├── src ├── .gitignore ├── types.h ├── enumsFFT.h ├── defs.h ├── arduinoFFT.h └── arduinoFFT.cpp ├── .gitignore ├── CMakeLists.txt ├── library.properties ├── CITATION.cff ├── library.json ├── keywords.txt ├── README.md ├── Examples ├── FFT_03 │ └── FFT_03.ino ├── FFT_04 │ └── FFT_04.ino ├── FFT_speedup │ └── FFT_speedup.ino ├── FFT_01 │ └── FFT_01.ino ├── FFT_02 │ └── FFT_02.ino └── FFT_05 │ └── FFT_05.ino └── LICENSE /src/.gitignore: -------------------------------------------------------------------------------- 1 | /arduinoFFT.h.gch 2 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | /.project 2 | /sync.ffs_db 3 | *.*bak 4 | -------------------------------------------------------------------------------- /CMakeLists.txt: -------------------------------------------------------------------------------- 1 | set(src_dirs ./src) 2 | set(include_dirs ./src) 3 | idf_component_register(SRC_DIRS ${src_dirs} 4 | INCLUDE_DIRS ${include_dirs}) 5 | -------------------------------------------------------------------------------- /library.properties: -------------------------------------------------------------------------------- 1 | name=arduinoFFT 2 | version=2.0.4 3 | author=Enrique Condes 4 | maintainer=Enrique Condes 5 | sentence=A library for implementing floating point Fast Fourier Transform calculations on the Arduino framework. 6 | paragraph=With this library you can calculate the frequencies present on a sampled signal. 7 | category=Data Processing 8 | url=https://github.com/kosme/arduinoFFT 9 | architectures=* 10 | includes=arduinoFFT.h 11 | -------------------------------------------------------------------------------- /CITATION.cff: -------------------------------------------------------------------------------- 1 | # This CITATION.cff file was generated with cffinit. 2 | # Visit https://bit.ly/cffinit to generate yours today! 3 | 4 | cff-version: 1.2.0 5 | title: ArduinoFFT 6 | message: >- 7 | If you use this software, please cite it using the 8 | metadata from this file. 9 | type: software 10 | authors: 11 | - given-names: Enrique 12 | family-names: Condes Brena 13 | email: econdes@outlook.com 14 | affiliation: University of Texas at Austin 15 | orcid: 'https://orcid.org/0009-0002-4563-3250' 16 | identifiers: 17 | - type: doi 18 | value: 10.5281/zenodo.14195818 19 | repository-code: 'https://github.com/kosme/arduinoFFT' 20 | abstract: Fast Fourier Transform implementation for microcontrollers 21 | keywords: 22 | - fft 23 | - arduino 24 | - dsp 25 | license: GPL-3.0-or-later 26 | commit: 96701da 27 | version: 2.0.4 28 | date-released: '2024-11-21' 29 | -------------------------------------------------------------------------------- /library.json: -------------------------------------------------------------------------------- 1 | { 2 | "name": "arduinoFFT", 3 | "keywords": "FFT, Fourier, FDT, frequency", 4 | "description": "A library for implementing floating point Fast Fourier Transform calculations.", 5 | "repository": 6 | { 7 | "type": "git", 8 | "url": "https://github.com/kosme/arduinoFFT.git" 9 | }, 10 | "authors": 11 | [ 12 | { 13 | "name": "Enrique Condes", 14 | "email": "enrique@shapeoko.com", 15 | "maintainer": true 16 | }, 17 | { 18 | "name": "Didier Longueville", 19 | "url": "http://www.arduinoos.com/", 20 | "email": "contact@arduinoos.com" 21 | }, 22 | { 23 | "name": "Bim Overbohm", 24 | "url": "https://github.com/HorstBaerbel", 25 | "email": "bim.overbohm@googlemail.com" 26 | } 27 | ], 28 | "version": "2.0.4", 29 | "frameworks": ["arduino","mbed","espidf"], 30 | "platforms": "*", 31 | "headers": "arduinoFFT.h" 32 | } 33 | -------------------------------------------------------------------------------- /keywords.txt: -------------------------------------------------------------------------------- 1 | ####################################### 2 | # Syntax Coloring Map For arduinoFFT 3 | ####################################### 4 | 5 | ####################################### 6 | # Datatypes (KEYWORD1) 7 | ####################################### 8 | 9 | ArduinoFFT KEYWORD1 10 | FFTDirection KEYWORD1 11 | FFTWindow KEYWORD1 12 | 13 | ####################################### 14 | # Methods and Functions (KEYWORD2) 15 | ####################################### 16 | 17 | complexToMagnitude KEYWORD2 18 | compute KEYWORD2 19 | dcRemoval KEYWORD2 20 | majorPeak KEYWORD2 21 | majorPeakParabola KEYWORD2 22 | revision KEYWORD2 23 | setArrays KEYWORD2 24 | windowing KEYWORD2 25 | 26 | ####################################### 27 | # Constants (LITERAL1) 28 | ####################################### 29 | 30 | Forward LITERAL1 31 | Reverse LITERAL1 32 | 33 | Blackman LITERAL1 34 | Blackman_Harris LITERAL1 35 | Blackman_Nuttall LITERAL1 36 | Flat_top LITERAL1 37 | Hamming LITERAL1 38 | Hann LITERAL1 39 | Nuttall LITERAL1 40 | Rectangle LITERAL1 41 | Triangle LITERAL1 42 | Welch LITERAL1 43 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | arduinoFFT [![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.14195818.svg)](https://doi.org/10.5281/zenodo.14195818) 2 | ========== 3 | 4 | # Fast Fourier Transform for Arduino 5 | 6 | This is a fork from https://code.google.com/p/makefurt/ which has been abandoned since 2011. 