ipynb
├── chap10soln.ipynb
├── chap11.ipynb
├── chap11soln.ipynb
├── chirp.py
├── convolution.py
├── dct.py
├── dft.py
├── dft_example.ipynb
├── diff_int.py
├── fb_1.csv
├── fourth_wave.ipynb
├── fourth_wave.png
├── noise.py
├── phase.ipynb
├── sampling.py
├── saxophone.ipynb
├── scipy2015_demo.ipynb
├── sounds.py
├── stalbans_a_mono.wav
├── systems.py
├── thinkdsp.py
├── thinkdsp_test.py
├── thinkplot.py
├── thinkstats2.py
├── tos-redalert.wav
└── voss.ipynb
├── environment.yml
├── pyproject.toml
├── requirements-dev.txt
└── requirements.txt
/.devcontainer/Dockerfile:
--------------------------------------------------------------------------------
1 | FROM mcr.microsoft.com/devcontainers/miniconda
2 |
3 | # Copy environment.yml (if found) to a temp location so we update the environment. Also
4 | # copy "noop.txt" so the COPY instruction does not fail if no environment.yml exists.
5 | COPY environment.yml* .devcontainer/noop.txt /tmp/conda-tmp/
6 | RUN if [ -f "/tmp/conda-tmp/environment.yml" ]; then umask 0002 && /opt/conda/bin/conda env update -n base -f /tmp/conda-tmp/environment.yml; fi \
7 | && rm -rf /tmp/conda-tmp
8 |
9 | # Install python 3.6
10 | RUN conda install -y python=3.6 \
11 | && pip install --no-cache-dir pipx \
12 | && pipx reinstall-all
13 |
14 | # [Optional] Uncomment this section to install additional OS packages.
15 | # RUN apt-get update && export DEBIAN_FRONTEND=noninteractive \
16 | # && apt-get -y install --no-install-recommends <your-package-list-here>
17 |
--------------------------------------------------------------------------------
/.devcontainer/devcontainer.json:
--------------------------------------------------------------------------------
1 | // For format details, see https://aka.ms/devcontainer.json. For config options, see the
2 | // README at: https://github.com/devcontainers/templates/tree/main/src/miniconda
3 | {
4 | "name": "Miniconda (Python 3)",
5 | "build": {
6 | "context": "..",
7 | "dockerfile": "Dockerfile"
8 | }
9 |
10 | // Features to add to the dev container. More info: https://containers.dev/features.
11 | // "features": {},
12 |
13 | // Use 'forwardPorts' to make a list of ports inside the container available locally.
14 | // "forwardPorts": [],
15 |
16 | // Use 'postCreateCommand' to run commands after the container is created.
17 | // "postCreateCommand": "python --version",
18 |
19 | // Configure tool-specific properties.
20 | // "customizations": {},
21 |
22 | // Uncomment to connect as root instead. More info: https://aka.ms/dev-containers-non-root.
23 | // "remoteUser": "root"
24 | }
25 |
--------------------------------------------------------------------------------
/.devcontainer/noop.txt:
--------------------------------------------------------------------------------
1 | This file is copied into the container along with environment.yml* from the
2 | parent folder. This is done to prevent the Dockerfile COPY instruction from
3 | failing if no environment.yml is found.
--------------------------------------------------------------------------------
/.github/workflows/tests.yml:
--------------------------------------------------------------------------------
1 | name: tests
2 |
3 | on:
4 | push:
5 | branches: [master]
6 | pull_request:
7 | schedule:
8 | # https://cron.help/#0_0_1_*_*
9 | # min hour day-of-month month day-of-week
10 | - cron: "0 0 1 * *"
11 | workflow_dispatch:
12 |
13 | jobs:
14 | tests:
15 | name: Tests (${{ matrix.os }}, Python ${{ matrix.python-version }})
16 | runs-on: ${{ matrix.os }}
17 | strategy:
18 | matrix:
19 | os: [ubuntu-latest, macos-latest, windows-latest]
20 | python-version: ["3.10"]
21 |
22 | steps:
23 | - uses: actions/checkout@v2
24 |
25 | - name: Set up Python ${{ matrix.python-version }}
26 | uses: actions/setup-python@v2
27 | with:
28 | python-version: ${{ matrix.python-version }}
29 |
30 | - name: Install dependencies
31 | run: |
32 | python -m pip install --upgrade pip
33 | pip install -r requirements-dev.txt
34 |
35 | - name: Run tests
36 | run: |
37 | make tests
38 |
--------------------------------------------------------------------------------
/.gitignore:
--------------------------------------------------------------------------------
1 | .ipynb_checkpoints/
2 |
--------------------------------------------------------------------------------
/Makefile:
--------------------------------------------------------------------------------
1 | PROJECT_NAME = ThinkDSP
2 | PYTHON_VERSION = 3.10
3 | PYTHON_INTERPRETER = python
4 |
5 |
6 |
7 | ## Set up Python environment
8 | create_environment:
9 | conda create -y --name $(PROJECT_NAME) python=$(PYTHON_VERSION)
10 | @echo ">>> conda env created. Activate with:\nconda activate $(PROJECT_NAME)"
11 |
12 |
13 | ## Install dependencies
14 | requirements:
15 | $(PYTHON_INTERPRETER) -m pip install -U pip setuptools wheel
16 | $(PYTHON_INTERPRETER) -m pip install -r requirements-dev.txt
17 |
18 |
19 | tests:
20 | # looks like we can't test chapters with interactives
21 | cd code; pytest --nbmake chap0[2346789].ipynb
22 |
--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
1 | # ThinkDSP
2 |
3 | *Think DSP* is an introduction to Digital Signal Processing in Python.
4 |
5 | [Order *Think DSP* from Amazon.com](http://amzn.to/1naaUCN).
6 |
7 | [Download *Think DSP* in PDF](http://greenteapress.com/thinkdsp/thinkdsp.pdf).
8 |
9 | [Read *Think DSP* in HTML](http://greenteapress.com/thinkdsp/html/index.html).
10 |
11 | The premise of this book (and the other books in the Think X series) is that if you know how to program, you can use that skill to learn other things. I am writing this book because I think the conventional approach to digital signal processing is backward: most books (and the classes that use them) present the material bottom-up, starting with mathematical abstractions like phasors.
12 |
13 | With a programming-based approach, I can go top-down, which means I can present the most important ideas right away. By the end of the first chapter, you can decompose a sound into its harmonics, modify the harmonics, and generate new sounds.
14 |
15 | Think DSP is a Free Book. It is available under the [Creative Commons Attribution-NonCommercial 3.0 Unported License](https://creativecommons.org/licenses/by-nc/3.0/), which means that you are free to copy, distribute, and modify it, as long as you attribute the work and don't use it for commercial purposes.
16 |
17 | Here's a notebook that previews what you will see in Chapter 1:
18 |
19 | * [chap01preview.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap01preview.ipynb)
20 |
21 | And if you want to see where we are headed, here's a preview of Chapter 10:
22 |
23 | * [chap10preview.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap10preview.ipynb)
24 |
25 |
26 | ## Running the code
27 |
28 | Most of the code for this book is in Jupyter notebooks.
29 | If you are not familiar with Jupyter, you can run a tutorial by [clicking here](https://jupyter.org/try). Then select "Try Classic Notebook". It will open a notebook with instructions for getting started.
30 |
31 | To run the ThinkDSP code, you have several options:
32 |
33 | Option 1: Run the notebooks on Google Colab.
34 |
35 | Option 2: Run the notebooks on Binder.
36 |
37 | Option 3: Use Conda to install the libraries you need and run the notebooks on your computer.
38 |
39 | Option 4: Use poetry to install the libraries you need and run the notebooks on your computer.
40 |
41 | The following sections explain these options in detail.
42 |
43 | Note: I have heard from a few people who tried to run the code in Spyder. Apparently there were problems, so I don't recommend it.
44 |
45 | ### Option 1: Run on Colab
46 |
47 | I have recently updated most of the notebooks in this repository so they run on Colab.
48 |
49 | You can open any of them by clicking on the links below. If you want to modify and save any of them, you can use Colab to save a copy in a Google Drive or your own GitHub repo, or on your computer.
50 |
51 | * [chap01.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap01.ipynb)
52 | * [chap01soln.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap01soln.ipynb)
53 | * [chap02.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap02.ipynb)
54 | * [chap02soln.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap02soln.ipynb)
55 | * [chap03.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap03.ipynb)
56 | * [chap03soln.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap03soln.ipynb)
57 | * [chap04.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap04.ipynb)
58 | * [chap04soln.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap04soln.ipynb)
59 | * [chap05.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap05.ipynb)
60 | * [chap05soln.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap05soln.ipynb)
61 | * [chap06.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap06.ipynb)
62 | * [chap06soln.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap06soln.ipynb)
63 | * [chap07.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap07.ipynb)
64 | * [chap07soln.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap07soln.ipynb)
65 | * [chap08.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap08.ipynb)
66 | * [chap08soln.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap08soln.ipynb)
67 | * [chap09.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap09.ipynb)
68 | * [chap09soln.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap09soln.ipynb)
69 | * [chap10.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap10.ipynb)
70 | * [chap10soln.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap10soln.ipynb)
71 | * [chap11.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap11.ipynb)
72 | * [chap11soln.ipynb](https://colab.research.google.com/github/AllenDowney/ThinkDSP/blob/master/code/chap11soln.ipynb)
73 |
74 |
75 | ### Option 2: Run on Binder
76 |
77 | To run the code for this book on Binder, press this button:
78 |
79 | [](http://mybinder.org/repo/AllenDowney/ThinkDSP)
80 |
81 | It takes a minute or so to start up, but then you should see the Jupyter home page with a list of files. Click on `code` to open the folder with the notebooks, then click on one of the notebooks (with the .ipynb extension).
82 |
83 |
84 | ### Option 3: Install Python+Jupyter
85 |
86 | First, download the files from this repository. If you are a Git user, you can run
87 |
88 | ```
89 | git clone --depth 1 https://github.com/AllenDowney/ThinkDSP.git
90 | ```
91 |
92 | Otherwise you can [download this Zip file](https://github.com/AllenDowney/ThinkDSP/archive/master.zip) and unzip it.
93 | Either way, you should end up with a directory called `ThinkDSP`.
94 |
95 | Now, if you don't already have Jupyter, I highly recommend installing Anaconda, which is a Python distribution that contains everything you need to run the ThinkDSP code. It is easy to install on Windows, Mac, and Linux, and because it does a
96 | user-level install, it will not interfere with other Python installations.
97 |
98 | [Information about installing Anaconda is here](https://www.anaconda.com/distribution/).
99 |
100 | If you have the choice of Python 2 or 3, choose Python 3.
101 |
102 | There are two ways to get the packages you need for ThinkDSP. You can install them by hand or create a Conda environment.
103 |
104 | To install them by hand run
105 |
106 | ```
107 | conda install jupyter numpy scipy pandas matplotlib seaborn
108 | ```
109 |
110 | Or, to create a conda environment, run
111 |
112 | ```
113 | cd ThinkDSP
114 | conda env create -f environment.yml
115 | conda activate ThinkDSP
116 | ```
117 |
118 |
119 | ### Option 4: Use poetry to manage the project on your computer or notebook locally.
120 |
121 | First, download the files from this repository. If you are a Git user, you can run
122 |
123 | ```
124 | git clone --depth 1 https://github.com/AllenDowney/ThinkDSP.git
125 | ```
126 |
127 | Then, assuming you have [poetry](https://python-poetry.org) installed on your machine, run
128 |
129 | ```
130 | cd ThinkDSP
131 | poetry install
132 | ```
133 |
134 | to install the libraries you need in a virtual environment. To activate the environment, run
135 |
136 | ```
137 | poetry shell
138 | ```
139 |
140 | Then you can run Jupyter.
141 |
142 |
143 | ## Run Jupyter
144 |
145 | To start Jupyter, run:
146 |
147 | ```
148 | jupyter notebook
149 | ```
150 |
151 | Jupyter should launch your default browser or open a tab in an existing browser window.
152 | If not, the Jupyter server should print a URL you can use. For example, when I launch Jupyter, I get
153 |
154 | ```
155 | ~/ThinkComplexity2$ jupyter notebook
156 | [I 10:03:20.115 NotebookApp] Serving notebooks from local directory: /home/downey/ThinkDSP
157 | [I 10:03:20.115 NotebookApp] 0 active kernels
158 | [I 10:03:20.115 NotebookApp] The Jupyter Notebook is running at: http://localhost:8888/
159 | [I 10:03:20.115 NotebookApp] Use Control-C to stop this server and shut down all kernels (twice to skip confirmation).
160 | ```
161 |
162 | In this case, the URL is [http://localhost:8888](http://localhost:8888).
163 | When you start your server, you might get a different URL.
164 | Whatever it is, if you paste it into a browser, you should see a home page with a list of directories.
165 |
166 | Click on `code` to open the folder with the notebooks, then click on one of the notebooks (with the .ipynb extension).
167 |
168 | Select the cell with the import statements and press "Shift-Enter" to run the code in the cell.
169 | If it works and you get no error messages, **you are all set**.
170 |
171 | If you get error messages about missing packages, you can install the packages you need using your
172 | package manager, or install Anaconda.
173 |
174 | If you run into problems with these instructions, let me know and I will make corrections. Good luck!
175 |
176 |
177 |
178 | ## Freesound
179 |
180 | Special thanks to Freesound (http://freesound.org), which is the source of many of the
181 | sound samples I use in this book, and to the Freesound users who
182 | uploaded those sounds. I include some of their wave files in
183 | the GitHub repository for this book, using the original file
184 | names, so it should be easy to find their sources.
185 |
186 | Unfortunately, most Freesound users don't make their real names
187 | available, so I can only thank them using their user names. Samples
188 | used in this book were contributed by Freesound users: iluppai,
189 | wcfl10, thirsk, docquesting, kleeb, landup, zippi1, themusicalnomad,
190 | bcjordan, rockwehrmann, marchascon7, jcveliz. Thank you all!
191 |
192 | Here are links to the sources:
193 |
194 | http://www.freesound.org/people/iluppai/sounds/100475/
195 |
196 | http://www.freesound.org/people/wcfl10/sounds/105977/
197 |
198 | http://www.freesound.org/people/Thirsk/sounds/120994/
199 |
200 | http://www.freesound.org/people/ciccarelli/sounds/132736/
201 |
202 | http://www.freesound.org/people/Kleeb/sounds/180960/
203 |
204 | http://www.freesound.org/people/zippi1/sounds/18871/
205 |
206 | http://www.freesound.org/people/themusicalnomad/sounds/253887/
207 |
208 | http://www.freesound.org/people/bcjordan/sounds/28042/
209 |
210 | http://www.freesound.org/people/rockwehrmann/sounds/72475/
211 |
212 | http://www.freesound.org/people/marcgascon7/sounds/87778/
213 |
214 | http://www.freesound.org/people/jcveliz/sounds/92002/
215 |
--------------------------------------------------------------------------------
/_config.yml:
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1 | theme: jekyll-theme-minimal
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/book/Makefile:
--------------------------------------------------------------------------------
1 | # instructions
2 |
3 | # Currently the staging area for greenteapress.com is on bob at
4 | # /home/downey/web/greenteapress
5 |
6 | # To build and sync a new release:
7 | # make
8 | # make hevea
9 | # make distrib
10 |
11 | PDFFLAGS = -dCompatibilityLevel=1.4 -dPDFSETTINGS=/prepress \
12 | -dCompressPages=true -dUseFlateCompression=true \
13 | -dEmbedAllFonts=true -dSubsetFonts=true -dMaxSubsetPct=100
14 |
15 |
16 | all: book.tex
17 | pdflatex book
18 | makeindex book.idx
19 | pdflatex book
20 | mv book.pdf thinkdsp.pdf
21 | evince thinkdsp.pdf
22 |
23 | HEVEABUILDLOG=build.log
24 |
25 | hevea:
26 | sed 's/\(figs\/[^.]*\).\(pdf\|png\)/\1.eps/' book.tex > thinkdsp.tex
27 | rm -rf html
28 | mkdir html
29 | hevea macros.hva -O -e latexonly htmlonly thinkdsp 2>&1 | tee ${HEVEABUILDLOG}
30 | # the following greps are a kludge to prevent imagen from seeing
31 | # the definitions in latexonly, and to avoid headers on the images
32 | grep -v latexonly thinkdsp.image.tex > a; mv a thinkdsp.image.tex
33 | sed s/\\\\usepackage{fancyhdr}// < thinkdsp.image.tex > a; mv a thinkdsp.image.tex
34 | imagen -png thinkdsp
35 | hacha thinkdsp.html
36 | cp up.png next.png back.png html
37 | cp custom.css thinkdsp.css
38 | mv index.html thinkdsp.css thinkdsp*.html thinkdsp*.png *motif.gif html
39 |
40 | DEST = /home/downey/web/greenteapress/thinkdsp
41 |
42 | distrib:
43 | rm -rf dist
44 | mkdir dist
45 | rsync -a thinkdsp.pdf html dist
46 | rsync -a dist/* $(DEST)
47 | chmod -R o+r $(DEST)/*
48 | cd $(DEST)/..; sh back
49 |
50 | plastex:
51 | # Before running plastex, we need the current directory in PYTHONPATH
52 | # export PYTHONPATH=$PYTHONPATH:.
53 | rm -rf /home/downey/thinkdsp/trunk/book/.svn
54 | plastex --renderer=DocBook --theme=book --image-resolution=300 --filename=book.xml book.tex
55 | rm -rf /home/downey/thinkdsp/trunk/book/.svn
56 |
57 | xxe:
58 | xmlcopyeditor ~/ThinkDSP/book/book/book.xml &
59 |
60 | lint:
61 | xmllint -noout book/book.xml
62 |
63 | OREILLY = atlas
64 |
65 | oreilly:
66 | rsync -a book/ $(OREILLY)
67 | rsync -a figs/* $(OREILLY)/figs/
68 | cd $(OREILLY); git add .
69 | cd $(OREILLY); git commit -m "Automated check in."
70 | cd $(OREILLY); git push
71 |
72 | clean:
73 | rm -f *~ *.aux *.log *.dvi *.idx *.ilg *.ind *.toc
74 |
75 |
76 | pdfpextr = \
77 | gs -sDEVICE=pdfwrite -dNOPAUSE -dBATCH -dSAFER \
78 | -dFirstPage=$(1) \
79 | -dLastPage=$(2) \
80 | -sOutputFile=$(4) \
81 | $(3)
82 |
83 | split:
84 | $(call pdfpextr,5,7,thinkos.pdf,chap00.pdf)
85 | $(call pdfpextr,13,20,thinkos.pdf,chap01.pdf)
86 | $(call pdfpextr,21,26,thinkos.pdf,chap02.pdf)
87 | $(call pdfpextr,27,34,thinkos.pdf,chap03.pdf)
88 | $(call pdfpextr,35,42,thinkos.pdf,chap04.pdf)
89 | $(call pdfpextr,43,50,thinkos.pdf,chap05.pdf)
90 | $(call pdfpextr,51,56,thinkos.pdf,chap06.pdf)
91 | $(call pdfpextr,57,68,thinkos.pdf,chap07.pdf)
92 | $(call pdfpextr,69,74,thinkos.pdf,chap08.pdf)
93 | $(call pdfpextr,75,82,thinkos.pdf,chap09.pdf)
94 | $(call pdfpextr,83,94,thinkos.pdf,chap10.pdf)
95 | $(call pdfpextr,95,101,thinkos.pdf,chap11.pdf)
96 |
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/book/diagram.tex:
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1 | % LaTeX source for ``Think DSP: Digital Signal Processing for Programmers''
2 | % Copyright 2013 Allen B. Downey.
3 |
4 | % License: Creative Commons Attribution-NonCommercial 3.0 Unported License.
5 | % http://creativecommons.org/licenses/by-nc/3.0/
6 | %
7 |
8 | \[
9 | \begin{matrix}
10 | & {\large \mathtt{M}} &
11 | \begin{bmatrix}
12 | 0.6 \\
13 | 0.25 \\
14 | 0.1 \\
15 | 0.05 \\
16 | \end{bmatrix}
17 | = \mathtt{amps}
18 | \\
19 | \\
20 | \begin{matrix}
21 | &.& \\
22 | &.& \\
23 | &t_n& \\
24 | &.& \\
25 | &.& \\
26 | \end{matrix}
27 | &
28 | \begin{bmatrix}
29 | . & . & . & . \\
30 | . & . & . & . \\
31 | a & b & c & d \\
32 | . & . & . & . \\
33 | . & . & . & . \\
34 | \end{bmatrix}
35 | &
36 | \begin{bmatrix}
37 | &.& \\
38 | &.& \\
39 | &e& \\
40 | &.& \\
41 | &.& \\
42 | \end{bmatrix} = \mathtt{ys}
43 | \\
44 | \\
45 | &
46 | \begin{matrix}
47 | . & f_k & . & . \\
48 | \end{matrix}
49 | &
50 | \\
51 | \end{matrix}
52 | \]
53 |
54 |
55 |
56 |
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/book/diagram2.tex:
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1 | % LaTeX source for ``Think DSP: Digital Signal Processing for Programmers''
2 | % Copyright 2013 Allen B. Downey.
3 |
4 | % License: Creative Commons Attribution-NonCommercial 3.0 Unported License.
5 | % http://creativecommons.org/licenses/by-nc/3.0/
6 | %
7 |
8 | \[
9 | \begin{matrix}
10 | f[0] & [ & g[0] & g[1] & g[2] & ... & & & ] \\
11 | f[1] & [ & & g[0] & g[1] & g[2] & ... & & ] \\
12 | f[2] & [ & & & g[0] & g[1] & g[2] & ...& ] \\
13 | \noalign{\vskip 2mm}
14 | \hline
15 | \noalign{\vskip 2mm}
16 | & [ & & & h[2] & & & & ] \\
17 | \end{matrix}
18 | \]
19 |
20 |
21 |
22 |
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5 | %%Orientation: portrait
6 | %%BoundingBox: 18 180 594 612
7 | %%EndComments
8 | %%BeginProlog
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12 | /l { lineto } bind def
13 | /r { rlineto } bind def
14 | /c { curveto } bind def
15 | /cl { closepath } bind def
16 | /box {
17 | m
18 | 1 index 0 r
19 | 0 exch r
20 | neg 0 r
21 | cl
22 | } bind def
23 | /clipbox {
24 | box
25 | clip
26 | newpath
27 | } bind def
28 | %!PS-Adobe-3.0 Resource-Font
29 | %%Title: DejaVu Sans
30 | %%Copyright: Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. Copyright (c) 2006 by Tavmjong Bah. All Rights Reserved. DejaVu changes are in public domain
31 | %%Creator: Converted from TrueType by PPR
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33 | /_d{bind def}bind def
34 | /_m{moveto}_d
35 | /_l{lineto}_d
36 | /_cl{closepath eofill}_d
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1 | </div>
2 |
3 | <div id="sidebar">
4 |
5 | <p>
6 | <h4>Are you using one of our books in a class?</h4> We'd like to know
7 | about it. Please consider filling out <a href="http://spreadsheets.google.com/viewform?formkey=dC0tNUZkMjBEdXVoRGljNm9FRmlTMHc6MA" onClick="javascript: pageTracker._trackPageview('/outbound/survey');">this short survey</a>.
8 |
9 | <p>
10 | <br>
11 |
12 | <p>
13 | <a href="http://www.amazon.com/gp/product/1449370780/ref=as_li_qf_sp_asin_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=1449370780&linkCode=as2&tag=greenteapre01-20">Think Bayes</a><img src="http://ir-na.amazon-adsystem.com/e/ir?t=greenteapre01-20&l=as2&o=1&a=1449370780" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />
14 |
15 | <p>
16 | <a href="http://www.amazon.com/gp/product/1449370780/ref=as_li_qf_sp_asin_il?ie=UTF8&camp=1789&creative=9325&creativeASIN=1449370780&linkCode=as2&tag=greenteapre01-20"><img border="0" src="http://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=1449370780&Format=_SL160_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=greenteapre01-20" onerror="this.style.display='none'" /></a><img src="http://ir-na.amazon-adsystem.com/e/ir?t=greenteapre01-20&l=as2&o=1&a=1449370780" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />
17 |
18 | <p>
19 | <a href="http://www.amazon.com/gp/product/144933072X/ref=as_li_tf_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=144933072X&linkCode=as2&tag=greenteapre01-20">Think Python</a><img src="http://www.assoc-amazon.com/e/ir?t=greenteapre01-20&l=as2&o=1&a=144933072X" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />
20 |
21 | <p>
22 | <a href="http://www.amazon.com/gp/product/144933072X/ref=as_li_tf_il?ie=UTF8&camp=1789&creative=9325&creativeASIN=144933072X&linkCode=as2&tag=greenteapre01-20"><img border="0" src="http://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=144933072X&Format=_SL160_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=greenteapre01-20" onerror="this.style.display='none'" /></a><img src="http://www.assoc-amazon.com/e/ir?t=greenteapre01-20&l=as2&o=1&a=144933072X" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />
23 |
24 | <p>
25 | <a href="http://www.amazon.com/gp/product/1491907339/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=1491907339&linkCode=as2&tag=greenteapre01-20&linkId=O7WYM6H6YBYUFNWU">Think Stats</a><img src="http://ir-na.amazon-adsystem.com/e/ir?t=greenteapre01-20&l=as2&o=1&a=1491907339" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />
26 |
27 | <p>
28 | <a href="http://www.amazon.com/gp/product/1491907339/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=1491907339&linkCode=as2&tag=greenteapre01-20&linkId=JVSYKQHYSUIEYRHL"><img border="0" src="http://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=1491907339&Format=_SL160_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=greenteapre01-20" onerror="this.style.display='none'" /></a><img src="http://ir-na.amazon-adsystem.com/e/ir?t=greenteapre01-20&l=as2&o=1&a=1491907339" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />
29 |
30 | <p>
31 | <a href="http://www.amazon.com/gp/product/1449314635/ref=as_li_tf_tl?ie=UTF8&tag=greenteapre01-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=1449314635">Think Complexity</a><img src="http://www.assoc-amazon.com/e/ir?t=greenteapre01-20&l=as2&o=1&a=1449314635" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />
32 |
33 | <p>
34 | <a href="http://www.amazon.com/gp/product/1449314635/ref=as_li_tf_il?ie=UTF8&camp=1789&creative=9325&creativeASIN=1449314635&linkCode=as2&tag=greenteapre01-20"><img border="0" src="http://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=1449314635&Format=_SL160_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=greenteapre01-20" onerror="this.style.display='none'" /></a><img src="http://www.assoc-amazon.com/e/ir?t=greenteapre01-20&l=as2&o=1&a=1449314635" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />
35 |
36 |
37 | </div>
38 | </div>
39 | </body>
40 |
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/book/header.html:
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1 | <div id="main">
2 | <div id="colorbar"></div>
3 | <div id="content">
4 |
5 | <div class="notice">
6 | <p>This HTML version of <it>Think DSP</it> is provided for convenience, but it
7 | is not the best format for the book. In particular, some of the
8 | math symbols are not rendered correctly.
9 |
10 | <p style="margin-bottom:0">You might prefer to read
11 | the <a href="https://greenteapress.com/thinkdsp/thinkdsp.pdf">PDF version</a>, or
12 | you can buy a hard copy from
13 | <a href="http://www.amazon.com/gp/product/1491938455/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=1491938455&linkCode=as2&tag=greenteapre01-20&linkId=2JJH4SWCAVVYSQHO">Amazon</a>.
14 | </div>
15 |
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/book/hevea.sty:
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1 | % hevea : hevea.sty
2 | % This is a very basic style file for latex document to be processed
3 | % with hevea. It contains definitions of LaTeX environment which are
4 | % processed in a special way by the translator.
5 | % Mostly :
6 | % - latexonly, not processed by hevea, processed by latex.
7 | % - htmlonly , the reverse.
8 | % - rawhtml, to include raw HTML in hevea output.
9 | % - toimage, to send text to the image file.
10 | % The package also provides hevea logos, html related commands (ahref
11 | % etc.), void cutting and image commands.
12 | \NeedsTeXFormat{LaTeX2e}
13 | \ProvidesPackage{hevea}[2002/01/11]
14 | \RequirePackage{comment}
15 | \newif\ifhevea\heveafalse
16 | \@ifundefined{ifimagen}{\newif\ifimagen\imagenfalse}
17 | \makeatletter%
18 | \newcommand{\heveasmup}[2]{%
19 | \raise #1\hbox{$\m@th$%
20 | \csname S@\f@size\endcsname
21 | \fontsize\sf@size 0%
22 | \math@fontsfalse\selectfont
23 | #2%
24 | }}%
25 | \DeclareRobustCommand{\hevea}{H\kern-.15em\heveasmup{.2ex}{E}\kern-.15emV\kern-.15em\heveasmup{.2ex}{E}\kern-.15emA}%
26 | \DeclareRobustCommand{\hacha}{H\kern-.15em\heveasmup{.2ex}{A}\kern-.15emC\kern-.1em\heveasmup{.2ex}{H}\kern-.15emA}%
27 | \DeclareRobustCommand{\html}{\protect\heveasmup{0.ex}{HTML}}
28 | %%%%%%%%% Hyperlinks hevea style
29 | \newcommand{\ahref}[2]{{#2}}
30 | \newcommand{\ahrefloc}[2]{{#2}}
31 | \newcommand{\aname}[2]{{#2}}
32 | \newcommand{\ahrefurl}[1]{\texttt{#1}}
33 | \newcommand{\footahref}[2]{#2\footnote{\texttt{#1}}}
34 | \newcommand{\mailto}[1]{\texttt{#1}}
35 | \newcommand{\imgsrc}[2][]{}
36 | \newcommand{\home}[1]{\protect\raisebox{-.75ex}{\char126}#1}
37 | \AtBeginDocument
38 | {\@ifundefined{url}
39 | {%url package is not loaded
40 | \let\url\ahref\let\oneurl\ahrefurl\let\footurl\footahref}
41 | {}}
42 | %% Void cutting instructions
43 | \newcounter{cuttingdepth}
44 | \newcommand{\tocnumber}{}
45 | \newcommand{\notocnumber}{}
46 | \newcommand{\cuttingunit}{}
47 | \newcommand{\cutdef}[2][]{}
48 | \newcommand{\cuthere}[2]{}
49 | \newcommand{\cutend}{}
50 | \newcommand{\htmlhead}[1]{}
51 | \newcommand{\htmlfoot}[1]{}
52 | \newcommand{\htmlprefix}[1]{}
53 | \newenvironment{cutflow}[1]{}{}
54 | \newcommand{\cutname}[1]{}
55 | \newcommand{\toplinks}[3]{}
56 | \newcommand{\setlinkstext}[3]{}
57 | \newcommand{\flushdef}[1]{}
58 | \newcommand{\footnoteflush}[1]{}
59 | %%%% Html only
60 | \excludecomment{rawhtml}
61 | \newcommand{\rawhtmlinput}[1]{}
62 | \excludecomment{htmlonly}
63 | %%%% Latex only
64 | \newenvironment{latexonly}{}{}
65 | \newenvironment{verblatex}{}{}
66 | %%%% Image file stuff
67 | \def\toimage{\endgroup}
68 | \def\endtoimage{\begingroup\def\@currenvir{toimage}}
69 | \def\verbimage{\endgroup}
70 | \def\endverbimage{\begingroup\def\@currenvir{verbimage}}
71 | \newcommand{\imageflush}[1][]{}
72 | %%% Bgcolor definition
73 | \newsavebox{\@bgcolorbin}
74 | \newenvironment{bgcolor}[2][]
75 | {\newcommand{\@mycolor}{#2}\begin{lrbox}{\@bgcolorbin}\vbox\bgroup}
76 | {\egroup\end{lrbox}%
77 | \begin{flushleft}%
78 | \colorbox{\@mycolor}{\usebox{\@bgcolorbin}}%
79 | \end{flushleft}}
80 | %%% Style sheets macros, defined as no-ops
81 | \newcommand{\newstyle}[2]{}
82 | \newcommand{\addstyle}[1]{}
83 | \newcommand{\setenvclass}[2]{}
84 | \newcommand{\getenvclass}[1]{}
85 | \newcommand{\loadcssfile}[1]{}
86 | \newenvironment{divstyle}[1]{}{}
87 | \newenvironment{cellstyle}[2]{}{}
88 | \newif\ifexternalcss
89 | %%% Postlude
90 | \makeatother
91 |
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1 | % put commands here that should be used for the HTML
2 | % version of the book but not Postscript or PDF
3 |
4 | \newcommand{\beforefig}{}
5 | \newcommand{\afterfig}{}
6 |
7 | \newcommand{\beforeverb}{\blue \large}
8 | \newcommand{\afterverb}{\black \normalsize}
9 |
10 | \newcommand{\adjustpage}[1]{}
11 |
12 | \newcommand{\clearemptydoublepage}{}
13 | \newcommand{\blankpage}{}
14 |
15 | \newcommand{\spacing}{}
16 | \newcommand{\endspacing}{}
17 |
18 | \newcommand{\frontmatter}{}
19 | \newcommand{\mainmatter}{}
20 |
21 | \newcommand{\theoremstyle}[1]{}
22 | \newcommand{\newtheoremstyle}[1]{}
23 |
24 | \newcommand{\vfill}{}
25 |
26 | \htmlhead{\rawhtmlinput{header.html}}
27 |
28 | \htmlfoot{\rawhtmlinput{footer.html}}
--------------------------------------------------------------------------------
/book/latexonly:
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1 | \sloppy
2 | %\setlength{\topmargin}{-0.375in}
3 | %\setlength{\oddsidemargin}{0.0in}
4 | %\setlength{\evensidemargin}{0.0in}
5 |
6 | % Uncomment these to center on 8.5 x 11
7 | %\setlength{\topmargin}{0.625in}
8 | %\setlength{\oddsidemargin}{0.875in}
9 | %\setlength{\evensidemargin}{0.875in}
10 |
11 | %\setlength{\textheight}{7.2in}
12 |
13 | \setlength{\headsep}{3ex}
14 | \setlength{\parindent}{0.0in}
15 | \setlength{\parskip}{1.7ex plus 0.5ex minus 0.5ex}
16 | \renewcommand{\baselinestretch}{1.02}
17 |
18 | % see LaTeX Companion page 62
19 | \setlength{\topsep}{-0.0\parskip}
20 | \setlength{\partopsep}{-0.5\parskip}
21 | \setlength{\itemindent}{0.0in}
22 | \setlength{\listparindent}{0.0in}
23 |
24 | % see LaTeX Companion page 26
25 | % these are copied from /usr/local/teTeX/share/texmf/tex/latex/base/book.cls
26 | % all I changed is afterskip
27 |
28 | \makeatletter
29 |
30 | \renewcommand{\section}{\@startsection
31 | {section} {1} {0mm}%
32 | {-3.5ex \@plus -1ex \@minus -.2ex}%
33 | {0.7ex \@plus.2ex}%
34 | {\normalfont\Large\bfseries}}
35 | \renewcommand\subsection{\@startsection {subsection}{2}{0mm}%
36 | {-3.25ex\@plus -1ex \@minus -.2ex}%
37 | {0.3ex \@plus .2ex}%
38 | {\normalfont\large\bfseries}}
39 | \renewcommand\subsubsection{\@startsection {subsubsection}{3}{0mm}%
40 | {-3.25ex\@plus -1ex \@minus -.2ex}%
41 | {0.3ex \@plus .2ex}%
42 | {\normalfont\normalsize\bfseries}}
43 |
44 | % The following line adds a little extra space to the column
45 | % in which the Section numbers appear in the table of contents
46 | \renewcommand{\l@section}{\@dottedtocline{1}{1.5em}{3.0em}}
47 | \setcounter{tocdepth}{1}
48 |
49 | \makeatother
50 |
51 | \newcommand{\beforefig}{\vspace{1.3\parskip}}
52 | \newcommand{\afterfig}{\vspace{-0.2\parskip}}
53 |
54 | \newcommand{\beforeverb}{\vspace{0.6\parskip}}
55 | \newcommand{\afterverb}{\vspace{0.6\parskip}}
56 |
57 | \newcommand{\adjustpage}[1]{\enlargethispage{#1\baselineskip}}
58 |
59 |
60 | % Note: the following command seems to cause problems for Acroreader
61 | % on Windows, so for now I am overriding it.