7 | 8 | This is version 2.0 of the library, which has a different [API](#api). 9 | 10 | Tested on Arduino 1.8.19 and 2.3.2. 11 | 12 | ## Installation on Arduino 13 | 14 | Use the Arduino Library Manager to install and keep it updated. Just look for arduinoFFT. Only for Arduino 1.5+ 15 | 16 | ## Manual installation on Arduino 17 | 18 | To install this library, just place this entire folder as a subfolder in your Arduino installation. When installed, this library should look like: 19 | 20 | `Arduino\libraries\arduinoFFT` (this library's folder) 21 | `Arduino\libraries\arduinoFFT\src\arduinoFFT.h` (the library header file. include this in your project) 22 | `Arduino\libraries\arduinoFFT\keywords.txt` (the syntax coloring file) 23 | `Arduino\libraries\arduinoFFT\Examples` (the examples in the "open" menu) 24 | `Arduino\libraries\arduinoFFT\LICENSE` (GPL license file) 25 | `Arduino\libraries\arduinoFFT\README.md` (this file) 26 | 27 | ## Building on Arduino 28 | 29 | After this library is installed, you just have to start the Arduino application. 30 | You may see a few warning messages as it's built. 31 | To use this library in a sketch, go to the Sketch | Import Library menu and 32 | select arduinoFFT. This will add a corresponding line to the top of your sketch: 33 | 34 | `#include ` 35 | 36 | ## API 37 | 38 | Documentation was moved to the project's [wiki](https://github.com/kosme/arduinoFFT/wiki). 39 | -------------------------------------------------------------------------------- /src/types.h: -------------------------------------------------------------------------------- 1 | //useful things to include in code 2 | 3 | #ifndef TYPES_H 4 | #define TYPES_H 5 | 6 | #ifndef WIN32 7 | // true/false defines 8 | #define FALSE 0 9 | #define TRUE -1 10 | #endif 11 | 12 | // datatype definitions macros 13 | typedef unsigned char u08; 14 | typedef signed char s08; 15 | typedef unsigned short u16; 16 | typedef signed short s16; 17 | typedef unsigned long u32; 18 | typedef signed long s32; 19 | typedef unsigned long long u64; 20 | typedef signed long long s64; 21 | 22 | // #ifndef __AVR__ 23 | #ifdef __MBED__ 24 | // use inttypes.h instead 25 | // C99 standard integer type definitions 26 | typedef unsigned char uint8_t; 27 | typedef signed char int8_t; 28 | typedef unsigned short uint16_t; 29 | typedef signed short int16_t; 30 | /*typedef unsigned long uint32_t; 31 | typedef signed long int32_t; 32 | typedef unsigned long uint64_t; 33 | typedef signed long int64_t; 34 | */ 35 | #endif 36 | 37 | // maximum value that can be held 38 | // by unsigned data types (8,16,32bits) 39 | #define MAX_U08 255 40 | #define MAX_U16 65535 41 | #define MAX_U32 4294967295 42 | 43 | // maximum values that can be held 44 | // by signed data types (8,16,32bits) 45 | #define MIN_S08 -128 46 | #define MAX_S08 127 47 | #define MIN_S16 -32768 48 | #define MAX_S16 32767 49 | #define MIN_S32 -2147483648 50 | #define MAX_S32 2147483647 51 | 52 | #ifndef WIN32 53 | // more type redefinitions 54 | typedef unsigned char BOOL; 55 | typedef unsigned char BYTE; 56 | typedef unsigned int WORD; 57 | typedef unsigned long DWORD; 58 | 59 | typedef unsigned char UCHAR; 60 | typedef unsigned int UINT; 61 | typedef unsigned short USHORT; 62 | typedef unsigned long ULONG; 63 | 64 | typedef char CHAR; 65 | typedef int INT; 66 | typedef long LONG; 67 | #endif 68 | 69 | #endif 70 | -------------------------------------------------------------------------------- /src/enumsFFT.h: -------------------------------------------------------------------------------- 1 | #ifndef enumsFFT_h 2 | #define enumsFFT_h 3 | /* Custom constants */ 4 | /* These defines keep compatibility with pre 2.0 code */ 5 | #define FFT_FORWARD FFTDirection::Forward 6 | #define FFT_REVERSE FFTDirection::Reverse 7 | 8 | /* Windowing type */ 9 | #define FFT_WIN_TYP_RECTANGLE FFTWindow::Rectangle /* rectangle (Box car) */ 10 | #define FFT_WIN_TYP_HAMMING FFTWindow::Hamming /* hamming */ 11 | #define FFT_WIN_TYP_HANN FFTWindow::Hann /* hann */ 12 | #define FFT_WIN_TYP_TRIANGLE FFTWindow::Triangle /* triangle (Bartlett) */ 13 | #define FFT_WIN_TYP_NUTTALL FFTWindow::Nuttall /* nuttall */ 14 | #define FFT_WIN_TYP_BLACKMAN FFTWindow::Blackman /* blackman */ 15 | #define FFT_WIN_TYP_BLACKMAN_NUTTALL \ 16 | FFTWindow::Blackman_Nuttall /* blackman nuttall */ 17 | #define FFT_WIN_TYP_BLACKMAN_HARRIS \ 18 | FFTWindow::Blackman_Harris /* blackman harris*/ 19 | #define FFT_WIN_TYP_FLT_TOP FFTWindow::Flat_top /* flat top */ 20 | #define FFT_WIN_TYP_WELCH FFTWindow::Welch /* welch */ 21 | /* End of compatibility defines */ 22 | 23 | /* Mathematial constants */ 24 | #define twoPi 6.28318531 25 | #define fourPi 12.56637061 26 | #define sixPi 18.84955593 27 | 28 | enum class FFTWindow { 29 | Rectangle, // rectangle (Box car) 30 | Hamming, // hamming 31 | Hann, // hann 32 | Triangle, // triangle (Bartlett) 33 | Nuttall, // nuttall 34 | Blackman, // blackman 35 | Blackman_Nuttall, // blackman nuttall 36 | Blackman_Harris, // blackman harris 37 | Flat_top, // flat top 38 | Welch, // welch 39 | Precompiled // Placeholder for using custom or precompiled window values 40 | }; 41 | 42 | enum class FFTDirection { Forward, Reverse }; 43 | #endif -------------------------------------------------------------------------------- /src/defs.h: -------------------------------------------------------------------------------- 1 | /*! \file avrlibdefs.h \brief AVRlib global defines and macros. */ 2 | //***************************************************************************** 3 | // 4 | // File Name : 'avrlibdefs.h' 5 | // Title : AVRlib global defines and macros include file 6 | // Author : Pascal Stang 7 | // Created : 7/12/2001 8 | // Revised : 9/30/2002 9 | // Version : 1.1 10 | // Target MCU : Atmel AVR series 11 | // Editor Tabs : 4 12 | // 13 | // Description : This include file is designed to contain items useful to all 14 | // code files and projects, regardless of specific implementation. 15 | // 16 | // This code is distributed under the GNU Public License 17 | // which can be found at http://www.gnu.org/licenses/gpl.txt 18 | // 19 | //***************************************************************************** 20 | 21 | 22 | #ifndef AVRLIBDEFS_H 23 | #define AVRLIBDEFS_H 24 | 25 | //#define F_CPU 4000000 26 | #define MEM_TYPE 1 27 | 28 | // Code compatibility to new AVR-libc 29 | // outb(), inb(), inw(), outw(), BV(), sbi(), cbi(), sei(), cli() 30 | #ifndef outb 31 | #define outb(addr, data) addr = (data) 32 | #endif 33 | #ifndef inb 34 | #define inb(addr) (addr) 35 | #endif 36 | #ifndef outw 37 | #define outw(addr, data) addr = (data) 38 | #endif 39 | #ifndef inw 40 | #define inw(addr) (addr) 41 | #endif 42 | #ifndef BV 43 | #define BV(bit) (1<<(bit)) 44 | #endif 45 | //#ifndef cbi 46 | // #define cbi(reg,bit) reg &= ~(BV(bit)) 47 | //#endif 48 | //#ifndef sbi 49 | // #define sbi(reg,bit) reg |= (BV(bit)) 50 | //#endif 51 | #ifndef cli 52 | #define cli() __asm__ __volatile__ ("cli" ::) 53 | #endif 54 | #ifndef sei 55 | #define sei() __asm__ __volatile__ ("sei" ::) 56 | #endif 57 | 58 | // support for individual port pin naming in the mega128 59 | // see port128.h for details 60 | #ifdef __AVR_ATmega128__ 61 | // not currently necessary due to inclusion 62 | // of these defines in newest AVR-GCC 63 | // do a quick test to see if include is needed 64 | #ifndef PD0 65 | //#include "port128.h" 66 | #endif 67 | #endif 68 | 69 | // use this for packed structures 70 | // (this is seldom necessary on an 8-bit architecture like AVR, 71 | // but can assist in code portability to AVR) 72 | #define GNUC_PACKED __attribute__((packed)) 73 | 74 | // port address helpers 75 | #define DDR(x) ((x)-1) // address of data direction register of port x 76 | #define PIN(x) ((x)-2) // address of input register of port x 77 | 78 | // MIN/MAX/ABS macros 79 | #define MIN(a,b) ((ab)?(a):(b)) 81 | #define ABS(x) ((x>0)?(x):(-x)) 82 | 83 | // constants 84 | #define PI 3.14159265359 85 | 86 | //Math 87 | #define sq(x) ((x)*(x)) 88 | #define constrain(amt,low,high) ((amt)<(low)?(low):((amt)>(high)?(high):(amt))) 89 | 90 | #endif 91 | -------------------------------------------------------------------------------- /Examples/FFT_03/FFT_03.ino: -------------------------------------------------------------------------------- 1 | /* 2 | 3 | Example of use of the FFT library to compute FFT for a signal sampled through the ADC. 4 | 5 | Copyright (C) 2018 Enrique Condés and Ragnar Ranøyen Homb 6 | Copyright (C) 2020 Bim Overbohm (template, speed improvements) 7 | 8 | This program is free software: you can redistribute it and/or modify 9 | it under the terms of the GNU General Public License as published by 10 | the Free Software Foundation, either version 3 of the License, or 11 | (at your option) any later version. 