62 | %\newcommand{\clearemptydoublepage}{
63 | % \newpage{\pagestyle{empty}\cleardoublepage}}
64 | \newcommand{\clearemptydoublepage}{\cleardoublepage}
65 |
66 | %\newcommand{\blankpage}{\pagestyle{empty}\vspace*{1in}\newpage}
67 | \newcommand{\blankpage}{\vspace*{1in}\newpage}
68 |
69 | % HEADERS
70 |
71 | \renewcommand{\chaptermark}[1]{\markboth{#1}{}}
72 | \renewcommand{\sectionmark}[1]{\markright{\thesection\ #1}{}}
73 |
74 | \lhead[\fancyplain{}{\bfseries\thepage}]%
75 | {\fancyplain{}{\bfseries\rightmark}}
76 | \rhead[\fancyplain{}{\bfseries\leftmark}]%
77 | {\fancyplain{}{\bfseries\thepage}}
78 | \cfoot{}
79 |
80 | \pagestyle{fancyplain}
81 |
82 |
83 | % turn off the rule under the header
84 | %\setlength{\headrulewidth}{0pt}
85 |
86 | % the following is a brute-force way to prevent the headers
87 | % from getting transformed into all-caps
88 | \renewcommand\MakeUppercase{}
89 |
90 | % Exercise environment
91 | \newtheoremstyle{myex}% name
92 | {9pt}% Space above
93 | {9pt}% Space below
94 | {}% Body font
95 | {}% Indent amount (empty = no indent, \parindent = para indent)
96 | {\bfseries}% Thm head font
97 | {}% Punctuation after thm head
98 | {0.5em}% Space after thm head: " " = normal interword space;
99 | % \newline = linebreak
100 | {}% Thm head spec (can be left empty, meaning `normal')
101 |
102 | \theoremstyle{myex}
103 |
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/book/localdef.py:
--------------------------------------------------------------------------------
1 | import plasTeX.Base as Base
2 |
3 | def idgen():
4 | """ Generate a unique ID """
5 | i = 1
6 | while 1:
7 | yield 'a%.10d' % i
8 | i += 1
9 |
10 | idgen = idgen()
11 |
12 | class Eqn(Base.Command):
13 | args = 'self'
14 |
15 | class Anchor(Base.Command):
16 | args = 'label:str'
17 | def invoke(self, tex):
18 | Base.Command.invoke(self, tex)
19 | self.ownerDocument.context.label(self.attributes['label'], self)
20 |
21 | class exercise(Base.Environment):
22 | counter = 'exercise'
23 |
24 | class index(Base.Command):
25 | args = 'termstring'
26 |
27 | def setEntry(self, s, seetype=0):
28 | # TYPE_NORMAL = 0
29 | # TYPE_SEE = 1
30 | # TYPE_SEEALSO = 2
31 | if type(s) != type(''):
32 | s = s.textContent
33 | if s.count('!'):
34 | priterm, secterm = s.split('!')
35 | if priterm.count('@'):
36 | prisort, primary = priterm.split('@')
37 | else:
38 | prisort, primary = None, priterm
39 | if secterm.count('@'):
40 | secsort, secondary = secterm.split('@')
41 | else:
42 | secsort, secondary = None, secterm
43 | elif s.count('@'):
44 | prisort, primary = s.split('@')
45 | secsort, secondary = None, None
46 | else:
47 | prisort, primary = None, s
48 | secsort, secondary = None, None
49 |
50 | # if secondary:
51 | # self.ownerDocument.userdata.setdefault('index', []).append(\
52 | # Base.IndexEntry([primary, secondary], self, [prisort, secsort], None, type=seetype))
53 | # else:
54 | # self.ownerDocument.userdata.setdefault('index', []).append(\
55 | # Base.IndexEntry([primary], self, [prisort], None, type=seetype))
56 | return prisort, primary, secsort, secondary
57 |
58 | def invoke(self, tex):
59 | Base.Command.invoke(self, tex)
60 | self.ownerDocument.context.label(idgen.next(), self)
61 | p0,p1,s0,s1 = self.setEntry(self.attributes['termstring'])
62 | if p0:
63 | self.prisort = '%s' % p0
64 | if p1:
65 | self.primary = '%s' % p1
66 | if s0:
67 | self.secsort = '%s' % s0
68 | if s1:
69 | self.secondary = '%s' % s1
70 |
71 | class scriptN(Base.Command):
72 | unicode = u'\U0001D4A9'
73 |
74 | class uxbar(Base.Command): pass
75 | class uybar(Base.Command): pass
76 | class unhat(Base.Command): pass
77 | class ule(Base.Command): pass
78 | class minus(Base.Command): pass
79 | class lowast(Base.Command): pass
80 | class Erdos(Base.Command): pass
81 |
82 |
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/code/Makefile:
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1 | DEST = /home/downey/web/greenteapress
2 |
3 | FIGS = \
4 | sounds1.pdf sounds1.eps \
5 | sounds2.pdf sounds2.eps \
6 | sounds3.pdf sounds3.eps \
7 | sounds4.pdf sounds4.eps \
8 | aliasing1.eps square-100-1.eps triangle-1100-1.eps triangle-200-1.eps \
9 | aliasing1.pdf square-100-1.pdf triangle-1100-1.pdf triangle-200-1.pdf \
10 | square-100-2.eps triangle-1100-2.eps triangle-200-2.eps \
11 | square-100-2.pdf triangle-1100-2.pdf triangle-200-2.pdf \
12 | chirp1.pdf chirp1.eps \
13 | chirp2.pdf chirp2.eps \
14 | chirp3.pdf chirp3.eps \
15 | windowing1.pdf windowing1.eps \
16 | windowing2.pdf windowing2.eps \
17 | windowing3.pdf windowing3.eps \
18 | whitenoise0.pdf whitenoise0.eps \
19 | whitenoise1.pdf whitenoise1.eps \
20 | whitenoise2.pdf whitenoise2.eps \
21 | rednoise0.pdf rednoise0.eps \
22 | rednoise3.pdf rednoise3.eps \
23 | pinknoise0.pdf pinknoise0.eps \
24 | noise-triple.pdf noise-triple.eps \
25 | noise1.pdf noise1.eps \
26 | autocorr1.pdf autocorr1.eps \
27 | autocorr2.pdf autocorr2.eps \
28 | autocorr3.pdf autocorr3.eps \
29 | autocorr4.pdf autocorr4.eps \
30 | autocorr5.pdf autocorr5.eps \
31 | autocorr6.pdf autocorr6.eps \
32 | autocorr7.pdf autocorr7.eps \
33 | autocorr8.pdf autocorr8.eps \
34 | autocorr9.pdf autocorr9.eps \
35 | dct1.pdf dct1.eps \
36 | dft1.pdf dft1.eps \
37 | dft2.pdf dft2.eps \
38 | dft3.pdf dft3.eps \
39 | convolution1.pdf convolution1.eps \
40 | convolution2.pdf convolution2.eps \
41 | convolution4.pdf convolution4.eps \
42 | convolution5.pdf convolution5.eps \
43 | convolution6.pdf convolution6.eps \
44 | convolution7.pdf convolution7.eps \
45 | convolution8.pdf convolution8.eps \
46 | convolution9.pdf convolution9.eps \
47 | diff_int1.pdf diff_int1.eps \
48 | diff_int2.pdf diff_int2.eps \
49 | diff_int3.pdf diff_int3.eps \
50 | diff_int4.pdf diff_int4.eps \
51 | diff_int5.pdf diff_int5.eps \
52 | diff_int6.pdf diff_int6.eps \
53 | diff_int7.pdf diff_int7.eps \
54 | diff_int8.pdf diff_int8.eps \
55 | diff_int9.pdf diff_int9.eps \
56 | systems1.pdf systems1.eps \
57 | systems6.pdf systems6.eps \
58 | systems7.pdf systems7.eps \
59 | systems8.pdf systems8.eps \
60 | sampling1.pdf sampling1.eps \
61 | sampling2.pdf sampling2.eps \
62 | sampling3.pdf sampling3.eps \
63 | sampling4.pdf sampling4.eps \
64 | sampling5.pdf sampling5.eps \
65 | sampling6.pdf sampling6.eps \
66 | sampling7.pdf sampling7.eps \
67 | sampling8.pdf sampling8.eps \
68 | sampling9.pdf sampling9.eps \
69 |
70 | FIGDEST = ../book/figs
71 |
72 | figs:
73 | rsync -a $(FIGS) $(FIGDEST)
74 |
75 |
76 | .PHONY: docs
77 |
78 | docs:
79 | pydoc -w thinkdsp
80 | rsync -a thinkdsp.html $(DEST)/thinkdsp
81 | #cd $(DEST); sh back
82 |
83 | $(DOCPY):
84 |
85 |
86 |
87 | NOTEBOOKS = \
88 | cacophony.ipynb \
89 | chap01.ipynb \
90 | chap01preview.ipynb \
91 | chap01soln.ipynb \
92 | chap02.ipynb \
93 | chap02soln.ipynb \
94 | chap03.ipynb \
95 | chap03soln.ipynb \
96 | chap04.ipynb \
97 | chap04soln.ipynb \
98 | chap05.ipynb \
99 | chap05soln.ipynb \
100 | chap06.ipynb \
101 | chap06soln.ipynb \
102 | chap07.ipynb \
103 | chap07soln.ipynb \
104 | chap08.ipynb \
105 | chap08soln.ipynb \
106 | chap09.ipynb \
107 | chap09soln.ipynb \
108 | chap10.ipynb \
109 | chap10preview.ipynb \
110 | chap10soln.ipynb \
111 | chap11.ipynb \
112 | chap11soln.ipynb \
113 | cumsum_example.ipynb \
114 | dft_example.ipynb \
115 | diff_int.ipynb \
116 | phase.ipynb \
117 | saxophone.ipynb \
118 | scipy2015_demo.ipynb \
119 | voss.ipynb \
120 |
121 | SCRIPTS = $(NOTEBOOKS:ipynb=py)
122 |
123 | make_scripts:
124 | for notebook in $(NOTEBOOKS) ; do \
125 | jupyter nbconvert --to script $notebook ; \
126 | done
127 |
128 | clean_scripts:
129 | # remove magic command and help functions so scripts
130 | # can run without interaction
131 | for script in $(SCRIPTS) ; do \
132 | grep -v "'matplotlib'" $script > temp ; \
133 | mv temp $script ; \
134 | sed -i s/get_ipython/\#get_ipython/ $script ; \
135 | sed -i s/\^help/\#help/ $script ; \
136 | sed -i s/\#\ In/from\ clf\ import\ clf\;clf\(\)\#\ In/ $script ; \
137 | done
138 |
139 |
140 | run_scripts:
141 | # remove magic command and help functions so scripts
142 | # can run without interaction
143 | for script in $(SCRIPTS) ; do \
144 | echo $script ; \
145 | ipython $script ; \
146 | done
147 |
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/code/aliasing.py:
--------------------------------------------------------------------------------
1 | """This file contains code used in "Think DSP",
2 | by Allen B. Downey, available from greenteapress.com
3 |
4 | Copyright 2013 Allen B. Downey
5 | License: GNU GPLv3 http://www.gnu.org/licenses/gpl.html
6 | """
7 |
8 | from __future__ import print_function, division
9 |
10 | import thinkdsp
11 | import thinkplot
12 |
13 | FORMATS = ['pdf', 'png']
14 |
15 | def triangle_example(freq):
16 | """Makes a figure showing a triangle wave.
17 |
18 | freq: frequency in Hz
19 | """
20 | framerate = 10000
21 | signal = thinkdsp.TriangleSignal(freq)
22 |
23 | duration = signal.period*3
24 | segment = signal.make_wave(duration, framerate=framerate)
25 | segment.plot()
26 | thinkplot.save(root='triangle-%d-1' % freq,
27 | xlabel='Time (s)',
28 | axis=[0, duration, -1.05, 1.05])
29 |
30 | wave = signal.make_wave(duration=0.5, framerate=framerate)
31 | spectrum = wave.make_spectrum()
32 |
33 | thinkplot.preplot(cols=2)
34 | spectrum.plot()
35 | thinkplot.config(xlabel='Frequency (Hz)',
36 | ylabel='Amplitude')
37 |
38 | thinkplot.subplot(2)
39 | spectrum.plot()
40 | thinkplot.config(ylim=[0, 500],
41 | xlabel='Frequency (Hz)')
42 |
43 | thinkplot.save(root='triangle-%d-2' % freq)
44 |
45 |
46 | def square_example(freq):
47 | """Makes a figure showing a square wave.
48 |
49 | freq: frequency in Hz
50 | """
51 | framerate = 10000
52 | signal = thinkdsp.SquareSignal(freq)
53 |
54 | duration = signal.period*3
55 | segment = signal.make_wave(duration, framerate=framerate)
56 | segment.plot()
57 | thinkplot.save(root='square-%d-1' % freq,
58 | xlabel='Time (s)',
59 | axis=[0, duration, -1.05, 1.05])
60 |
61 | wave = signal.make_wave(duration=0.5, framerate=framerate)
62 | spectrum = wave.make_spectrum()
63 | spectrum.plot()
64 | thinkplot.save(root='square-%d-2' % freq,
65 | xlabel='Frequency (Hz)',
66 | ylabel='Amplitude')
67 |
68 |
69 | def aliasing_example(offset=0.000003):
70 | """Makes a figure showing the effect of aliasing.
71 | """
72 | framerate = 10000
73 |
74 | def plot_segment(freq):
75 | signal = thinkdsp.CosSignal(freq)
76 | duration = signal.period*4
77 | thinkplot.Hlines(0, 0, duration, color='gray')
78 | segment = signal.make_wave(duration, framerate=framerate*10)
79 | segment.plot(linewidth=0.5, color='gray')
80 | segment = signal.make_wave(duration, framerate=framerate)
81 | segment.plot_vlines(label=freq, linewidth=4)
82 |
83 | thinkplot.preplot(rows=2)
84 | plot_segment(4500)
85 | thinkplot.config(axis=[-0.00002, 0.0007, -1.05, 1.05])
86 |
87 | thinkplot.subplot(2)
88 | plot_segment(5500)
89 | thinkplot.config(axis=[-0.00002, 0.0007, -1.05, 1.05])
90 |
91 | thinkplot.save(root='aliasing1',
92 | xlabel='Time (s)',
93 | formats=FORMATS)
94 |
95 |
96 | def main():
97 | triangle_example(freq=200)
98 | triangle_example(freq=1100)
99 | square_example(freq=100)
100 | aliasing_example()
101 |
102 |
103 | if __name__ == '__main__':
104 | main()
105 |
--------------------------------------------------------------------------------
/code/autocorr.py:
--------------------------------------------------------------------------------
1 | """This file contains code used in "Think DSP",
2 | by Allen B. Downey, available from greenteapress.com
3 |
4 | Copyright 2014 Allen B. Downey
5 | License: GNU GPLv3 http://www.gnu.org/licenses/gpl.html
6 | """
7 |
8 | from __future__ import print_function, division
9 |
10 | import thinkdsp
11 | import thinkplot
12 | import thinkstats2
13 | import numpy as np
14 |
15 | PI2 = 2 * np.pi
16 |
17 |
18 | def make_sine(offset):
19 | """Makes a 440 Hz sine wave with the given phase offset.
20 |
21 | offset: phase offset in radians
22 |
23 | returns: Wave objects
24 | """
25 | signal = thinkdsp.SinSignal(freq=440, offset=offset)
26 | wave = signal.make_wave(duration=0.5, framerate=10000)
27 | return wave
28 |
29 |
30 | def corrcoef(xs, ys):
31 | """Coefficient of correlation.
32 |
33 | ddof=0 indicates that we should normalize by N, not N-1.
34 |
35 | xs: sequence
36 | ys: sequence
37 |
38 | returns: float
39 | """
40 | return np.corrcoef(xs, ys)[0, 1]
41 |
42 |
43 | def plot_sines():
44 | """Makes figures showing correlation of sine waves with offsets.
45 | """
46 | wave1 = make_sine(0)
47 | wave2 = make_sine(offset=1)
48 |
49 | thinkplot.preplot(2)
50 | wave1.segment(duration=0.01).plot(label='wave1')
51 | wave2.segment(duration=0.01).plot(label='wave2')
52 |
53 | corr_matrix = np.corrcoef(wave1.ys, wave2.ys, ddof=0)
54 | print(corr_matrix)
55 |
56 | thinkplot.save(root='autocorr1',
57 | xlabel='Time (s)',
58 | ylim=[-1.05, 1.05])
59 |
60 | offsets = np.linspace(0, PI2, 101)
61 |
62 | corrs = []
63 | for offset in offsets:
64 | wave2 = make_sine(offset)
65 | corr = corrcoef(wave1.ys, wave2.ys)
66 | corrs.append(corr)
67 |
68 | thinkplot.plot(offsets, corrs)
69 | thinkplot.save(root='autocorr2',
70 | xlabel='Offset (radians)',
71 | ylabel='Correlation',
72 | xlim=[0, PI2],
73 | ylim=[-1.05, 1.05])
74 |
75 |
76 | def plot_shifted(wave, offset=0.002, start=0.2):
77 | """Plots two segments of a wave with different start times.
78 |
79 | wave: Wave
80 | offset: difference in start time (seconds)
81 | start: start time in seconds
82 | """
83 | thinkplot.preplot(num=2)
84 | segment1 = wave.segment(start=start, duration=0.01)
85 | segment1.plot(linewidth=2, alpha=0.8)
86 |
87 | segment2 = wave.segment(start=start-offset, duration=0.01)
88 | segment2.shift(offset)
89 | segment2.plot(linewidth=2, alpha=0.4)
90 |
91 | corr = segment1.corr(segment2)
92 | text = r'$\rho =$ %.2g' % corr
93 | thinkplot.text(start+0.0005, -0.8, text)
94 | thinkplot.config(xlabel='Time (s)', ylim=[-1.05, 1.05])
95 |
96 |
97 | def serial_corr(wave, lag=1):
98 | """Computes serial correlation with given lag.
99 |
100 | wave: Wave
101 | lag: integer, how much to shift the wave
102 |
103 | returns: float correlation coefficient
104 | """
105 | n = len(wave)
106 | y1 = wave.ys[lag:]
107 | y2 = wave.ys[:n-lag]
108 | corr = corrcoef(y1, y2)
109 | return corr
110 |
111 |
112 | def plot_serial_corr():
113 | """Makes a plot showing serial correlation for pink noise.
114 | """
115 | np.random.seed(19)
116 |
117 | betas = np.linspace(0, 2, 21)
118 | corrs = []
119 |
120 | for beta in betas:
121 | signal = thinkdsp.PinkNoise(beta=beta)
122 | wave = signal.make_wave(duration=1.0, framerate=11025)
123 | corr = serial_corr(wave)
124 | corrs.append(corr)
125 |
126 | thinkplot.plot(betas, corrs)
127 | thinkplot.config(xlabel=r'Pink noise parameter, $\beta#39;,
128 | ylabel='Serial correlation',
129 | ylim=[0, 1.05])
130 | thinkplot.save(root='autocorr3')
131 |
132 |
133 | def autocorr(wave):
134 | """Computes and plots the autocorrelation function.
135 |
136 | wave: Wave
137 | """
138 | lags = range(len(wave.ys)//2)
139 | corrs = [serial_corr(wave, lag) for lag in lags]
140 | return lags, corrs
141 |
142 |
143 | def plot_pink_autocorr(beta, label):
144 | """Makes a plot showing autocorrelation for pink noise.
145 |
146 | beta: parameter of pink noise
147 | label: string label for the plot
148 | """
149 | signal = thinkdsp.PinkNoise(beta=beta)
150 | wave = signal.make_wave(duration=1.0, framerate=11025)
151 | lags, corrs = autocorr(wave)
152 | thinkplot.plot(lags, corrs, label=label)
153 |
154 |
155 | def plot_autocorr():
156 | """Plots autocorrelation for pink noise with different parameters
157 | """
158 | np.random.seed(19)
159 | thinkplot.preplot(3)
160 |
161 | for beta in [1.7, 1.0, 0.3]:
162 | label = r'$\beta$ = %.1f' % beta
163 | plot_pink_autocorr(beta, label)
164 |
165 | thinkplot.config(xlabel='Lag',
166 | ylabel='Correlation',
167 | xlim=[-5, 1000],
168 | ylim=[-0.05, 1.05])
169 | thinkplot.save(root='autocorr4')
170 |
171 |
172 | def plot_singing_chirp():
173 | """Makes a spectrogram of the vocal chirp recording.