12 | 13 | This program is distributed in the hope that it will be useful, 14 | but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | GNU General Public License for more details. 17 | 18 | You should have received a copy of the GNU General Public License 19 | along with this program. If not, see . 20 | 21 | */ 22 | 23 | #include "arduinoFFT.h" 24 | 25 | /* 26 | These values can be changed in order to evaluate the functions 27 | */ 28 | #define CHANNEL A0 29 | const uint16_t samples = 64; //This value MUST ALWAYS be a power of 2 30 | const double samplingFrequency = 100; //Hz, must be less than 10000 due to ADC 31 | unsigned int sampling_period_us; 32 | unsigned long microseconds; 33 | 34 | /* 35 | These are the input and output vectors 36 | Input vectors receive computed results from FFT 37 | */ 38 | double vReal[samples]; 39 | double vImag[samples]; 40 | 41 | /* Create FFT object */ 42 | ArduinoFFT FFT = ArduinoFFT(vReal, vImag, samples, samplingFrequency); 43 | 44 | #define SCL_INDEX 0x00 45 | #define SCL_TIME 0x01 46 | #define SCL_FREQUENCY 0x02 47 | #define SCL_PLOT 0x03 48 | 49 | void setup() 50 | { 51 | sampling_period_us = round(1000000*(1.0/samplingFrequency)); 52 | Serial.begin(115200); 53 | while(!Serial); 54 | Serial.println("Ready"); 55 | } 56 | 57 | void loop() 58 | { 59 | /*SAMPLING*/ 60 | microseconds = micros(); 61 | for(int i=0; i> 1), SCL_FREQUENCY); 84 | double x = FFT.majorPeak(); 85 | Serial.println(x, 6); //Print out what frequency is the most dominant. 86 | while(1); /* Run Once */ 87 | // delay(2000); /* Repeat after delay */ 88 | } 89 | 90 | void PrintVector(double *vData, uint16_t bufferSize, uint8_t scaleType) 91 | { 92 | for (uint16_t i = 0; i < bufferSize; i++) 93 | { 94 | double abscissa; 95 | /* Print abscissa value */ 96 | switch (scaleType) 97 | { 98 | case SCL_INDEX: 99 | abscissa = (i * 1.0); 100 | break; 101 | case SCL_TIME: 102 | abscissa = ((i * 1.0) / samplingFrequency); 103 | break; 104 | case SCL_FREQUENCY: 105 | abscissa = ((i * 1.0 * samplingFrequency) / samples); 106 | break; 107 | } 108 | Serial.print(abscissa, 6); 109 | if(scaleType==SCL_FREQUENCY) 110 | Serial.print("Hz"); 111 | Serial.print(" "); 112 | Serial.println(vData[i], 4); 113 | } 114 | Serial.println(); 115 | } 116 | -------------------------------------------------------------------------------- /Examples/FFT_04/FFT_04.ino: -------------------------------------------------------------------------------- 1 | /* 2 | 3 | Example of use of the FFT library 4 | 5 | Copyright (C) 2018 Enrique Condes 6 | Copyright (C) 2020 Bim Overbohm (template, speed improvements) 7 | 8 | This program is free software: you can redistribute it and/or modify 9 | it under the terms of the GNU General Public License as published by 10 | the Free Software Foundation, either version 3 of the License, or 11 | (at your option) any later version. 12 | 13 | This program is distributed in the hope that it will be useful, 14 | but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | GNU General Public License for more details. 17 | 18 | You should have received a copy of the GNU General Public License 19 | along with this program. If not, see . 20 | 21 | */ 22 | 23 | /* 24 | In this example, the Arduino simulates the sampling of a sinusoidal 1000 Hz 25 | signal with an amplitude of 100, sampled at 5000 Hz. Samples are stored 26 | inside the vReal array. The samples are windowed according to Hamming 27 | function. The FFT is computed using the windowed samples. Then the magnitudes 28 | of each of the frequencies that compose the signal are calculated. Finally, 29 | the frequency spectrum magnitudes are printed. If you use the Arduino IDE 30 | serial plotter, you will see a single spike corresponding to the 1000 Hz 31 | frequency. 32 | */ 33 | 34 | #include "arduinoFFT.h" 35 | 36 | /* 37 | These values can be changed in order to evaluate the functions 38 | */ 39 | const uint16_t samples = 64; //This value MUST ALWAYS be a power of 2 40 | const double signalFrequency = 1000; 41 | const double samplingFrequency = 5000; 42 | const uint8_t amplitude = 100; 43 | 44 | /* 45 | These are the input and output vectors 46 | Input vectors receive computed results from FFT 47 | */ 48 | double vReal[samples]; 49 | double vImag[samples]; 50 | 51 | ArduinoFFT FFT = ArduinoFFT(vReal, vImag, samples, samplingFrequency); 52 | 53 | #define SCL_INDEX 0x00 54 | #define SCL_TIME 0x01 55 | #define SCL_FREQUENCY 0x02 56 | #define SCL_PLOT 0x03 57 | 58 | void setup() 59 | { 60 | Serial.begin(115200); 61 | while(!Serial); 62 | Serial.println("Ready"); 63 | } 64 | 65 | void loop() 66 | { 67 | /* Build raw data */ 68 | double ratio = twoPi * signalFrequency / samplingFrequency; // Fraction of a complete cycle stored at each sample (in radians) 69 | for (uint16_t i = 0; i < samples; i++) 70 | { 71 | vReal[i] = int8_t(amplitude * sin(i * ratio) / 2.0);/* Build data with positive and negative values*/ 72 | //vReal[i] = uint8_t((amplitude * (sin(i * ratio) + 1.0)) / 2.0);/* Build data displaced on the Y axis to include only positive values*/ 73 | vImag[i] = 0.0; //Imaginary part must be zeroed in case of looping to avoid wrong calculations and overflows 74 | } 75 | FFT.windowing(FFTWindow::Hamming, FFTDirection::Forward); /* Weigh data */ 76 | FFT.compute(FFTDirection::Forward); /* Compute FFT */ 77 | FFT.complexToMagnitude(); /* Compute magnitudes */ 78 | PrintVector(vReal, samples>>1, SCL_PLOT); 79 | double x = FFT.majorPeak(); 80 | while(1); /* Run Once */ 81 | // delay(2000); /* Repeat after delay */ 82 | } 83 | 84 | void PrintVector(double *vData, uint16_t bufferSize, uint8_t scaleType) 85 | { 86 | for (uint16_t i = 0; i < bufferSize; i++) 87 | { 88 | double abscissa; 89 | /* Print abscissa value */ 90 | switch (scaleType) 91 | { 92 | case SCL_INDEX: 93 | abscissa = (i * 1.0); 94 | break; 95 | case SCL_TIME: 96 | abscissa = ((i * 1.0) / samplingFrequency); 97 | break; 98 | case SCL_FREQUENCY: 99 | abscissa = ((i * 1.0 * samplingFrequency) / samples); 100 | break; 101 | } 102 | if(scaleType!=SCL_PLOT) 103 | { 104 | Serial.print(abscissa, 6); 105 | if(scaleType==SCL_FREQUENCY) 106 | Serial.print("Hz"); 107 | Serial.print(" "); 108 | } 109 | Serial.println(vData[i], 4); 110 | } 111 | Serial.println(); 112 | } 113 | -------------------------------------------------------------------------------- /Examples/FFT_speedup/FFT_speedup.ino: -------------------------------------------------------------------------------- 1 | /* 2 | 3 | Example of use of the FFT library to compute FFT for a signal sampled through the ADC 4 | with speedup through different arduinoFFT options. Based on examples/FFT_03/FFT_03.ino 5 | 6 | Copyright (C) 2020 Bim Overbohm (template, speed improvements) 7 | 8 | This program is free software: you can redistribute it and/or modify 9 | it under the terms of the GNU General Public License as published by 10 | the Free Software Foundation, either version 3 of the License, or 11 | (at your option) any later version. 12 | 13 | This program is distributed in the hope that it will be useful, 14 | but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | GNU General Public License for more details. 17 | 18 | You should have received a copy of the GNU General Public License 19 | along with this program. If not, see . 20 | 21 | */ 22 | 23 | // There are two speedup options for some of the FFT code: 24 | 25 | // Define this to use reciprocal multiplication for division and some more speedups that might decrease precision 26 | //#define FFT_SPEED_OVER_PRECISION 27 | 28 | // Define this to use a low-precision square root approximation instead of the regular sqrt() call 29 | // This might only work for specific use cases, but is significantly faster. Only works for ArduinoFFT. 30 | //#define FFT_SQRT_APPROXIMATION 31 | 32 | #include "arduinoFFT.h" 33 | 34 | /* 35 | These values can be changed in order to evaluate the functions 36 | */ 37 | #define CHANNEL A0 38 | const uint16_t samples = 64; //This value MUST ALWAYS be a power of 2 39 | const float samplingFrequency = 100; //Hz, must be less than 10000 due to ADC 40 | unsigned int sampling_period_us; 41 | unsigned long microseconds; 42 | 43 | /* 44 | These are the input and output vectors 45 | Input vectors receive computed results from FFT 46 | */ 47 | float vReal[samples]; 48 | float vImag[samples]; 49 | 50 | /* Create FFT object with weighing factor storage */ 51 | ArduinoFFT FFT = ArduinoFFT(vReal, vImag, samples, samplingFrequency, true); 52 | 53 | #define SCL_INDEX 0x00 54 | #define SCL_TIME 0x01 55 | #define SCL_FREQUENCY 0x02 56 | #define SCL_PLOT 0x03 57 | 58 | void setup() 59 | { 60 | sampling_period_us = round(1000000*(1.0/samplingFrequency)); 61 | Serial.begin(115200); 62 | Serial.println("Ready"); 63 | } 64 | 65 | void loop() 66 | { 67 | /*SAMPLING*/ 68 | microseconds = micros(); 69 | for(int i=0; i> 1), SCL_FREQUENCY); 92 | float x = FFT.majorPeak(); 93 | Serial.println(x, 6); //Print out what frequency is the most dominant. 