174 | """
175 | wave = thinkdsp.read_wave('28042__bcjordan__voicedownbew.wav')
176 | wave.normalize()
177 |
178 | duration = 0.01
179 | segment = wave.segment(start=0.2, duration=duration)
180 |
181 | # plot two copies of the wave with a shift
182 | plot_shifted(wave, start=0.2, offset=0.0023)
183 | thinkplot.save(root='autocorr7')
184 |
185 | # plot the autocorrelation function
186 | lags, corrs = autocorr(segment)
187 | thinkplot.plot(lags, corrs)
188 | thinkplot.config(xlabel='Lag (index)',
189 | ylabel='Correlation',
190 | ylim=[-1.05, 1.05],
191 | xlim=[0, 225])
192 | thinkplot.save(root='autocorr8')
193 |
194 | # plot the spectrogram
195 | gram = wave.make_spectrogram(seg_length=1024)
196 | gram.plot(high=4200)
197 |
198 | thinkplot.config(xlabel='Time (s)',
199 | ylabel='Frequency (Hz)',
200 | xlim=[0, 1.4],
201 | ylim=[0, 4200])
202 | thinkplot.save(root='autocorr5')
203 |
204 | # plot the spectrum of one segment
205 | spectrum = segment.make_spectrum()
206 | spectrum.plot(high=1000)
207 | thinkplot.config(xlabel='Frequency (Hz)', ylabel='Amplitude')
208 | thinkplot.save(root='autocorr6')
209 |
210 |
211 | def plot_correlate():
212 | """Plots the autocorrelation function computed by np.
213 | """
214 | wave = thinkdsp.read_wave('28042__bcjordan__voicedownbew.wav')
215 | wave.normalize()
216 | segment = wave.segment(start=0.2, duration=0.01)
217 |
218 | lags, corrs = autocorr(segment)
219 |
220 | N = len(segment)
221 | corrs2 = np.correlate(segment.ys, segment.ys, mode='same')
222 | lags = np.arange(-N//2, N//2)
223 | thinkplot.plot(lags, corrs2)
224 | thinkplot.config(xlabel='Lag',
225 | ylabel='Correlation',
226 | xlim=[-N//2, N//2])
227 | thinkplot.save(root='autocorr9')
228 |
229 |
230 | def main():
231 | plot_sines()
232 | plot_serial_corr()
233 | plot_autocorr()
234 | plot_singing_chirp()
235 | plot_correlate()
236 |
237 |
238 | if __name__ == '__main__':
239 | main()
240 |
--------------------------------------------------------------------------------
/code/chap07soln.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "## ThinkDSP\n",
8 | "\n",
9 | "This notebook contains solutions to exercises in Chapter 7: Discrete Fourier Transform\n",
10 | "\n",
11 | "Copyright 2015 Allen Downey\n",
12 | "\n",
13 | "License: [Creative Commons Attribution 4.0 International](http://creativecommons.org/licenses/by/4.0/)"
14 | ]
15 | },
16 | {
17 | "cell_type": "code",
18 | "execution_count": 1,
19 | "metadata": {},
20 | "outputs": [],
21 | "source": [
22 | "import numpy as np\n",
23 | "PI2 = 2 * np.pi"
24 | ]
25 | },
26 | {
27 | "cell_type": "markdown",
28 | "metadata": {},
29 | "source": [
30 | "## Exercise 1\n",
31 | "\n",
32 | "In this chapter, I showed how we can express the DFT and inverse DFT\n",
33 | "as matrix multiplications. These operations take time proportional to\n",
34 | "$N^2$, where $N$ is the length of the wave array. That is fast enough\n",
35 | "for many applications, but there is a faster\n",
36 | "algorithm, the Fast Fourier Transform (FFT), which takes time\n",
37 | "proportional to $N \\log N$.\n",
38 | "\n",
39 | "The key to the FFT is the Danielson-Lanczos lemma:\n",
40 | "\n",
41 | "$DFT(y)[n] = DFT(e)[n] + \\exp(-2 \\pi i n / N) DFT(o)[n]$\n",
42 | "\n",
43 | "Where $ DFT(y)[n]$ is the $n$th element of the DFT of $y$; $e$ is the even elements of $y$, and $o$ is the odd elements of $y$.\n",
44 | "\n",
45 | "This lemma suggests a recursive algorithm for the DFT:\n",
46 | "\n",
47 | "1. Given a wave array, $y$, split it into its even elements, $e$, and its odd elements, $o$.\n",
48 | "\n",
49 | "2. Compute the DFT of $e$ and $o$ by making recursive calls.\n",
50 | "\n",
51 | "3. Compute $DFT(y)$ for each value of $n$ using the Danielson-Lanczos lemma.\n",
52 | "\n",
53 | "For the base case of this recursion, you could wait until the length\n",
54 | "of $y$ is 1. In that case, $DFT(y) = y$. Or if the length of $y$\n",
55 | "is sufficiently small, you could compute its DFT by matrix multiplication,\n",
56 | "possibly using a precomputed matrix.\n",
57 | "\n",
58 | "Hint: I suggest you implement this algorithm incrementally by starting\n",
59 | "with a version that is not truly recursive. In Step 2, instead of\n",
60 | "making a recursive call, use `dft` or `np.fft.fft`. Get Step 3 working,\n",
61 | "and confirm that the results are consistent with the other\n",
62 | "implementations. Then add a base case and confirm that it works.\n",
63 | "Finally, replace Step 2 with recursive calls.\n",
64 | "\n",
65 | "One more hint: Remember that the DFT is periodic; you might find `np.tile` useful.\n",
66 | "\n",
67 | "You can read more about the FFT at https://en.wikipedia.org/wiki/Fast_Fourier_transform."
68 | ]
69 | },
70 | {
71 | "cell_type": "markdown",
72 | "metadata": {},
73 | "source": [
74 | "As the test case, I'll start with a small real signal and compute its FFT:"
75 | ]
76 | },
77 | {
78 | "cell_type": "code",
79 | "execution_count": 2,
80 | "metadata": {
81 | "jupyter": {
82 | "outputs_hidden": false
83 | }
84 | },
85 | "outputs": [
86 | {
87 | "name": "stdout",
88 | "output_type": "stream",
89 | "text": [
90 | "[ 0.2+0.j -1.2-0.2j 0.2+0.j -1.2+0.2j]\n"
91 | ]
92 | }
93 | ],
94 | "source": [
95 | "ys = [-0.5, 0.1, 0.7, -0.1]\n",
96 | "hs = np.fft.fft(ys)\n",
97 | "print(hs)"
98 | ]
99 | },
100 | {
101 | "cell_type": "markdown",
102 | "metadata": {},
103 | "source": [
104 | "Here's my implementation of DFT from the book:"
105 | ]
106 | },
107 | {
108 | "cell_type": "code",
109 | "execution_count": 3,
110 | "metadata": {
111 | "jupyter": {
112 | "outputs_hidden": false
113 | }
114 | },
115 | "outputs": [],
116 | "source": [
117 | "def dft(ys):\n",
118 | " N = len(ys)\n",
119 | " ts = np.arange(N) / N\n",
120 | " freqs = np.arange(N)\n",
121 | " args = np.outer(ts, freqs)\n",
122 | " M = np.exp(1j * PI2 * args)\n",
123 | " amps = M.conj().transpose().dot(ys)\n",
124 | " return amps"
125 | ]
126 | },
127 | {
128 | "cell_type": "markdown",
129 | "metadata": {},
130 | "source": [
131 | "We can confirm that this implementation gets the same result."
132 | ]
133 | },
134 | {
135 | "cell_type": "code",
136 | "execution_count": 4,
137 | "metadata": {
138 | "jupyter": {
139 | "outputs_hidden": false
140 | }
141 | },
142 | "outputs": [
143 | {
144 | "data": {
145 | "text/plain": [
146 | "5.864775846765962e-16"
147 | ]
148 | },
149 | "execution_count": 4,
150 | "metadata": {},
151 | "output_type": "execute_result"
152 | }
153 | ],
154 | "source": [
155 | "hs2 = dft(ys)\n",
156 | "np.sum(np.abs(hs - hs2))"
157 | ]
158 | },
159 | {
160 | "cell_type": "markdown",
161 | "metadata": {},
162 | "source": [
163 | "As a step toward making a recursive FFT, I'll start with a version that splits the input array and uses np.fft.fft to compute the FFT of the halves."
164 | ]
165 | },
166 | {
167 | "cell_type": "code",
168 | "execution_count": 5,
169 | "metadata": {
170 | "jupyter": {
171 | "outputs_hidden": false
172 | }
173 | },
174 | "outputs": [],
175 | "source": [
176 | "def fft_norec(ys):\n",
177 | " N = len(ys)\n",
178 | " He = np.fft.fft(ys[::2])\n",
179 | " Ho = np.fft.fft(ys[1::2])\n",
180 | " \n",
181 | " ns = np.arange(N)\n",
182 | " W = np.exp(-1j * PI2 * ns / N)\n",
183 | " \n",
184 | " return np.tile(He, 2) + W * np.tile(Ho, 2)"
185 | ]
186 | },
187 | {
188 | "cell_type": "markdown",
189 | "metadata": {},
190 | "source": [
191 | "And we get the same results:"
192 | ]
193 | },
194 | {
195 | "cell_type": "code",
196 | "execution_count": 6,
197 | "metadata": {
198 | "jupyter": {
199 | "outputs_hidden": false
200 | }
201 | },
202 | "outputs": [
203 | {
204 | "data": {
205 | "text/plain": [
206 | "0.0"
207 | ]
208 | },
209 | "execution_count": 6,
210 | "metadata": {},
211 | "output_type": "execute_result"
212 | }
213 | ],
214 | "source": [
215 | "hs3 = fft_norec(ys)\n",
216 | "np.sum(np.abs(hs - hs3))"
217 | ]
218 | },
219 | {
220 | "cell_type": "markdown",
221 | "metadata": {},
222 | "source": [
223 | "Finally, we can replace `np.fft.fft` with recursive calls, and add a base case:"
224 | ]
225 | },
226 | {
227 | "cell_type": "code",
228 | "execution_count": 7,
229 | "metadata": {
230 | "jupyter": {
231 | "outputs_hidden": false
232 | }
233 | },
234 | "outputs": [],
235 | "source": [
236 | "def fft(ys):\n",
237 | " N = len(ys)\n",
238 | " if N == 1:\n",
239 | " return ys\n",
240 | " \n",
241 | " He = fft(ys[::2])\n",
242 | " Ho = fft(ys[1::2])\n",
243 | " \n",
244 | " ns = np.arange(N)\n",
245 | " W = np.exp(-1j * PI2 * ns / N)\n",
246 | " \n",
247 | " return np.tile(He, 2) + W * np.tile(Ho, 2)"
248 | ]
249 | },
250 | {
251 | "cell_type": "markdown",
252 | "metadata": {},
253 | "source": [
254 | "And we get the same results:"
255 | ]
256 | },
257 | {
258 | "cell_type": "code",
259 | "execution_count": 8,
260 | "metadata": {
261 | "jupyter": {
262 | "outputs_hidden": false
263 | }
264 | },
265 | "outputs": [
266 | {
267 | "data": {
268 | "text/plain": [
269 | "1.6653345369377348e-16"
270 | ]
271 | },
272 | "execution_count": 8,
273 | "metadata": {},
274 | "output_type": "execute_result"
275 | }
276 | ],
277 | "source": [
278 | "hs4 = fft(ys)\n",
279 | "np.sum(np.abs(hs - hs4))"
280 | ]
281 | },
282 | {
283 | "cell_type": "markdown",
284 | "metadata": {},
285 | "source": [
286 | "This implementation of FFT takes time proportional to $n \\log n$. It also takes space proportional to $n \\log n$, and it wastes some time making and copying arrays. It can be improved to run \"in place\"; in that case, it requires no additional space, and spends less time on overhead."
287 | ]
288 | },
289 | {
290 | "cell_type": "code",
291 | "execution_count": null,
292 | "metadata": {
293 | "collapsed": true,
294 | "jupyter": {
295 | "outputs_hidden": true
296 | }
297 | },
298 | "outputs": [],
299 | "source": []
300 | }
301 | ],
302 | "metadata": {
303 | "kernelspec": {
304 | "display_name": "Python 3",
305 | "language": "python",
306 | "name": "python3"
307 | },
308 | "language_info": {
309 | "codemirror_mode": {
310 | "name": "ipython",
311 | "version": 3
312 | },
313 | "file_extension": ".py",
314 | "mimetype": "text/x-python",
315 | "name": "python",
316 | "nbconvert_exporter": "python",
317 | "pygments_lexer": "ipython3",
318 | "version": "3.8.5"
319 | }
320 | },
321 | "nbformat": 4,
322 | "nbformat_minor": 4
323 | }
324 |
--------------------------------------------------------------------------------
/code/chirp.py:
--------------------------------------------------------------------------------
1 | """This file contains code used in "Think DSP",
2 | by Allen B. Downey, available from greenteapress.com
3 |
4 | Copyright 2015 Allen B. Downey
5 | License: GNU GPLv3 http://www.gnu.org/licenses/gpl.html
6 | """
7 |
8 | from __future__ import print_function, division
9 |
10 | import math
11 | import numpy as np
12 |
13 | import thinkdsp
14 | import thinkplot
15 |
16 | import matplotlib.pyplot as pyplot
17 |
18 | import warnings
19 | warnings.filterwarnings('ignore')
20 |
21 | PI2 = np.pi * 2
22 |
23 |
24 | def linear_chirp_evaluate(ts, low=440, high=880, amp=1.0):
25 | """Computes the waveform of a linear chirp and prints intermediate values.
26 |
27 | low: starting frequency
28 | high: ending frequency
29 | amp: amplitude
30 | """
31 | print('ts', ts)
32 |
33 | freqs = np.linspace(low, high, len(ts)-1)
34 | print('freqs', freqs)
35 |
36 | dts = np.diff(ts)
37 | print('dts', dts)
38 |
39 | dphis = np.insert(PI2 * freqs * dts, 0, 0)
40 | print('dphis', dphis)
41 |
42 | phases = np.cumsum(dphis)
43 | print('phases', phases)
44 |
45 | ys = amp * np.cos(phases)
46 | print('ys', ys)
47 |
48 | return ys
49 |
50 |
51 | def discontinuity(num_periods=30, hamming=False):
52 | """Plots the spectrum of a sinusoid with/without windowing.
53 |
54 | num_periods: how many periods to compute
55 | hamming: boolean whether to apply Hamming window
56 | """
57 | signal = thinkdsp.SinSignal(freq=440)
58 | duration = signal.period * num_periods
59 | wave = signal.make_wave(duration)
60 |
61 | if hamming:
62 | wave.hamming()
63 |
64 | print(len(wave.ys), wave.ys[0], wave.ys[-1])
65 | spectrum = wave.make_spectrum()
66 | spectrum.plot(high=880)
67 |
68 |
69 | def three_spectrums():
70 | """Makes a plot showing three spectrums for a sinusoid.
71 | """
72 | thinkplot.preplot(rows=1, cols=3)
73 |
74 | pyplot.subplots_adjust(wspace=0.3, hspace=0.4,
75 | right=0.95, left=0.1,
76 | top=0.95, bottom=0.1)
77 |
78 | xticks = range(0, 900, 200)
79 |
80 | thinkplot.subplot(1)
81 | thinkplot.config(xticks=xticks)
82 | discontinuity(num_periods=30, hamming=False)
83 |
84 | thinkplot.subplot(2)
85 | thinkplot.config(xticks=xticks, xlabel='Frequency (Hz)')
86 | discontinuity(num_periods=30.25, hamming=False)
87 |
88 | thinkplot.subplot(3)
89 | thinkplot.config(xticks=xticks)
90 | discontinuity(num_periods=30.25, hamming=True)
91 |
92 | thinkplot.save(root='windowing1')
93 |
94 |
95 | def window_plot():
96 | """Makes a plot showing a sinusoid, hamming window, and their product.
97 | """
98 | signal = thinkdsp.SinSignal(freq=440)
99 | duration = signal.period * 10.25
100 | wave1 = signal.make_wave(duration)
101 | wave2 = signal.make_wave(duration)
102 |
103 | ys = np.hamming(len(wave1.ys))
104 | ts = wave1.ts
105 | window = thinkdsp.Wave(ys, ts, wave1.framerate)
106 |
107 | wave2.hamming()
108 |
109 | thinkplot.preplot(rows=3, cols=1)
110 |
111 | pyplot.subplots_adjust(wspace=0.3, hspace=0.3,
112 | right=0.95, left=0.1,
113 | top=0.95, bottom=0.05)
114 |
115 | thinkplot.subplot(1)
116 | wave1.plot()
117 | thinkplot.config(axis=[0, duration, -1.07, 1.07])
118 |
119 | thinkplot.subplot(2)
120 | window.plot()
121 | thinkplot.config(axis=[0, duration, -1.07, 1.07])
122 |
123 | thinkplot.subplot(3)
124 | wave2.plot()
125 | thinkplot.config(axis=[0, duration, -1.07, 1.07],
126 | xlabel='Time (s)')
127 |
128 | thinkplot.save(root='windowing2')
129 |
130 |
131 | def chirp_spectrum():
132 | """Plots the spectrum of a one-second one-octave linear chirp.
133 | """
134 | signal = thinkdsp.Chirp(start=220, end=440)
135 | wave = signal.make_wave(duration=1)
136 |
137 | thinkplot.preplot(3, cols=3)
138 | duration = 0.01
139 | wave.segment(0, duration).plot(xfactor=1000)
140 | thinkplot.config(ylim=[-1.05, 1.05])
141 |
142 | thinkplot.subplot(2)
143 | wave.segment(0.5, duration).plot(xfactor=1000)
144 | thinkplot.config(yticklabels='invisible',
145 | xlabel='Time (ms)')
146 |
147 | thinkplot.subplot(3)
148 | wave.segment(0.9, duration).plot(xfactor=1000)
149 | thinkplot.config(yticklabels='invisible')
150 |
151 | thinkplot.save('chirp3')
152 |
153 |
154 | spectrum = wave.make_spectrum()
155 | spectrum.plot(high=700)
156 | thinkplot.save('chirp1',
157 | xlabel='Frequency (Hz)',
158 | ylabel='Amplitude')
159 |
160 |
161 | def chirp_spectrogram():
162 | """Makes a spectrogram of a one-second one-octave linear chirp.