94 | while(1); /* Run Once */ 95 | // delay(2000); /* Repeat after delay */ 96 | } 97 | 98 | void PrintVector(float *vData, uint16_t bufferSize, uint8_t scaleType) 99 | { 100 | for (uint16_t i = 0; i < bufferSize; i++) 101 | { 102 | float abscissa; 103 | /* Print abscissa value */ 104 | switch (scaleType) 105 | { 106 | case SCL_INDEX: 107 | abscissa = (i * 1.0); 108 | break; 109 | case SCL_TIME: 110 | abscissa = ((i * 1.0) / samplingFrequency); 111 | break; 112 | case SCL_FREQUENCY: 113 | abscissa = ((i * 1.0 * samplingFrequency) / samples); 114 | break; 115 | } 116 | Serial.print(abscissa, 6); 117 | if(scaleType==SCL_FREQUENCY) 118 | Serial.print("Hz"); 119 | Serial.print(" "); 120 | Serial.println(vData[i], 4); 121 | } 122 | Serial.println(); 123 | } 124 | -------------------------------------------------------------------------------- /Examples/FFT_01/FFT_01.ino: -------------------------------------------------------------------------------- 1 | /* 2 | 3 | Example of use of the FFT library 4 | 5 | Copyright (C) 2014 Enrique Condes 6 | Copyright (C) 2020 Bim Overbohm (template, speed improvements) 7 | 8 | This program is free software: you can redistribute it and/or modify 9 | it under the terms of the GNU General Public License as published by 10 | the Free Software Foundation, either version 3 of the License, or 11 | (at your option) any later version. 12 | 13 | This program is distributed in the hope that it will be useful, 14 | but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | GNU General Public License for more details. 17 | 18 | You should have received a copy of the GNU General Public License 19 | along with this program. If not, see . 20 | 21 | */ 22 | 23 | /* 24 | In this example, the Arduino simulates the sampling of a sinusoidal 1000 Hz 25 | signal with an amplitude of 100, sampled at 5000 Hz. Samples are stored 26 | inside the vReal array. The samples are windowed according to Hamming 27 | function. The FFT is computed using the windowed samples. Then the magnitudes 28 | of each of the frequencies that compose the signal are calculated. Finally, 29 | the frequency with the highest peak is obtained, being that the main frequency 30 | present in the signal. 31 | */ 32 | 33 | #include "arduinoFFT.h" 34 | 35 | /* 36 | These values can be changed in order to evaluate the functions 37 | */ 38 | const uint16_t samples = 64; //This value MUST ALWAYS be a power of 2 39 | const double signalFrequency = 1000; 40 | const double samplingFrequency = 5000; 41 | const uint8_t amplitude = 100; 42 | 43 | /* 44 | These are the input and output vectors 45 | Input vectors receive computed results from FFT 46 | */ 47 | double vReal[samples]; 48 | double vImag[samples]; 49 | 50 | /* Create FFT object */ 51 | ArduinoFFT FFT = ArduinoFFT(vReal, vImag, samples, samplingFrequency); 52 | 53 | #define SCL_INDEX 0x00 54 | #define SCL_TIME 0x01 55 | #define SCL_FREQUENCY 0x02 56 | #define SCL_PLOT 0x03 57 | 58 | void setup() 59 | { 60 | Serial.begin(115200); 61 | while(!Serial); 62 | Serial.println("Ready"); 63 | } 64 | 65 | void loop() 66 | { 67 | /* Build raw data */ 68 | double ratio = twoPi * signalFrequency / samplingFrequency; // Fraction of a complete cycle stored at each sample (in radians) 69 | for (uint16_t i = 0; i < samples; i++) 70 | { 71 | vReal[i] = int8_t(amplitude * sin(i * ratio) / 2.0);/* Build data with positive and negative values*/ 72 | //vReal[i] = uint8_t((amplitude * (sin(i * ratio) + 1.0)) / 2.0);/* Build data displaced on the Y axis to include only positive values*/ 73 | vImag[i] = 0.0; //Imaginary part must be zeroed in case of looping to avoid wrong calculations and overflows 74 | } 75 | /* Print the results of the simulated sampling according to time */ 76 | Serial.println("Data:"); 77 | PrintVector(vReal, samples, SCL_TIME); 78 | FFT.windowing(FFTWindow::Hamming, FFTDirection::Forward); /* Weigh data */ 79 | Serial.println("Weighed data:"); 80 | PrintVector(vReal, samples, SCL_TIME); 81 | FFT.compute(FFTDirection::Forward); /* Compute FFT */ 82 | Serial.println("Computed Real values:"); 83 | PrintVector(vReal, samples, SCL_INDEX); 84 | Serial.println("Computed Imaginary values:"); 85 | PrintVector(vImag, samples, SCL_INDEX); 86 | FFT.complexToMagnitude(); /* Compute magnitudes */ 87 | Serial.println("Computed magnitudes:"); 88 | PrintVector(vReal, (samples >> 1), SCL_FREQUENCY); 89 | double x = FFT.majorPeak(); 90 | Serial.println(x, 6); 91 | while(1); /* Run Once */ 92 | // delay(2000); /* Repeat after delay */ 93 | } 94 | 95 | void PrintVector(double *vData, uint16_t bufferSize, uint8_t scaleType) 96 | { 97 | for (uint16_t i = 0; i < bufferSize; i++) 98 | { 99 | double abscissa; 100 | /* Print abscissa value */ 101 | switch (scaleType) 102 | { 103 | case SCL_INDEX: 104 | abscissa = (i * 1.0); 105 | break; 106 | case SCL_TIME: 107 | abscissa = ((i * 1.0) / samplingFrequency); 108 | break; 109 | case SCL_FREQUENCY: 110 | abscissa = ((i * 1.0 * samplingFrequency) / samples); 111 | break; 112 | } 113 | Serial.print(abscissa, 6); 114 | if(scaleType==SCL_FREQUENCY) 115 | Serial.print("Hz"); 116 | Serial.print(" "); 117 | Serial.println(vData[i], 4); 118 | } 119 | Serial.println(); 120 | } 121 | -------------------------------------------------------------------------------- /Examples/FFT_02/FFT_02.ino: -------------------------------------------------------------------------------- 1 | /* 2 | 3 | Example of use of the FFT library to compute FFT for several signals over a range of frequencies. 4 | The exponent is calculated once before the execution since it is a constant. 5 | This saves resources during the execution of the sketch and reduces the compiled size. 6 | The sketch shows the time that the computing is taking. 7 | 8 | Copyright (C) 2014 Enrique Condes 9 | Copyright (C) 2020 Bim Overbohm (template, speed improvements) 10 | 11 | This program is free software: you can redistribute it and/or modify 12 | it under the terms of the GNU General Public License as published by 13 | the Free Software Foundation, either version 3 of the License, or 14 | (at your option) any later version. 15 | 16 | This program is distributed in the hope that it will be useful, 17 | but WITHOUT ANY WARRANTY; without even the implied warranty of 18 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 19 | GNU General Public License for more details. 20 | 21 | You should have received a copy of the GNU General Public License 22 | along with this program. If not, see . 23 | 24 | */ 25 | 26 | #include "arduinoFFT.h" 27 | 28 | /* 29 | These values can be changed in order to evaluate the functions 30 | */ 31 | const uint16_t samples = 64; 32 | const double sampling = 40; 33 | const uint8_t amplitude = 4; 34 | const double startFrequency = 2; 35 | const double stopFrequency = 16.4; 36 | const double step_size = 0.1; 37 | 38 | /* 39 | These are the input and output vectors 40 | Input vectors receive computed results from FFT 41 | */ 42 | double vReal[samples]; 43 | double vImag[samples]; 44 | 45 | /* Create FFT object */ 46 | ArduinoFFT FFT = ArduinoFFT(vReal, vImag, samples, sampling); 47 | 48 | unsigned long startTime; 49 | 50 | #define SCL_INDEX 0x00 51 | #define SCL_TIME 0x01 52 | #define SCL_FREQUENCY 0x02 53 | #define SCL_PLOT 0x03 54 | 55 | void setup() 56 | { 57 | Serial.begin(115200); 58 | while(!Serial); 59 | Serial.println("Ready"); 60 | } 61 | 62 | void loop() 63 | { 64 | Serial.println("Frequency\tDetected\ttakes (ms)"); 65 | Serial.println("=======================================\n"); 66 | for(double frequency = startFrequency; frequency<=stopFrequency; frequency+=step_size) 67 | { 68 | /* Build raw data */ 69 | double ratio = twoPi * frequency / sampling; // Fraction of a complete cycle stored at each sample (in radians) 70 | for (uint16_t i = 0; i < samples; i++) 71 | { 72 | vReal[i] = int8_t(amplitude * sin(i * ratio) / 2.0);/* Build data with positive and negative values*/ 73 | vImag[i] = 0; //Reset the imaginary values vector for each new frequency 74 | } 75 | /*Serial.println("Data:"); 76 | PrintVector(vReal, samples, SCL_TIME);*/ 77 | startTime=millis(); 78 | FFT.windowing(FFTWindow::Hamming, FFTDirection::Forward); /* Weigh data */ 79 | /*Serial.println("Weighed data:"); 80 | PrintVector(vReal, samples, SCL_TIME);*/ 81 | FFT.compute(FFTDirection::Forward); /* Compute FFT */ 82 | /*Serial.println("Computed Real values:"); 83 | PrintVector(vReal, samples, SCL_INDEX); 84 | Serial.println("Computed Imaginary values:"); 85 | PrintVector(vImag, samples, SCL_INDEX);*/ 86 | FFT.complexToMagnitude(); /* Compute magnitudes */ 87 | /*Serial.println("Computed magnitudes:"); 88 | PrintVector(vReal, (samples >> 1), SCL_FREQUENCY);*/ 89 | double x = FFT.majorPeak(); 90 | Serial.print(frequency); 91 | Serial.print(": \t\t"); 92 | Serial.print(x, 4); 93 | Serial.print("\t\t"); 94 | Serial.print(millis()-startTime); 95 | Serial.println(" ms"); 96 | // delay(2000); /* Repeat after delay */ 97 | } 98 | while(1); /* Run Once */ 99 | } 100 | 101 | void PrintVector(double *vData, uint16_t bufferSize, uint8_t scaleType) 102 | { 103 | for (uint16_t i = 