163 | """
164 | signal = thinkdsp.Chirp(start=220, end=440)
165 | wave = signal.make_wave(duration=1, framerate=11025)
166 | spectrogram = wave.make_spectrogram(seg_length=512)
167 |
168 | print('time res', spectrogram.time_res)
169 | print('freq res', spectrogram.freq_res)
170 | print('product', spectrogram.time_res * spectrogram.freq_res)
171 |
172 | spectrogram.plot(high=700)
173 |
174 | thinkplot.save('chirp2',
175 | xlabel='Time (s)',
176 | ylabel='Frequency (Hz)')
177 |
178 |
179 | def overlapping_windows():
180 | """Makes a figure showing overlapping hamming windows.
181 | """
182 | n = 256
183 | window = np.hamming(n)
184 |
185 | thinkplot.preplot(num=5)
186 | start = 0
187 | for i in range(5):
188 | xs = np.arange(start, start+n)
189 | thinkplot.plot(xs, window)
190 |
191 | start += n/2
192 |
193 | thinkplot.save(root='windowing3',
194 | xlabel='Index',
195 | axis=[0, 800, 0, 1.05])
196 |
197 |
198 | def invert_spectrogram():
199 | """Tests Spectrogram.make_wave.
200 | """
201 | signal = thinkdsp.Chirp(start=220, end=440)
202 | wave = signal.make_wave(duration=1, framerate=11025)
203 | spectrogram = wave.make_spectrogram(seg_length=512)
204 |
205 | wave2 = spectrogram.make_wave()
206 |
207 | for i, (y1, y2) in enumerate(zip(wave.ys, wave2.ys)):
208 | if abs(y1 - y2) > 1e-14:
209 | print(i, y1, y2)
210 |
211 |
212 | def main():
213 | chirp_spectrum()
214 | chirp_spectrogram()
215 | overlapping_windows()
216 | window_plot()
217 | three_spectrums()
218 |
219 |
220 | if __name__ == '__main__':
221 | main()
222 |
--------------------------------------------------------------------------------
/code/convolution.py:
--------------------------------------------------------------------------------
1 | """This file contains code used in "Think DSP",
2 | by Allen B. Downey, available from greenteapress.com
3 |
4 | Copyright 2014 Allen B. Downey
5 | License: GNU GPLv3 http://www.gnu.org/licenses/gpl.html
6 | """
7 |
8 | from __future__ import print_function, division
9 |
10 | import thinkdsp
11 | import thinkplot
12 |
13 | import numpy as np
14 | import pandas as pd
15 |
16 | import scipy.signal
17 |
18 | PI2 = np.pi * 2
19 |
20 |
21 | def plot_bitcoin():
22 | """Plot BitCoin prices and a smoothed time series.
23 | """
24 | nrows = 1625
25 | df = pandas.read_csv('coindesk-bpi-USD-close.csv',
26 | nrows=nrows, parse_dates=[0])
27 | ys = df.Close.values
28 |
29 | window = np.ones(30)
30 | window /= sum(window)
31 | smoothed = np.convolve(ys, window, mode='valid')
32 |
33 | N = len(window)
34 | smoothed = thinkdsp.shift_right(smoothed, N//2)
35 |
36 | thinkplot.plot(ys, color='0.7', label='daily')
37 | thinkplot.plot(smoothed, label='30 day average')
38 | thinkplot.config(xlabel='time (days)',
39 | ylabel='price',
40 | xlim=[0, nrows],
41 | loc='lower right')
42 | thinkplot.save(root='convolution1')
43 |
44 |
45 | GRAY = "0.7"
46 |
47 | def plot_facebook():
48 | """Plot Facebook prices and a smoothed time series.
49 | """
50 | names = ['date', 'open', 'high', 'low', 'close', 'volume']
51 | df = pd.read_csv('fb_1.csv', header=0, names=names, parse_dates=[0])
52 | close = df.close.values[::-1]
53 | dates = df.date.values[::-1]
54 | days = (dates - dates[0]) / np.timedelta64(1,'D')
55 |
56 | M = 30
57 | window = np.ones(M)
58 | window /= sum(window)
59 | smoothed = np.convolve(close, window, mode='valid')
60 | smoothed_days = days[M//2: len(smoothed) + M//2]
61 |
62 | thinkplot.plot(days, close, color=GRAY, label='daily close')
63 | thinkplot.plot(smoothed_days, smoothed, label='30 day average')
64 |
65 | last = days[-1]
66 | thinkplot.config(xlabel='Time (days)',
67 | ylabel='Price ($)',
68 | xlim=[-7, last+7],
69 | legend=True,
70 | loc='lower right')
71 | thinkplot.save(root='convolution1')
72 |
73 |
74 | def plot_boxcar():
75 | """Makes a plot showing the effect of convolution with a boxcar window.
76 | """
77 | # start with a square signal
78 | signal = thinkdsp.SquareSignal(freq=440)
79 | wave = signal.make_wave(duration=1, framerate=44100)
80 |
81 | # and a boxcar window
82 | window = np.ones(11)
83 | window /= sum(window)
84 |
85 | # select a short segment of the wave
86 | segment = wave.segment(duration=0.01)
87 |
88 | # and pad with window out to the length of the array
89 | N = len(segment)
90 | padded = thinkdsp.zero_pad(window, N)
91 |
92 | # compute the first element of the smoothed signal
93 | prod = padded * segment.ys
94 | print(sum(prod))
95 |
96 | # compute the rest of the smoothed signal
97 | smoothed = np.zeros(N)
98 | rolled = padded
99 | for i in range(N):
100 | smoothed[i] = sum(rolled * segment.ys)
101 | rolled = np.roll(rolled, 1)
102 |
103 | # plot the results
104 | segment.plot(color=GRAY)
105 | smooth = thinkdsp.Wave(smoothed, framerate=wave.framerate)
106 | smooth.plot()
107 | thinkplot.config(xlabel='Time(s)', ylim=[-1.05, 1.05])
108 | thinkplot.save(root='convolution2')
109 |
110 | # compute the same thing using np.convolve
111 | segment.plot(color=GRAY)
112 | ys = np.convolve(segment.ys, window, mode='valid')
113 | smooth2 = thinkdsp.Wave(ys, framerate=wave.framerate)
114 | smooth2.plot()
115 | thinkplot.config(xlabel='Time(s)', ylim=[-1.05, 1.05])
116 | thinkplot.save(root='convolution3')
117 |
118 | # plot the spectrum before and after smoothing
119 | spectrum = wave.make_spectrum()
120 | spectrum.plot(color=GRAY)
121 |
122 | ys = np.convolve(wave.ys, window, mode='same')
123 | smooth = thinkdsp.Wave(ys, framerate=wave.framerate)
124 | spectrum2 = smooth.make_spectrum()
125 | spectrum2.plot()
126 | thinkplot.config(xlabel='Frequency (Hz)',
127 | ylabel='Amplitude',
128 | xlim=[0, 22050])
129 | thinkplot.save(root='convolution4')
130 |
131 | # plot the ratio of the original and smoothed spectrum
132 | amps = spectrum.amps
133 | amps2 = spectrum2.amps
134 | ratio = amps2 / amps
135 | ratio[amps<560] = 0
136 | thinkplot.plot(ratio)
137 |
138 | thinkplot.config(xlabel='Frequency (Hz)',
139 | ylabel='Amplitude ratio',
140 | xlim=[0, 22050])
141 | thinkplot.save(root='convolution5')
142 |
143 |
144 | # plot the same ratio along with the FFT of the window
145 | padded = thinkdsp.zero_pad(window, len(wave))
146 | dft_window = np.fft.rfft(padded)
147 |
148 | thinkplot.plot(abs(dft_window), color=GRAY, label='DFT(window)')
149 | thinkplot.plot(ratio, label='amplitude ratio')
150 |
151 | thinkplot.config(xlabel='Frequency (Hz)',
152 | ylabel='Amplitude ratio',
153 | xlim=[0, 22050])
154 | thinkplot.save(root='convolution6')
155 |
156 |
157 | def plot_gaussian():
158 | """Makes a plot showing the effect of convolution with a boxcar window.
159 | """
160 | # start with a square signal
161 | signal = thinkdsp.SquareSignal(freq=440)
162 | wave = signal.make_wave(duration=1, framerate=44100)
163 | spectrum = wave.make_spectrum()
164 |
165 | # and a boxcar window
166 | boxcar = np.ones(11)
167 | boxcar /= sum(boxcar)
168 |
169 | # and a gaussian window
170 | gaussian = scipy.signal.gaussian(M=11, std=2)
171 | gaussian /= sum(gaussian)
172 |
173 | thinkplot.preplot(2)
174 | thinkplot.plot(boxcar, label='boxcar')
175 | thinkplot.plot(gaussian, label='Gaussian')
176 | thinkplot.config(xlabel='Index', legend=True)
177 | thinkplot.save(root='convolution7')
178 |
179 | ys = np.convolve(wave.ys, gaussian, mode='same')
180 | smooth = thinkdsp.Wave(ys, framerate=wave.framerate)
181 | spectrum2 = smooth.make_spectrum()
182 |
183 | # plot the ratio of the original and smoothed spectrum
184 | amps = spectrum.amps
185 | amps2 = spectrum2.amps
186 | ratio = amps2 / amps
187 | ratio[amps<560] = 0
188 |
189 | # plot the same ratio along with the FFT of the window
190 | padded = thinkdsp.zero_pad(gaussian, len(wave))
191 | dft_gaussian = np.fft.rfft(padded)
192 |
193 | thinkplot.plot(abs(dft_gaussian), color=GRAY, label='Gaussian filter')
194 | thinkplot.plot(ratio, label='amplitude ratio')
195 |
196 | thinkplot.config(xlabel='Frequency (Hz)',
197 | ylabel='Amplitude ratio',
198 | xlim=[0, 22050])
199 | thinkplot.save(root='convolution8')
200 |
201 |
202 | def fft_convolve(signal, window):
203 | """Computes convolution using FFT.
204 | """
205 | fft_signal = np.fft.fft(signal)
206 | fft_window = np.fft.fft(window)
207 | return np.fft.ifft(fft_signal * fft_window)
208 |
209 |
210 | def fft_autocorr(signal):
211 | """Computes the autocorrelation function using FFT.
212 | """
213 | N = len(signal)
214 | signal = thinkdsp.zero_pad(signal, 2*N)
215 | window = np.flipud(signal)
216 |
217 | corrs = fft_convolve(signal, window)
218 | corrs = np.roll(corrs, N//2+1)[:N]
219 | return corrs
220 |
221 |
222 | def plot_fft_convolve():
223 | """Makes a plot showing that FFT-based convolution works.
224 | """
225 | names = ['date', 'open', 'high', 'low', 'close', 'volume']
226 | df = pd.read_csv('fb_1.csv',
227 | header=0, names=names, parse_dates=[0])
228 | close = df.close.values[::-1]
229 |
230 | # compute a 30-day average using np.convolve
231 | window = scipy.signal.gaussian(M=30, std=6)
232 | window /= window.sum()
233 | smoothed = np.convolve(close, window, mode='valid')
234 |
235 | # compute the same thing using fft_convolve
236 | N = len(close)
237 | padded = thinkdsp.zero_pad(window, N)
238 |
239 | M = len(window)
240 | smoothed4 = fft_convolve(close, padded)[M-1:]
241 |
242 | # check for the biggest difference
243 | diff = smoothed - smoothed4
244 | print(max(abs(diff)))
245 |
246 | # compute autocorrelation using np.correlate
247 | corrs = np.correlate(close, close, mode='same')
248 | corrs2 = fft_autocorr(close)
249 |
250 | # check for the biggest difference
251 | diff = corrs - corrs2
252 | print(max(abs(diff)))
253 |
254 | # plot the results
255 | lags = np.arange(N) - N//2
256 | thinkplot.plot(lags, corrs, color=GRAY, linewidth=7, label='np.convolve')
257 | thinkplot.plot(lags, corrs2.real, linewidth=2, label='fft_convolve')
258 | thinkplot.config(xlabel='Lag',
259 | ylabel='Correlation',
260 | xlim=[-N//2, N//2])
261 | thinkplot.save(root='convolution9')
262 |
263 |
264 | def main():
265 | plot_facebook()
266 | plot_boxcar()
267 | plot_gaussian()
268 | plot_fft_convolve()
269 | #plot_bitcoin()
270 |
271 |
272 | if __name__ == '__main__':
273 | main()
274 |
--------------------------------------------------------------------------------
/code/dct.py:
--------------------------------------------------------------------------------
1 | """This file contains code used in "Think DSP",
2 | by Allen B. Downey, available from greenteapress.com
3 |
4 | Copyright 2014 Allen B. Downey
5 | License: GNU GPLv3 http://www.gnu.org/licenses/gpl.html
6 | """
7 |
8 | from __future__ import print_function, division
9 |
10 | import numpy as np
11 |
12 | import thinkdsp
13 | import thinkplot
14 |
15 | PI2 = np.pi * 2
16 |
17 |
18 | def synthesize1(amps, fs, ts):
19 | """Synthesize a mixture of cosines with given amps and fs.
20 |
21 | amps: amplitudes
22 | fs: frequencies in Hz
23 | ts: times to evaluate the signal
24 |
25 | returns: wave array
26 | """
27 | components = [thinkdsp.CosSignal(freq, amp)
28 | for amp, freq in zip(amps, fs)]
29 | signal = thinkdsp.SumSignal(*components)
30 |
31 | ys = signal.evaluate(ts)
32 | return ys
33 |
34 |
35 | def synthesize2(amps, fs, ts):
36 | """Synthesize a mixture of cosines with given amps and fs.
37 |
38 | amps: amplitudes
39 | fs: frequencies in Hz
40 | ts: times to evaluate the signal
41 |
42 | returns: wave array
43 | """
44 | args = np.outer(ts, fs)
45 | M = np.cos(PI2 * args)
46 | ys = np.dot(M, amps)
47 | return ys
48 |
49 |
50 | def analyze1(ys, fs, ts):
51 | """Analyze a mixture of cosines and return amplitudes.
52 |
53 | Works for the general case where M is not orthogonal.
54 |
55 | ys: wave array
56 | fs: frequencies in Hz
57 | ts: times where the signal was evaluated
58 |
59 | returns: vector of amplitudes
60 | """
61 | args = np.outer(ts, fs)
62 | M = np.cos(PI2 * args)
63 | amps = np.linalg.solve(M, ys)
64 | return amps
65 |
66 |
67 | def analyze2(ys, fs, ts):
68 | """Analyze a mixture of cosines and return amplitudes.
69 |
70 | Assumes that fs and ts are chosen so that M is orthogonal.
71 |
72 | ys: wave array
73 | fs: frequencies in Hz
74 | ts: times where the signal was evaluated
75 |
76 | returns: vector of amplitudes
77 | """
78 | args = np.outer(ts, fs)
79 | M = np.cos(PI2 * args)
80 | amps = np.dot(M, ys) / 2
81 | return amps
82 |
83 |
84 | def dct_iv(ys):
85 | """Computes DCT-IV.
86 |
87 | ys: wave array
88 |
89 | returns: vector of amplitudes
90 | """
91 | N = len(ys)
92 | ts = (0.5 + np.arange(N)) / N
93 | fs = (0.5 + np.arange(N)) / 2
94 | args = np.outer(ts, fs)
95 | M = np.cos(PI2 * args)
96 | amps = np.dot(M, ys) / 2
97 | return amps
98 |
99 |
100 | def synthesize_example():
101 | """Synthesizes a sum of sinusoids and plays it.
102 | """
103 | amps = np.array([0.6, 0.25, 0.1, 0.05])
104 | fs = [100, 200, 300, 400]
105 |
106 | framerate = 11025
107 | ts = np.linspace(0, 1, 11025)
108 | ys = synthesize2(amps, fs, ts)
109 | wave = thinkdsp.Wave(ys, framerate)
110 | wave.normalize()
111 | wave.apodize()
112 | wave.play()
113 |
114 | n = len(fs)
115 | amps2 = analyze1(ys[:n], fs, ts[:n])
116 | print(amps)
117 | print(amps2)
118 |
119 |
120 | def test1():
121 | amps = np.array([0.6, 0.25, 0.1, 0.05])
122 | N = 4.0
123 | time_unit = 0.001
124 | ts = np.arange(N) / N * time_unit
125 | max_freq = N / time_unit / 2
126 | fs = np.arange(N) / N * max_freq
127 | args = np.outer(ts, fs)
128 | M = np.cos(PI2 * args)
129 | return M
130 |
131 |
132 | def test2():
133 | """
134 | """
135 | amps = np.array([0.6, 0.25, 0.1, 0.05])
136 | N = 4.0
137 | ts = (0.5 + np.arange(N)) / N
138 | fs = (0.5 + np.arange(N)) / 2
139 | print('amps', amps)
140 | print('ts', ts)
141 | print('fs', fs)
142 | ys = synthesize2(amps, fs, ts)
143 | amps2 = analyze2(ys, fs, ts)
144 | print('amps', amps)
145 | print('amps2', amps2)
146 |
147 |
148 | def test_dct():
149 | """
150 | """
151 | amps = np.array([0.6, 0.25, 0.1, 0.05])
152 | N = 4.0
153 | ts = (0.5 + np.arange(N)) / N
154 | fs = (0.5 + np.arange(N)) / 2
155 | ys = synthesize2(amps, fs, ts)
156 |
157 | amps2 = dct_iv(ys)
158 | print('amps', amps)
159 | print('amps2', amps2)
160 |
161 |
162 | def dct_plot():
163 | signal = thinkdsp.TriangleSignal(freq=400)
164 | wave = signal.make_wave(duration=1.0, framerate=10000)
165 | dct = wave.make_dct()
166 | dct.plot()
167 | thinkplot.config(xlabel='Frequency (Hz)', ylabel='DCT')
168 | thinkplot.save(root='dct1',
169 | formats=['pdf', 'eps'])
170 |
171 |
172 | def main():
173 | np.set_printoptions(precision=3, suppress=True)
174 |
175 | test1()
176 | test2()
177 | dct_plot()
178 |
179 |
180 | if __name__ == '__main__':
181 | main()
182 |
--------------------------------------------------------------------------------
/code/dft.py:
--------------------------------------------------------------------------------
1 | """This file contains code used in "Think DSP",
2 | by Allen B. Downey, available from greenteapress.com
3 |
4 | Copyright 2014 Allen B. Downey
5 | License: GNU GPLv3 http://www.gnu.org/licenses/gpl.html
6 | """
7 |
8 | from __future__ import print_function, division
9 |
10 | import math
11 | import numpy
12 |
13 | import thinkdsp
14 | import thinkplot
15 |
16 | PI2 = np.pi * 2
17 |
18 |
19 | def synthesize1(amps, freqs, ts):
20 | """Synthesize a mixture of complex sinusoids with given amps and freqs.
21 |
22 | amps: amplitudes
23 | freqs: frequencies in Hz
24 | ts: times to evaluate the signal
25 |
26 | returns: wave array
27 | """
28 | components = [thinkdsp.ComplexSinusoid(freq, amp)
29 | for amp, freq in zip(amps, freqs)]
30 | signal = thinkdsp.SumSignal(*components)
31 |
32 | ys = signal.evaluate(ts)
33 | return ys
34 |
35 |
36 | def synthesize2(amps, freqs, ts):
37 | """Synthesize a mixture of cosines with given amps and freqs.
38 |
39 | amps: amplitudes
40 | freqs: frequencies in Hz
41 | ts: times to evaluate the signal
42 |
43 | returns: wave array
44 | """
45 | i = complex(0, 1)
46 | args = numpy.outer(ts, freqs)
47 | M = numpy.exp(i * PI2 * args)
48 | ys = numpy.dot(M, amps)
49 | return ys
50 |
51 |
52 | def analyze1(ys, freqs, ts):
53 | """Analyze a mixture of cosines and return amplitudes.
54 |
55 | Works for the general case where M is not orthogonal.
56 |
57 | ys: wave array
58 | freqs: frequencies in Hz
59 | ts: times where the signal was evaluated
60 |
61 | returns: vector of amplitudes
62 | """
63 | args = numpy.outer(ts, freqs)
64 | M = numpy.exp(i * PI2 * args)
65 | amps = numpy.linalg.solve(M, ys)
66 | return amps
67 |
68 |
69 | def analyze2(ys, freqs, ts):
70 | """Analyze a mixture of cosines and return amplitudes.
71 |
72 | Assumes that freqs and ts are chosen so that M is orthogonal.
73 |
74 | ys: wave array
75 | freqs: frequencies in Hz
76 | ts: times where the signal was evaluated
77 |
78 | returns: vector of amplitudes
79 | """
80 |
81 | def analyze2(ys, freqs, ts):
82 | args = numpy.outer(ts, freqs)
83 | M = numpy.exp(i * PI2 * args)
84 | amps = M.conj().transpose().dot(ys) / N
85 | return amps
86 |
87 |
88 | def dft(ys):
89 | i = complex(0, 1)
90 | N = len(ys)
91 | ts = numpy.arange(N) / N
92 | freqs = numpy.arange(N)
93 | args = numpy.outer(ts, freqs)
94 | M = numpy.exp(i * PI2 * args)
95 | amps = M.conj().transpose().dot(ys)
96 | return amps
97 |
98 |
99 | def idft(amps):
100 | ys = dft(amps) / N
101 | return ys
102 |
103 |
104 | def make_figures():
105 | """Makes figures showing complex signals.
106 | """
107 | amps = numpy.array([0.6, 0.25, 0.1, 0.05])
108 | freqs = [100, 200, 300, 400]
109 | framerate = 11025
110 |
111 | ts = numpy.linspace(0, 1, framerate)
112 | ys = synthesize1(amps, freqs, ts)
113 | print(ys)
114 |
115 | thinkplot.preplot(2)
116 | n = framerate / 25
117 | thinkplot.plot(ts[:n], ys[:n].real, label='real')
118 | thinkplot.plot(ts[:n], ys[:n].imag, label='imag')
119 | thinkplot.save(root='dft1',
120 | xlabel='Time (s)',
121 | ylim=[-1.05, 1.05],
122 | loc='lower right')
123 |
124 | ys = synthesize2(amps, freqs, ts)
125 |
126 | amps2 = amps * numpy.exp(1.5j)
127 | ys2 = synthesize2(amps2, freqs, ts)
128 |
129 | thinkplot.preplot(2)
130 | thinkplot.plot(ts[:n], ys.real[:n], label=r'$\phi_0 = 0#39;)
131 | thinkplot.plot(ts[:n], ys2.real[:n], label=r'$\phi_0 = 1.5#39;)
132 | thinkplot.save(root='dft2',
133 | xlabel='Time (s)',
134 | ylim=[-1.05, 1.05],
135 | loc='lower right')
136 |
137 |
138 | framerate = 10000
139 | signal = thinkdsp.SawtoothSignal(freq=500)
140 | wave = signal.make_wave(duration=0.1, framerate=framerate)
141 | hs = dft(wave.ys)
142 | amps = numpy.absolute(hs)
143 |
144 | N = len(hs)
145 | fs = numpy.arange(N) * framerate / N
146 | thinkplot.plot(fs, amps)
147 | thinkplot.save(root='dft3',
148 | xlabel='Frequency (Hz)',
149 | ylabel='Amplitude',
150 | legend=False)
151 |
152 |
153 |
154 | def main():
155 | numpy.set_printoptions(precision=3, suppress=True)
156 | make_figures()
157 |
158 |
159 | if __name__ == '__main__':
160 | main()
161 |
--------------------------------------------------------------------------------
/code/dft_example.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "# Implementing DFT\n",
8 | "\n",
9 | "Copyright 2019 Allen Downey, [MIT License](http://opensource.org/licenses/MIT)"
10 | ]
11 | },
12 | {
13 | "cell_type": "code",
14 | "execution_count": 1,
15 | "metadata": {},
16 | "outputs": [],
17 | "source": [
18 | "import numpy as np"
19 | ]
20 | },
21 | {
22 | "cell_type": "markdown",
23 | "metadata": {},
24 | "source": [
25 | "Let's start with a known result. The DFT of an impulse is a constant."
26 | ]
27 | },
28 | {
29 | "cell_type": "code",
30 | "execution_count": 2,
31 | "metadata": {},
32 | "outputs": [],
33 | "source": [
34 | "N = 4\n",
35 | "x = [1, 0, 0, 0]"
36 | ]
37 | },
38 | {
39 | "cell_type": "code",
40 | "execution_count": 3,
41 | "metadata": {},
42 | "outputs": [
43 | {
44 | "data": {
45 | "text/plain": [
46 | "array([1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j])"
47 | ]
48 | },
49 | "execution_count": 3,
50 | "metadata": {},
51 | "output_type": "execute_result"
52 | }
53 | ],
54 | "source": [
55 | "np.fft.fft(x)"
56 | ]
57 | },
58 | {
59 | "cell_type": "markdown",
60 | "metadata": {},
61 | "source": [
62 | "### Literal translation\n",
63 | "\n",
64 | "The usual way the DFT is expressed is as a summation. Following the notation on [Wikipedia](https://en.wikipedia.org/wiki/Discrete_Fourier_transform):\n",
65 | "\n",
66 | "$ X_k = \\sum_{n=0}^N x_n \\cdot e^{-2 \\pi i n k / N} $\n",
67 | "\n",
68 | "Here's a straightforward translation of that formula into Python."
69 | ]
70 | },
71 | {
72 | "cell_type": "code",
73 | "execution_count": 4,
74 | "metadata": {},
75 | "outputs": [],
76 | "source": [
77 | "pi = np.pi\n",
78 | "exp = np.exp"
79 | ]
80 | },
81 | {
82 | "cell_type": "code",
83 | "execution_count": 5,
84 | "metadata": {},
85 | "outputs": [
86 | {
87 | "data": {
88 | "text/plain": [
89 | "(1+0j)"
90 | ]
91 | },
92 | "execution_count": 5,
93 | "metadata": {},
94 | "output_type": "execute_result"
95 | }
96 | ],
97 | "source": [
98 | "k = 0\n",
99 | "sum(x[n] * exp(-2j * pi * k * n / N) for n in range(N))"
100 | ]
101 | },
102 | {
103 | "cell_type": "markdown",
104 | "metadata": {},
105 | "source": [
106 | "Wrapping this code in a function makes the roles of `k` and `n` clearer, where `k` is a free parameter and `n` is the bound variable of the summation."
107 | ]
108 | },
109 | {
110 | "cell_type": "code",
111 | "execution_count": 6,
112 | "metadata": {},
113 | "outputs": [],
114 | "source": [
115 | "def dft_k(x, k):\n",
116 | " return sum(x[n] * exp(-2j * pi * k * n / N) for n in range(N))"
117 | ]
118 | },
119 | {
120 | "cell_type": "markdown",
121 | "metadata": {},
122 | "source": [
123 | "Of course, we usually we compute $X$ all at once, so we can wrap this function in another function:"
124 | ]
125 | },
126 | {
127 | "cell_type": "code",
128 | "execution_count": 7,
129 | "metadata": {},
130 | "outputs": [],
131 | "source": [
132 | "def dft(x):\n",
133 | " N = len(x)\n",
134 | " X = [dft_k(x, k) for k in range(N)]\n",
135 | " return X"
136 | ]
137 | },
138 | {
139 | "cell_type": "code",
140 | "execution_count": 8,
141 | "metadata": {},
142 | "outputs": [
143 | {
144 | "data": {
145 | "text/plain": [
146 | "[(1+0j), (1+0j), (1+0j), (1+0j)]"
147 | ]
148 | },
149 | "execution_count": 8,
150 | "metadata": {},
151 | "output_type": "execute_result"
152 | }
153 | ],
154 | "source": [
155 | "dft(x)"
156 | ]
157 | },
158 | {
159 | "cell_type": "markdown",
160 | "metadata": {},
161 | "source": [
162 | "And the results check out."
163 | ]
164 | },
165 | {
166 | "cell_type": "markdown",
167 | "metadata": {},
168 | "source": [
169 | "### DFT as a matrix operation\n",
170 | "\n",
171 | "It is also common to express the DFT as a [matrix operation](https://en.wikipedia.org/wiki/DFT_matrix):\n",
172 | "\n",
173 | "$ X = W x $\n",
174 | "\n",
175 | "with \n",
176 | "\n",
177 | "$ W_{j, k} = \\omega^{j k} $\n",
178 | "\n",
179 | "and\n",
180 | "\n",
181 | "$ \\omega = e^{-2 \\pi i / N}$\n",
182 | "\n",
183 | "If we recognize the construction of $W$ as an outer product, we can use `np.outer` to compute it.\n",
184 | "\n",
185 | "Here's an implementation of DFT using outer product to construct the DFT matrix, and dot product to compute the DFT."
186 | ]
187 | },
188 | {
189 | "cell_type": "code",
190 | "execution_count": 9,
191 | "metadata": {},
192 | "outputs": [],
193 | "source": [
194 | "def dft(x):\n",
195 | " N = len(x)\n",
196 | " ks = range(N)\n",
197 | " args = -2j * pi * np.outer(ks, ks) / N\n",
198 | " W = exp(args)\n",
199 | " X = W.dot(x)\n",
200 | " return X"
201 | ]
202 | },
203 | {
204 | "cell_type": "markdown",
205 | "metadata": {},
206 | "source": [
207 | "And the results check out."
208 | ]
209 | },
210 | {
211 | "cell_type": "code",
212 | "execution_count": 10,
213 | "metadata": {
214 | "scrolled": true
215 | },
216 | "outputs": [
217 | {
218 | "data": {
219 | "text/plain": [
220 | "array([1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j])"
221 | ]
222 | },
223 | "execution_count": 10,
224 | "metadata": {},
225 | "output_type": "execute_result"
226 | }
227 | ],
228 | "source": [
229 | "dft(x)"
230 | ]
231 | },
232 | {
233 | "cell_type": "markdown",
234 | "metadata": {},
235 | "source": [
236 | "### Implementing FFT\n",
237 | "\n",
238 | "Finally, we can implement the FFT by translating from math notation:\n",
239 | "\n",
240 | "$ X_k = E_k + e^{-2 \\pi i k / N} O_k $\n",
241 | "\n",
242 | "Where $E$ is the FFT of the even elements of $x$ and $O$ is the DFT of the odd elements of $x$.\n",
243 | "\n",
244 | "Here's what that looks like in code."
245 | ]
246 | },
247 | {
248 | "cell_type": "code",
249 | "execution_count": 11,
250 | "metadata": {},
251 | "outputs": [],
252 | "source": [
253 | "def fft(x):\n",
254 | " N = len(x)\n",
255 | " if N == 1:\n",
256 | " return x\n",
257 | " \n",
258 | " E = fft(x[::2])\n",
259 | " O = fft(x[1::2])\n",
260 | " \n",
261 | " ks = np.arange(N)\n",
262 | " args = -2j * pi * ks / N\n",
263 | " W = np.exp(args)\n",
264 | " \n",
265 | " return np.tile(E, 2) + W * np.tile(O, 2)"
266 | ]
267 | },
268 | {
269 | "cell_type": "markdown",
270 | "metadata": {},
271 | "source": [
272 | "The length of $E$ and $O$ is half the length of $W$, so I use `np.tile` to double them up.\n",
273 | "\n",
274 | "And the results check out."
275 | ]
276 | },
277 | {
278 | "cell_type": "code",
279 | "execution_count": 12,
280 | "metadata": {},
281 | "outputs": [
282 | {
283 | "data": {
284 | "text/plain": [
285 | "array([1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j])"
286 | ]
287 | },
288 | "execution_count": 12,
289 | "metadata": {},
290 | "output_type": "execute_result"
291 | }
292 | ],
293 | "source": [
294 | "fft(x)"
295 | ]
296 | },
297 | {
298 | "cell_type": "code",
299 | "execution_count": null,
300 | "metadata": {},
301 | "outputs": [],
302 | "source": []
303 | }
304 | ],
305 | "metadata": {
306 | "anaconda-cloud": {},
307 | "kernelspec": {
308 | "display_name": "Python 3",
309 | "language": "python",
310 | "name": "python3"
311 | },
312 | "language_info": {
313 | "codemirror_mode": {
314 | "name": "ipython",
315 | "version": 3
316 | },
317 | "file_extension": ".py",
318 | "mimetype": "text/x-python",
319 | "name": "python",
320 | "nbconvert_exporter": "python",
321 | "pygments_lexer": "ipython3",
322 | "version": "3.6.10"
323 | }
324 | },
325 | "nbformat": 4,
326 | "nbformat_minor": 4
327 | }
328 |
--------------------------------------------------------------------------------
/code/diff_int.py:
--------------------------------------------------------------------------------
1 | """This file contains code used in "Think DSP",
2 | by Allen B. Downey, available from greenteapress.com
3 |
4 | Copyright 2014 Allen B. Downey
5 | License: GNU GPLv3 http://www.gnu.org/licenses/gpl.html
6 | """
7 |
8 | from __future__ import print_function, division
9 |
10 | import numpy as np
11 | import pandas as pd
12 |
13 | import thinkdsp
14 | import thinkplot
15 |
16 | PI2 = np.pi * 2
17 | GRAY = '0.7'
18 |
19 |
20 | def plot_wave_and_spectrum(wave, root):
21 | """Makes a plot showing a wave and its spectrum.
22 |
23 | wave: Wave object
24 | root: string used to generate filenames
25 | """
26 | thinkplot.preplot(cols=2)
27 | wave.plot()
28 | thinkplot.config(xlabel='Time (days)',
29 | ylabel='Price ($)')
30 |
31 | thinkplot.subplot(2)
32 | spectrum = wave.make_spectrum()
33 | print(spectrum.estimate_slope())
34 | spectrum.plot()
35 | thinkplot.config(xlabel='Frequency (1/days)',
36 | ylabel='Amplitude',
37 | xlim=[0, spectrum.fs[-1]],
38 | xscale='log',
39 | yscale='log')
40 |
41 | thinkplot.save(root=root)
42 |
43 |
44 | def plot_sawtooth_and_spectrum(wave, root):
45 | """Makes a plot showing a sawtoothwave and its spectrum.
46 | """
47 | thinkplot.preplot(cols=2)
48 | wave.plot()
49 | thinkplot.config(xlabel='Time (s)')
50 |
51 | thinkplot.subplot(2)
52 | spectrum = wave.make_spectrum()
53 | spectrum.plot()
54 | thinkplot.config(xlabel='Frequency (Hz)',
55 | #ylabel='Amplitude',
56 | xlim=[0, spectrum.fs[-1]])
57 |
58 | thinkplot.save(root)
59 |
60 |
61 | def make_filter(window, wave):
62 | """Computes the filter that corresponds to a window.
63 |
64 | window: NumPy array
65 | wave: wave used to choose the length and framerate
66 |
67 | returns: new Spectrum
68 | """
69 | padded = thinkdsp.zero_pad(window, len(wave))
70 | window_wave = thinkdsp.Wave(padded, framerate=wave.framerate)
71 | window_spectrum = window_wave.make_spectrum()
72 | return window_spectrum
73 |
74 |
75 | def plot_filters(close):
76 | """Plots the filter that corresponds to diff, deriv, and integral.
77 | """
78 | thinkplot.preplot(3, cols=2)
79 |
80 | diff_window = np.array([1.0, -1.0])
81 | diff_filter = make_filter(diff_window, close)
82 | diff_filter.plot(label='diff')
83 |
84 | deriv_filter = close.make_spectrum()
85 | deriv_filter.hs = PI2 * 1j * deriv_filter.fs
86 | deriv_filter.plot(label='derivative')
87 |
88 | thinkplot.config(xlabel='Frequency (1/day)',
89 | ylabel='Amplitude ratio',
90 | loc='upper left')
91 |
92 | thinkplot.subplot(2)
93 | integ_filter = deriv_filter.copy()
94 | integ_filter.hs = 1 / (PI2 * 1j * integ_filter.fs)
95 |
96 | integ_filter.plot(label='integral')
97 | thinkplot.config(xlabel='Frequency (1/day)',
98 | ylabel='Amplitude ratio',
99 | yscale='log')
100 | thinkplot.save('diff_int3')
101 |
102 |
103 | def plot_diff_deriv(close):
104 | change = thinkdsp.Wave(np.diff(close.ys), framerate=1)
105 |
106 | deriv_spectrum = close.make_spectrum().differentiate()
107 | deriv = deriv_spectrum.make_wave()
108 |
109 | low, high = 0, 50
110 | thinkplot.preplot(2)
111 | thinkplot.plot(change.ys[low:high], label='diff')
112 | thinkplot.plot(deriv.ys[low:high], label='derivative')
113 |
114 | thinkplot.config(xlabel='Time (day)', ylabel='Price change ($)')
115 | thinkplot.save('diff_int4')
116 |
117 |
118 | def plot_integral(close):
119 |
120 | deriv_spectrum = close.make_spectrum().differentiate()
121 |
122 | integ_spectrum = deriv_spectrum.integrate()
123 | print(integ_spectrum.hs[0])
124 | integ_spectrum.hs[0] = 0
125 |
126 | thinkplot.preplot(2)
127 | integ_wave = integ_spectrum.make_wave()
128 | close.plot(label='closing prices')
129 | integ_wave.plot(label='integrated derivative')
130 | thinkplot.config(xlabel='Time (day)', ylabel='Price ($)',
131 | legend=True, loc='upper left')
132 |
133 | thinkplot.save('diff_int5')
134 |
135 |
136 | def plot_ratios(in_wave, out_wave):
137 |
138 | # compare filters for cumsum and integration
139 | diff_window = np.array([1.0, -1.0])
140 | padded = thinkdsp.zero_pad(diff_window, len(in_wave))
141 | diff_wave = thinkdsp.Wave(padded, framerate=in_wave.framerate)
142 | diff_filter = diff_wave.make_spectrum()
143 |
144 | cumsum_filter = diff_filter.copy()
145 | cumsum_filter.hs = 1 / cumsum_filter.hs
146 | cumsum_filter.plot(label='cumsum filter', color=GRAY, linewidth=7)
147 |
148 | integ_filter = cumsum_filter.copy()
149 | integ_filter.hs = integ_filter.framerate / (PI2 * 1j * integ_filter.fs)
150 | integ_filter.plot(label='integral filter')
151 |
152 | thinkplot.config(xlim=[0, integ_filter.max_freq],
153 | yscale='log', legend=True)
154 | thinkplot.save('diff_int8')
155 |
156 | # compare cumsum filter to actual ratios
157 | cumsum_filter.plot(label='cumsum filter', color=GRAY, linewidth=7)
158 |
159 | in_spectrum = in_wave.make_spectrum()
160 | out_spectrum = out_wave.make_spectrum()
161 | ratio_spectrum = out_spectrum.ratio(in_spectrum, thresh=1)
162 | ratio_spectrum.plot(label='ratio', style='.', markersize=4)
163 |
164 | thinkplot.config(xlabel='Frequency (Hz)',
165 | ylabel='Amplitude ratio',
166 | xlim=[0, integ_filter.max_freq],
167 | yscale='log', legend=True)
168 | thinkplot.save('diff_int9')
169 |
170 |
171 |
172 | def plot_diff_filters(wave):
173 |
174 | window1 = np.array([1, -1])
175 | window2 = np.array([-1, 4, -3]) / 2.0
176 | window3 = np.array([2, -9, 18, -11]) / 6.0
177 | window4 = np.array([-3, 16, -36, 48, -25]) / 12.0
178 | window5 = np.array([12, -75, 200, -300, 300, -137]) / 60.0
179 |
180 | thinkplot.preplot(5)
181 | for i, window in enumerate([window1, window2, window3, window4, window5]):
182 | padded = thinkdsp.zero_pad(window, len(wave))
183 | fft_window = np.fft.rfft(padded)
184 | n = len(fft_window)
185 | thinkplot.plot(abs(fft_window)[:], label=i+1)
186 |
187 | thinkplot.show()
188 |
189 |
190 | def main():
191 | names = ['date', 'open', 'high', 'low', 'close', 'volume']
192 | df = pd.read_csv('fb_1.csv', header=0, names=names, parse_dates=[0])
193 | ys = df.close.values[::-1]
194 | close = thinkdsp.Wave(ys, framerate=1)
195 | plot_wave_and_spectrum(close, root='diff_int1')
196 |
197 | change = thinkdsp.Wave(np.diff(ys), framerate=1)
198 | plot_wave_and_spectrum(change, root='diff_int2')
199 |
200 | plot_filters(close)
201 |
202 | plot_diff_deriv(close)
203 |
204 | signal = thinkdsp.SawtoothSignal(freq=50)
205 | in_wave = signal.make_wave(duration=0.1, framerate=44100)
206 | plot_sawtooth_and_spectrum(in_wave, 'diff_int6')
207 |
208 | out_wave = in_wave.cumsum()
209 | out_wave.unbias()
210 | plot_sawtooth_and_spectrum(out_wave, 'diff_int7')
211 |
212 | plot_integral(close)
213 | plot_ratios(in_wave, out_wave)
214 |
215 |
216 | if __name__ == '__main__':
217 | main()
218 |
--------------------------------------------------------------------------------
/code/fourth_wave.png:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/AllenDowney/ThinkDSP/f1cc15de31f658d5df287332a30659fb16eb41d5/code/fourth_wave.png
--------------------------------------------------------------------------------
/code/noise.py:
--------------------------------------------------------------------------------
1 | """This file contains code used in "Think DSP",
2 | by Allen B. Downey, available from greenteapress.com
3 |
4 | Copyright 2014 Allen B. Downey
5 | License: GNU GPLv3 http://www.gnu.org/licenses/gpl.html
6 | """
7 |
8 | from __future__ import print_function, division
9 |
10 | import numpy
11 | import thinkstats2
12 | import thinkdsp
13 | import thinkplot
14 |
15 |
16 | def process_noise(signal, root='white'):
17 | """Plots wave and spectrum for noise signals.
18 |
19 | signal: Signal
20 | root: string used to generate file names
21 | """
22 | framerate = 11025
23 | wave = signal.make_wave(duration=0.5, framerate=framerate)
24 |
25 | # 0: waveform
26 | segment = wave.segment(duration=0.1)
27 | segment.plot(linewidth=1, alpha=0.5)
28 | thinkplot.save(root=root+'noise0',
29 | xlabel='Time (s)',
30 | ylim=[-1.05, 1.05])
31 |
32 | spectrum = wave.make_spectrum()
33 |
34 | # 1: spectrum
35 | spectrum.plot_power(linewidth=1, alpha=0.5)
36 | thinkplot.save(root=root+'noise1',
37 | xlabel='Frequency (Hz)',
38 | ylabel='Power',
39 | xlim=[0, spectrum.fs[-1]])
40 |
41 | slope, _, _, _, _ = spectrum.estimate_slope()
42 | print('estimated slope', slope)
43 |
44 | # 2: integrated spectrum
45 | integ = spectrum.make_integrated_spectrum()
46 | integ.plot_power()
47 | thinkplot.save(root=root+'noise2',
48 | xlabel='Frequency (Hz)',
49 | ylabel='Cumulative fraction of total power',
50 | xlim=[0, framerate/2])
51 |
52 | # 3: log-log power spectrum
53 | spectrum.hs[0] = 0
54 | thinkplot.preplot(cols=2)
55 | spectrum.plot_power(linewidth=1, alpha=0.5)
56 | thinkplot.config(xlabel='Frequency (Hz)',
57 | ylabel='Power',
58 | xlim=[0, framerate/2])
59 |
60 | thinkplot.subplot(2)
61 | spectrum.plot_power(linewidth=1, alpha=0.5)
62 | thinkplot.config(xlabel='Frequency (Hz)',
63 | xscale='log',
64 | yscale='log',
65 | xlim=[0, framerate/2])
66 |
67 | thinkplot.save(root=root+'noise3')
68 |
69 |
70 | def plot_gaussian_noise():
71 | """Shows the distribution of the spectrum of Gaussian noise.
72 | """
73 | thinkdsp.random_seed(18)
74 | signal = thinkdsp.UncorrelatedGaussianNoise()
75 | wave = signal.make_wave(duration=0.5, framerate=11025)
76 | spectrum = wave.make_spectrum()
77 |
78 | thinkplot.preplot(2, cols=2)
79 | thinkstats2.NormalProbabilityPlot(spectrum.real, label='real')
80 | thinkplot.config(xlabel='Normal sample',
81 | ylabel='Amplitude',
82 | ylim=[-250, 250],
83 | loc='lower right')
84 |
85 | thinkplot.subplot(2)
86 | thinkstats2.NormalProbabilityPlot(spectrum.imag, label='imag')
87 | thinkplot.config(xlabel='Normal sample',
88 | ylim=[-250, 250],
89 | loc='lower right')
90 |
91 | thinkplot.save(root='noise1')
92 |
93 |
94 | def plot_pink_noise():
95 | """Makes a plot showing power spectrums for pink noise.
96 | """
97 | thinkdsp.random_seed(20)
98 |
99 | duration = 1.0
100 | framerate = 512
101 |
102 | def make_spectrum(signal):
103 | wave = signal.make_wave(duration=duration, framerate=framerate)
104 | spectrum = wave.make_spectrum()
105 | spectrum.hs[0] = 0
106 | return spectrum
107 |
108 | signal = thinkdsp.UncorrelatedUniformNoise()
109 | white = make_spectrum(signal)
110 |
111 | signal = thinkdsp.PinkNoise()
112 | pink = make_spectrum(signal)
113 |
114 | signal = thinkdsp.BrownianNoise()
115 | red = make_spectrum(signal)
116 |
117 | linewidth = 2
118 | # colorbrewer2.org 4-class sequential OrRd
119 | white.plot_power(label='white', color='#fdcc8a', linewidth=linewidth)
120 | pink.plot_power(label='pink', color='#fc8d59', linewidth=linewidth)
121 | red.plot_power(label='red', color='#d7301f', linewidth=linewidth)
122 | thinkplot.save(root='noise-triple',
123 | xlabel='Frequency (Hz)',
124 | ylabel='Power',
125 | xscale='log',
126 | yscale='log',
127 | xlim=[1, red.fs[-1]])
128 |
129 |
130 | def main():
131 | thinkdsp.random_seed(17)
132 | plot_pink_noise()
133 |
134 | thinkdsp.random_seed(17)
135 | plot_gaussian_noise()
136 |
137 | thinkdsp.random_seed(20)
138 | signal = thinkdsp.UncorrelatedUniformNoise()
139 | process_noise(signal, root='white')
140 |
141 | thinkdsp.random_seed(20)
142 | signal = thinkdsp.PinkNoise(beta=1.0)
143 | process_noise(signal, root='pink')
144 |
145 | thinkdsp.random_seed(17)
146 | signal = thinkdsp.BrownianNoise()
147 | process_noise(signal, root='red')
148 |
149 |
150 | if __name__ == '__main__':
151 | main()
152 |
--------------------------------------------------------------------------------
/code/sampling.py:
--------------------------------------------------------------------------------
1 | """This file contains code used in "Think DSP",
2 | by Allen B. Downey, available from greenteapress.com
3 |
4 | Copyright 2015 Allen B. Downey
5 | License: GNU GPLv3 http://www.gnu.org/licenses/gpl.html
6 | """
7 |
8 | from __future__ import print_function, division
9 |
10 | import thinkdsp
11 | import thinkplot
12 |
13 | import numpy as np
14 | import matplotlib.pyplot as plt
15 |
16 | PI2 = 2 * np.pi
17 | FORMATS = ['pdf', 'eps']
18 |
19 |
20 | def plot_beeps():
21 | wave = thinkdsp.read_wave('253887__themusicalnomad__positive-beeps.wav')
22 | wave.normalize()
23 |
24 | thinkplot.preplot(3)
25 |
26 | # top left
27 | ax1 = plt.subplot2grid((4, 2), (0, 0), rowspan=2)
28 | plt.setp(ax1.get_xticklabels(), visible=False)
29 |
30 | wave.plot()
31 | thinkplot.config(title='Input waves', legend=False)
32 |
33 | # bottom left
34 | imp_sig = thinkdsp.Impulses([0.01, 0.4, 0.8, 1.2],
35 | amps=[1, 0.5, 0.25, 0.1])
36 | impulses = imp_sig.make_wave(start=0, duration=1.3,
37 | framerate=wave.framerate)
38 |
39 | ax2 = plt.subplot2grid((4, 2), (2, 0), rowspan=2, sharex=ax1)
40 | impulses.plot()
41 | thinkplot.config(xlabel='Time (s)')
42 |
43 | # center right
44 | convolved = wave.convolve(impulses)
45 |
46 | ax3 = plt.subplot2grid((4, 2), (1, 1), rowspan=2)
47 | plt.title('Convolution')
48 | convolved.plot()
49 | thinkplot.config(xlabel='Time (s)')
50 |
51 | thinkplot.save(root='sampling1',
52 | formats=FORMATS,
53 | legend=False)
54 |
55 | XLIM = [-22050, 22050]
56 |
57 | def plot_am():
58 | wave = thinkdsp.read_wave('105977__wcfl10__favorite-station.wav')
59 | wave.unbias()
60 | wave.normalize()
61 |
62 | # top
63 | ax1 = thinkplot.preplot(6, rows=4)
64 | spectrum = wave.make_spectrum(full=True)
65 | spectrum.plot(label='spectrum')
66 |
67 | thinkplot.config(xlim=XLIM, xticklabels='invisible')
68 |
69 | #second
70 | carrier_sig = thinkdsp.CosSignal(freq=10000)
71 | carrier_wave = carrier_sig.make_wave(duration=wave.duration,
72 | framerate=wave.framerate)
73 | modulated = wave * carrier_wave
74 |
75 | ax2 = thinkplot.subplot(2, sharey=ax1)
76 | modulated.make_spectrum(full=True).plot(label='modulated')
77 | thinkplot.config(xlim=XLIM, xticklabels='invisible')
78 |
79 | # third
80 | demodulated = modulated * carrier_wave
81 | demodulated_spectrum = demodulated.make_spectrum(full=True)
82 |
83 | ax3 = thinkplot.subplot(3, sharey=ax1)
84 | demodulated_spectrum.plot(label='demodulated')
85 | thinkplot.config(xlim=XLIM, xticklabels='invisible')
86 |
87 | #fourth
88 | ax4 = thinkplot.subplot(4, sharey=ax1)
89 | demodulated_spectrum.low_pass(10000)
90 | demodulated_spectrum.plot(label='filtered')
91 | thinkplot.config(xlim=XLIM, xlabel='Frequency (Hz)')
92 |
93 | thinkplot.save(root='sampling2',
94 | formats=FORMATS)
95 |
96 | #carrier_spectrum = carrier_wave.make_spectrum(full=True)
97 | #carrier_spectrum.plot()
98 |
99 |
100 | #convolved = spectrum.convolve(carrier_spectrum)
101 | #convolved.plot()
102 |
103 |
104 | #reconvolved = convolved.convolve(carrier_spectrum)
105 | #reconvolved.plot()
106 |
107 |
108 | def sample(wave, factor):
109 | """Simulates sampling of a wave.
110 |
111 | wave: Wave object
112 | factor: ratio of the new framerate to the original
113 | """
114 | ys = np.zeros(len(wave))
115 | ys[::factor] = wave.ys[::factor]
116 | ts = wave.ts[:]
117 | return thinkdsp.Wave(ys, ts, wave.framerate)
118 |
119 |
120 | def make_impulses(wave, factor):
121 | ys = np.zeros(len(wave))
122 | ys[::factor] = 1
123 | ts = np.arange(len(wave)) / wave.framerate
124 | return thinkdsp.Wave(ys, ts, wave.framerate)
125 |
126 |
127 | def plot_segments(original, filtered):
128 | start = 1
129 | duration = 0.01
130 | original.segment(start=start, duration=duration).plot(color='gray')
131 | filtered.segment(start=start, duration=duration).plot()
132 |
133 |
134 | def plot_sampling(wave, root):
135 | ax1 = thinkplot.preplot(2, rows=2)
136 | wave.make_spectrum(full=True).plot(label='spectrum')
137 |
138 | thinkplot.config(xlim=XLIM, xticklabels='invisible')
139 |
140 | ax2 = thinkplot.subplot(2)
141 | sampled = sample(wave, 4)
142 | sampled.make_spectrum(full=True).plot(label='sampled')
143 | thinkplot.config(xlim=XLIM, xlabel='Frequency (Hz)')
144 |
145 | thinkplot.save(root=root,
146 | formats=FORMATS)
147 |
148 |
149 | def plot_sampling2(wave, root):
150 | ax1 = thinkplot.preplot(6, rows=4)
151 | wave.make_spectrum(full=True).plot(label='spectrum')
152 | thinkplot.config(xlim=XLIM, xticklabels='invisible')
153 |
154 | ax2 = thinkplot.subplot(2)
155 | impulses = make_impulses(wave, 4)
156 | impulses.make_spectrum(full=True).plot(label='impulses')
157 | thinkplot.config(xlim=XLIM, xticklabels='invisible')
158 |
159 | ax3 = thinkplot.subplot(3)
160 | sampled = wave * impulses
161 | spectrum = sampled.make_spectrum(full=True)
162 | spectrum.plot(label='sampled')
163 | thinkplot.config(xlim=XLIM, xticklabels='invisible')
164 |
165 | ax4 = thinkplot.subplot(4)
166 | spectrum.low_pass(5512.5)
167 | spectrum.plot(label='filtered')
168 | thinkplot.config(xlim=XLIM, xlabel='Frequency (Hz)')
169 |
170 | thinkplot.save(root=root,
171 | formats=FORMATS)
172 |
173 |
174 | def plot_sampling3(wave, root):
175 | ax1 = thinkplot.preplot(6, rows=3)
176 | wave.make_spectrum(full=True).plot(label='spectrum')
177 | thinkplot.config(xlim=XLIM, xticklabels='invisible')
178 |
179 | impulses = make_impulses(wave, 4)
180 |
181 | ax2 = thinkplot.subplot(2)
182 | sampled = wave * impulses
183 | spectrum = sampled.make_spectrum(full=True)
184 | spectrum.plot(label='sampled')
185 | thinkplot.config(xlim=XLIM, xticklabels='invisible')
186 |
187 | ax3 = thinkplot.subplot(3)
188 | spectrum.low_pass(5512.5)
189 | spectrum.plot(label='filtered')
190 | thinkplot.config(xlim=XLIM, xlabel='Frequency (Hz)')
191 |
192 | thinkplot.save(root=root,
193 | formats=FORMATS)
194 |
195 | #filtered = spectrum.make_wave()
196 | #plot_segments(wave, filtered)
197 |
198 |
199 | def make_boxcar(spectrum, factor):
200 | """Makes a boxcar filter for the given spectrum.
201 |
202 | spectrum: Spectrum to be filtered
203 | factor: sampling factor
204 | """
205 | fs = np.copy(spectrum.fs)
206 | hs = np.zeros_like(spectrum.hs)
207 |
208 | cutoff = spectrum.framerate / 2 / factor
209 | for i, f in enumerate(fs):
210 | if abs(f) <= cutoff:
211 | hs[i] = 1
212 | return thinkdsp.Spectrum(hs, fs, spectrum.framerate, full=spectrum.full)
213 |
214 |
215 |
216 | def plot_sinc_demo(wave, factor, start=None, duration=None):
217 |
218 | def make_sinc(t, i, y):
219 | """Makes a shifted, scaled copy of the sinc function."""
220 | sinc = boxcar.make_wave()
221 | sinc.shift(t)
222 | sinc.roll(i)
223 | sinc.scale(y * factor)
224 | return sinc
225 |
226 | def plot_mini_sincs(wave):
227 | """Plots sinc functions for each sample in wave."""
228 | t0 = wave.ts[0]
229 | for i in range(0, len(wave), factor):
230 | sinc = make_sinc(t0, i, wave.ys[i])
231 | seg = sinc.segment(start, duration)
232 | seg.plot(color='green', linewidth=0.5, alpha=0.3)
233 | if i == 0:
234 | total = sinc
235 | else:
236 | total += sinc
237 |
238 | seg = total.segment(start, duration)
239 | seg.plot(color='blue', alpha=0.5)
240 |
241 | sampled = sample(wave, factor)
242 | spectrum = sampled.make_spectrum()
243 | boxcar = make_boxcar(spectrum, factor)
244 |
245 | start = wave.start if start is None else start
246 | duration = wave.duration if duration is None else duration
247 |
248 | sampled.segment(start, duration).plot_vlines(color='gray')
249 | wave.segment(start, duration).plot(color='gray')
250 | plot_mini_sincs(wave)
251 |
252 |
253 | def plot_sincs(wave):
254 | start = 1.0
255 | duration = 0.01
256 | factor = 4
257 |
258 | short = wave.segment(start=start, duration=duration)
259 | #short.plot()
260 |
261 | sampled = sample(short, factor)
262 | #sampled.plot_vlines(color='gray')
263 |
264 | spectrum = sampled.make_spectrum(full=True)
265 | boxcar = make_boxcar(spectrum, factor)
266 |
267 | sinc = boxcar.make_wave()
268 | sinc.shift(sampled.ts[0])
269 | sinc.roll(len(sinc)//2)
270 |
271 | thinkplot.preplot(2, cols=2)
272 | sinc.plot()
273 | thinkplot.config(xlabel='Time (s)')
274 |
275 | thinkplot.subplot(2)
276 | boxcar.plot()
277 | thinkplot.config(xlabel='Frequency (Hz)',
278 | ylim=[0, 1.05],
279 | xlim=[-boxcar.max_freq, boxcar.max_freq])
280 |
281 | thinkplot.save(root='sampling6',
282 | formats=FORMATS)
283 |
284 | return
285 |
286 | # CAUTION: don't call plot_sinc_demo with a large wave or it will
287 | # fill memory and crash
288 | plot_sinc_demo(short, 4)
289 | thinkplot.config(xlabel='Time (s)')
290 | thinkplot.save(root='sampling7',
291 | formats=FORMATS)
292 |
293 | start = short.start + 0.004
294 | duration = 0.00061
295 | plot_sinc_demo(short, 4, start, duration)
296 | thinkplot.config(xlabel='Time (s)',
297 | xlim=[start, start+duration],
298 | ylim=[-0.06, 0.17], legend=False)
299 | thinkplot.save(root='sampling8',
300 | formats=FORMATS)
301 |
302 |
303 | def kill_yticklabels():
304 | axis = plt.gca()
305 | plt.setp(axis.get_yticklabels(), visible=False)
306 |
307 |
308 | def show_impulses(wave, factor, i):
309 | thinkplot.subplot(i)
310 | thinkplot.preplot(2)
311 | impulses = make_impulses(wave, factor)
312 | impulses.segment(0, 0.001).plot_vlines(linewidth=2, xfactor=1000)
313 | if i == 1:
314 | thinkplot.config(title='Impulse train',
315 | ylim=[0, 1.05])
316 | else:
317 | thinkplot.config(xlabel='Time (ms)',
318 | ylim=[0, 1.05])
319 |
320 | thinkplot.subplot(i+1)
321 | impulses.make_spectrum(full=True).plot()
322 | kill_yticklabels()
323 | if i == 1:
324 | thinkplot.config(title='DFT of impulse train',
325 | xlim=[-22400, 22400])
326 | else:
327 | thinkplot.config(xlabel='Frequency (Hz)',
328 | xlim=[-22400, 22400])
329 |
330 |
331 | def plot_impulses(wave):
332 | thinkplot.preplot(rows=2, cols=2)
333 | show_impulses(wave, 4, 1)
334 | show_impulses(wave, 8, 3)
335 | thinkplot.save('sampling9',
336 | formats=FORMATS)
337 |
338 |
339 | def main():
340 | wave = thinkdsp.read_wave('328878__tzurkan__guitar-phrase-tzu.wav')
341 | wave.normalize()
342 |
343 | plot_sampling3(wave, 'sampling5')
344 | plot_sincs(wave)
345 |
346 | plot_beeps()
347 | plot_am()
348 |
349 | wave = thinkdsp.read_wave('263868__kevcio__amen-break-a-160-bpm.wav')
350 | wave.normalize()
351 | plot_impulses(wave)
352 |
353 | plot_sampling(wave, 'sampling3')
354 | plot_sampling2(wave, 'sampling4')
355 |
356 |
357 | if __name__ == '__main__':
358 | main()
359 |
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/code/sounds.py:
--------------------------------------------------------------------------------
1 | """This file contains code used in "Think DSP",
2 | by Allen B. Downey, available from greenteapress.com
3 |
4 | Copyright 2014 Allen B. Downey
5 | License: GNU GPLv3 http://www.gnu.org/licenses/gpl.html
6 | """
7 |
8 | from __future__ import print_function, division
9 |
10 | import thinkdsp
11 | import thinkplot
12 |
13 | FORMATS = ['pdf', 'eps']
14 |
15 |
16 | def plot_tuning(start=7.0, duration=0.006835):
17 | """Plots three cycles of a bell playing A4.
18 |
19 | start: start time in seconds
20 | duration: float
21 | """
22 | period = duration/3
23 | freq = 1/period
24 | print(period, freq)
25 | assert abs(freq - 438.917337235) < 1e-7
26 |
27 | wave = thinkdsp.read_wave('18871__zippi1__sound-bell-440hz.wav')
28 |
29 | segment = wave.segment(start, duration)
30 | segment.normalize()
31 |
32 | thinkplot.preplot(1)
33 | segment.plot()
34 | thinkplot.Save(root='sounds1',
35 | xlabel='Time (s)',
36 | axis=[start, start+duration, -1.05, 1.05],
37 | formats=FORMATS,
38 | legend=False)
39 |
40 |
41 | def plot_violin(start=1.30245, duration=0.00683):
42 | """Plots three cycles of a violin playing A4.
43 |
44 | duration: float
45 | """
46 | period = duration/3
47 | freq = 1/period
48 | print(period, freq)
49 | assert abs(freq - 439.238653001) < 1e-7
50 |
51 | wave = thinkdsp.read_wave('92002__jcveliz__violin-origional.wav')
52 |
53 | segment = wave.segment(start, duration)
54 | segment.normalize()
55 |
56 | thinkplot.preplot(1)
57 | segment.plot()
58 | thinkplot.Save(root='sounds2',
59 | xlabel='Time (s)',
60 | axis=[start, start+duration, -1.05, 1.05],
61 | formats=FORMATS,
62 | legend=False)
63 |
64 |
65 | def segment_violin(start=1.2, duration=0.6):
66 | """Load a violin recording and plot its spectrum.
67 |
68 | start: start time of the segment in seconds
69 | duration: in seconds
70 | """
71 | wave = thinkdsp.read_wave('92002__jcveliz__violin-origional.wav')
72 |
73 | # extract a segment
74 | segment = wave.segment(start, duration)
75 | segment.normalize()
76 |
77 | # plot the spectrum
78 | spectrum = segment.make_spectrum()
79 |
80 | thinkplot.preplot(1)
81 | spectrum.plot(high=10000)
82 | thinkplot.Save(root='sounds3',
83 | xlabel='Frequency (Hz)',
84 | ylabel='Amplitude',
85 | formats=FORMATS,
86 | legend=False)
87 |
88 | # print the top 5 peaks
89 | peaks = spectrum.peaks()
90 | for amp, freq in peaks[:10]:
91 | print(freq, amp)
92 | assert abs(peaks[0][0] - 3762.382899) < 1e-7
93 |
94 |
95 | def mix_cosines():
96 | """Plots three periods of a mix of cosines.
97 | """
98 |
99 | # create a SumSignal
100 | cos_sig = thinkdsp.CosSignal(freq=440, amp=1.0, offset=0)
101 | sin_sig = thinkdsp.SinSignal(freq=880, amp=0.5, offset=0)
102 |
103 | mix = sin_sig + cos_sig
104 |
105 | # create a wave
106 | wave = mix.make_wave(duration=1.0, start=0, framerate=11025)
107 | print('Number of samples', len(wave))
108 | print('Timestep in ms', 1000 / wave.framerate)
109 | assert len(wave) == wave.framerate
110 |
111 | # select a segment
112 | period = mix.period
113 | segment = wave.segment(start=0, duration=period*3)
114 |
115 | # plot the segment
116 | thinkplot.preplot(1)
117 | segment.plot()
118 | thinkplot.Save(root='sounds4',
119 | xlabel='Time (s)',
120 | axis=[0, period*3, -1.55, 1.55],
121 | formats=FORMATS,
122 | legend=False)
123 |
124 |
125 | def main():
126 | plot_tuning()
127 | plot_violin()
128 | segment_violin()
129 | mix_cosines()
130 |
131 |
132 | if __name__ == '__main__':
133 | main()
134 |
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/code/stalbans_a_mono.wav:
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https://raw.githubusercontent.com/AllenDowney/ThinkDSP/f1cc15de31f658d5df287332a30659fb16eb41d5/code/stalbans_a_mono.wav
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/code/systems.py:
--------------------------------------------------------------------------------
1 | """This file contains code used in "Think DSP",
2 | by Allen B. Downey, available from greenteapress.com
3 |
4 | Copyright 2014 Allen B. Downey
5 | License: GNU GPLv3 http://www.gnu.org/licenses/gpl.html
6 | """
7 |
8 | from __future__ import print_function, division
9 |
10 | import thinkdsp
11 | import thinkplot
12 |
13 | import numpy as np
14 |
15 |
16 | def plot_filter():
17 | """Plots the filter that corresponds to a 2-element moving average.
18 | """
19 | impulse = np.zeros(8)
20 | impulse[0] = 1
21 | wave = thinkdsp.Wave(impulse, framerate=8)
22 |
23 | impulse_spectrum = wave.make_spectrum(full=True)
24 | window_array = np.array([0.5, 0.5, 0, 0, 0, 0, 0, 0,])
25 | window = thinkdsp.Wave(window_array, framerate=8)
26 | filtr = window.make_spectrum(full=True)
27 |
28 | filtr.plot()
29 | thinkplot.config(xlabel='Frequency', ylabel='Amplitude')
30 | thinkplot.save('systems1')
31 |
32 |
33 | def read_response():
34 | """Reads the impulse response file and removes the initial silence.
35 | """
36 | response = thinkdsp.read_wave('180960__kleeb__gunshot.wav')
37 | start = 0.26
38 | response = response.segment(start=start)
39 | response.shift(-start)
40 | response.normalize()
41 | return response
42 |
43 |
44 | def plot_response(response):
45 | """Plots an input wave and the corresponding output.
46 | """
47 | thinkplot.preplot(cols=2)
48 | response.plot()
49 | thinkplot.config(xlabel='Time (s)',
50 | xlim=[0.26, response.end],
51 | ylim=[-1.05, 1.05])
52 |
53 | thinkplot.subplot(2)
54 | transfer = response.make_spectrum()
55 | transfer.plot()
56 | thinkplot.config(xlabel='Frequency (Hz)',
57 | xlim=[0, 22500],
58 | ylabel='Amplitude')
59 | thinkplot.save(root='systems6')
60 |
61 | violin = thinkdsp.read_wave('92002__jcveliz__violin-origional.wav')
62 |
63 | start = 0.11
64 | violin = violin.segment(start=start)
65 | violin.shift(-start)
66 |
67 | violin.truncate(len(response))
68 | violin.normalize()
69 | spectrum = violin.make_spectrum()
70 |
71 | output = (spectrum * transfer).make_wave()
72 | output.normalize()
73 |
74 | thinkplot.preplot(rows=2)
75 | violin.plot(label='input')
76 | thinkplot.config(xlim=[0, violin.end],
77 | ylim=[-1.05, 1.05])
78 |
79 | thinkplot.subplot(2)
80 | output.plot(label='output')
81 | thinkplot.config(xlabel='Time (s)',
82 | xlim=[0, violin.end],
83 | ylim=[-1.05, 1.05])
84 |
85 | thinkplot.save(root='systems7')
86 |
87 |
88 | def shifted_scaled(wave, shift, factor):
89 | res = wave.copy()
90 | res.shift(shift)
91 | res.scale(factor)
92 | return res
93 |
94 |
95 | def plot_convolution(response):
96 | """Plots the impulse response and a shifted, scaled copy.
97 | """
98 | shift = 1
99 | factor = 0.5
100 |
101 | gun2 = response + shifted_scaled(response, shift, factor)
102 | gun2.plot()
103 | thinkplot.config(xlabel='Time (s)',
104 | ylim=[-1.05, 1.05],
105 | legend=False)
106 | thinkplot.save(root='systems8')
107 |
108 |
109 | def plot_sawtooth(response):
110 | signal = thinkdsp.SawtoothSignal(freq=441)
111 | wave = signal.make_wave(duration=0.1, framerate=response.framerate)
112 |
113 | total = 0
114 | for t, y in zip(wave.ts, wave.ys):
115 | total += shifted_scaled(response, t, y)
116 |
117 | total.normalize()
118 |
119 | high = 5000
120 | wave.make_spectrum().plot(high=high, color='0.7', label='original')
121 | segment = total.segment(duration=0.2)
122 | segment.make_spectrum().plot(high=high, label='convolved')
123 | thinkplot.config(xlabel='Frequency (Hz)', ylabel='Amplitude')
124 | thinkplot.save(root='systems9')
125 |
126 |
127 | def main():
128 | plot_filter()
129 |
130 | response = read_response()
131 | plot_response(response)
132 | plot_convolution(response)
133 |
134 |
135 | if __name__ == '__main__':
136 | main()
137 |
--------------------------------------------------------------------------------
/code/thinkdsp_test.py:
--------------------------------------------------------------------------------
1 | """This file contains code for use with "Think Stats",
2 | by Allen B. Downey, available from greenteapress.com
3 |
4 | Copyright 2014 Allen B. Downey
5 | License: GNU GPLv3 http://www.gnu.org/licenses/gpl.html
6 | """
7 |
8 | from __future__ import print_function, division
9 |
10 | import unittest
11 | import thinkdsp
12 |
13 | import numpy as np
14 |
15 |
16 | class Test(unittest.TestCase):
17 | def assertArrayAlmostEqual(self, a, b):
18 | total_error = np.sum(np.abs(a-b))
19 | self.assertAlmostEqual(total_error, 0)
20 |
21 | def testMakeSpectrum(self):
22 | # rfft with n even
23 | ys = np.arange(10)
24 | wave = thinkdsp.Wave(ys, framerate=10)
25 | spectrum = wave.make_spectrum()
26 | self.assertAlmostEqual(spectrum.hs[0], 45)
27 | wave2 = spectrum.make_wave()
28 | #print(wave2.ys)
29 | self.assertArrayAlmostEqual(wave.ys, wave2.ys)
30 |
31 | # rfft with n odd
32 | ys = np.arange(11)
33 | wave = thinkdsp.Wave(ys, framerate=10)
34 | spectrum = wave.make_spectrum()
35 | self.assertAlmostEqual(spectrum.hs[0], 55)
36 |
37 | # TODO: make rfft invertible when n is odd
38 | #wave2 = spectrum.make_wave()
39 | #print(wave2.ys)
40 | #self.assertArrayAlmostEqual(wave.ys, wave2.ys)
41 |
42 | # fft with n even
43 | ys = np.arange(10)
44 | wave = thinkdsp.Wave(ys, framerate=10)
45 | spectrum = wave.make_spectrum(full=True)
46 | self.assertAlmostEqual(spectrum.hs[0], 45)
47 | wave2 = spectrum.make_wave()
48 | #print(wave2.ys)
49 | self.assertArrayAlmostEqual(wave.ys, wave2.ys)
50 |
51 | # fft with n odd
52 | ys = np.arange(11)
53 | wave = thinkdsp.Wave(ys, framerate=10)
54 | spectrum = wave.make_spectrum(full=True)
55 | self.assertAlmostEqual(spectrum.hs[0], 55)
56 | wave2 = spectrum.make_wave()
57 | #print(wave2.ys)
58 | self.assertArrayAlmostEqual(wave.ys, wave2.ys)
59 |
60 | def testComplexSinusoid(self):
61 | signal = thinkdsp.ComplexSinusoid(440, 0.7, 1.1)
62 | result = signal.evaluate(2.1) * complex(-1.5, -0.5)
63 | self.assertAlmostEqual(result, -0.164353351475-1.09452637056j)
64 |
65 | def testChirp(self):
66 | signal = thinkdsp.Chirp(100, 200, 0.5)
67 | result = signal.evaluate([1.001, 1.002, 1.005])
68 | self.assertAlmostEqual(result[0], 0.5)
69 | self.assertAlmostEqual(result[2], -0.49384417)
70 |
71 | def testExpoChirp(self):
72 | signal = thinkdsp.ExpoChirp(100, 200, 0.5)
73 | result = signal.evaluate([0, 0.001, 0.002])
74 | self.assertAlmostEqual(result[0], 0.5)
75 | self.assertAlmostEqual(result[2], -0.27167286)
76 |
77 | def testWaveAdd(self):
78 | ys = np.array([1, 2, 3, 4])
79 | wave1 = thinkdsp.Wave(ys, framerate=1)
80 | wave2 = wave1.copy()
81 | wave2.shift(2)
82 | wave = wave1 + wave2
83 |
84 | self.assertEqual(len(wave), 6)
85 | self.assertAlmostEqual(sum(wave.ys), 20)
86 |
87 | def testDct(self):
88 | signal = thinkdsp.CosSignal(freq=2)
89 | wave = signal.make_wave(duration=1, framerate=8)
90 | dct = wave.make_dct()
91 |
92 | self.assertAlmostEqual(dct.fs[0], 0.25)
93 |
94 | def testImpulses(self):
95 | imp_sig = thinkdsp.Impulses([0.01, 0.4, 0.8, 1.2],
96 | amps=[1, 0.5, 0.25, 0.1])
97 | impulses = imp_sig.make_wave(start=0, duration=1.3,
98 | framerate=11025)
99 |
100 | self.assertEqual(len(impulses), 14332)
101 |
102 |
103 | if __name__ == "__main__":
104 | unittest.main()
105 |
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/code/tos-redalert.wav:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/AllenDowney/ThinkDSP/f1cc15de31f658d5df287332a30659fb16eb41d5/code/tos-redalert.wav
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/environment.yml:
--------------------------------------------------------------------------------
1 | name: ThinkDSP
2 |
3 | dependencies:
4 | - python>=3.6
5 | - jupyter
6 | - numpy>=1.16
7 | - matplotlib
8 | - seaborn
9 | - pandas
10 | - scipy
11 |
12 |
--------------------------------------------------------------------------------
/pyproject.toml:
--------------------------------------------------------------------------------
1 | [tool.poetry]
2 | name = "thinkdsp"
3 | version = "0.1.0"
4 | description = ""
5 | authors = ["Allen Downey <allen.downey@olin.edu>"]
6 |
7 | [tool.poetry.dependencies]
8 | python = "^3.8"
9 | jupyter = "^1.0.0"
10 | numpy = "^1.19.4"
11 | matplotlib = "^3.3.3"
12 | seaborn = "^0.11.0"
13 | pandas = "^1.1.4"
14 | scipy = "^1.5.4"
15 |
16 | [tool.poetry.dev-dependencies]
17 |
18 | [build-system]
19 | requires = ["poetry>=0.12"]
20 | build-backend = "poetry.masonry.api"
21 |
--------------------------------------------------------------------------------
/requirements-dev.txt:
--------------------------------------------------------------------------------
1 | -r requirements.txt
2 | black
3 | flake8
4 | nbmake
5 | pytest
6 |
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/requirements.txt:
--------------------------------------------------------------------------------
1 | jupyter
2 | numpy
3 | matplotlib
4 | pandas
5 | scipy
6 |
--------------------------------------------------------------------------------