0; i < bufferSize; i++) 104 | { 105 | double abscissa; 106 | /* Print abscissa value */ 107 | switch (scaleType) 108 | { 109 | case SCL_INDEX: 110 | abscissa = (i * 1.0); 111 | break; 112 | case SCL_TIME: 113 | abscissa = ((i * 1.0) / sampling); 114 | break; 115 | case SCL_FREQUENCY: 116 | abscissa = ((i * 1.0 * sampling) / samples); 117 | break; 118 | } 119 | Serial.print(abscissa, 6); 120 | if(scaleType==SCL_FREQUENCY) 121 | Serial.print("Hz"); 122 | Serial.print(" "); 123 | Serial.println(vData[i], 4); 124 | } 125 | Serial.println(); 126 | } 127 | -------------------------------------------------------------------------------- /Examples/FFT_05/FFT_05.ino: -------------------------------------------------------------------------------- 1 | /* 2 | 3 | Example of use of the FFT library 4 | 5 | Copyright (C) 2014 Enrique Condes 6 | Copyright (C) 2020 Bim Overbohm (template, speed improvements) 7 | 8 | This program is free software: you can redistribute it and/or modify 9 | it under the terms of the GNU General Public License as published by 10 | the Free Software Foundation, either version 3 of the License, or 11 | (at your option) any later version. 12 | 13 | This program is distributed in the hope that it will be useful, 14 | but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | GNU General Public License for more details. 17 | 18 | You should have received a copy of the GNU General Public License 19 | along with this program. If not, see . 20 | 21 | */ 22 | 23 | /* 24 | In this example, the Arduino simulates the sampling of a sinusoidal 1000 Hz 25 | signal with an amplitude of 100, sampled at 5000 Hz. Samples are stored 26 | inside the vReal array. The samples are windowed according to Hamming 27 | function. The FFT is computed using the windowed samples. Then the magnitudes 28 | of each of the frequencies that compose the signal are calculated. Finally, 29 | the frequency with the highest peak is obtained, being that the main frequency 30 | present in the signal. This frequency is printed, along with the magnitude of 31 | the peak. 32 | */ 33 | 34 | #include "arduinoFFT.h" 35 | 36 | /* 37 | These values can be changed in order to evaluate the functions 38 | */ 39 | const uint16_t samples = 64; //This value MUST ALWAYS be a power of 2 40 | const double signalFrequency = 1000; 41 | const double samplingFrequency = 5000; 42 | const uint8_t amplitude = 100; 43 | 44 | /* 45 | These are the input and output vectors 46 | Input vectors receive computed results from FFT 47 | */ 48 | double vReal[samples]; 49 | double vImag[samples]; 50 | 51 | /* Create FFT object */ 52 | ArduinoFFT FFT = ArduinoFFT(vReal, vImag, samples, samplingFrequency); 53 | 54 | #define SCL_INDEX 0x00 55 | #define SCL_TIME 0x01 56 | #define SCL_FREQUENCY 0x02 57 | #define SCL_PLOT 0x03 58 | 59 | void setup() 60 | { 61 | Serial.begin(115200); 62 | while(!Serial); 63 | Serial.println("Ready"); 64 | } 65 | 66 | void loop() 67 | { 68 | /* Build raw data */ 69 | double ratio = twoPi * signalFrequency / samplingFrequency; // Fraction of a complete cycle stored at each sample (in radians) 70 | for (uint16_t i = 0; i < samples; i++) 71 | { 72 | vReal[i] = int8_t(amplitude * sin(i * ratio) / 2.0);/* Build data with positive and negative values*/ 73 | //vReal[i] = uint8_t((amplitude * (sin(i * ratio) + 1.0)) / 2.0);/* Build data displaced on the Y axis to include only positive values*/ 74 | vImag[i] = 0.0; //Imaginary part must be zeroed in case of looping to avoid wrong calculations and overflows 75 | } 76 | /* Print the results of the simulated sampling according to time */ 77 | Serial.println("Data:"); 78 | PrintVector(vReal, samples, SCL_TIME); 79 | FFT.windowing(FFTWindow::Hamming, FFTDirection::Forward); /* Weigh data */ 80 | Serial.println("Weighed data:"); 81 | PrintVector(vReal, samples, SCL_TIME); 82 | FFT.compute(FFTDirection::Forward); /* Compute FFT */ 83 | Serial.println("Computed Real values:"); 84 | PrintVector(vReal, samples, SCL_INDEX); 85 | Serial.println("Computed Imaginary values:"); 86 | PrintVector(vImag, samples, SCL_INDEX); 87 | FFT.complexToMagnitude(); /* Compute magnitudes */ 88 | Serial.println("Computed magnitudes:"); 89 | PrintVector(vReal, (samples >> 1), SCL_FREQUENCY); 90 | double x; 91 | double v; 92 | FFT.majorPeak(&x, &v); 93 | Serial.print(x, 6); 94 | Serial.print(", "); 95 | Serial.println(v, 6); 96 | while(1); /* Run Once */ 97 | // delay(2000); /* Repeat after delay */ 98 | } 99 | 100 | void PrintVector(double *vData, uint16_t bufferSize, uint8_t scaleType) 101 | { 102 | for (uint16_t i = 0; i < bufferSize; i++) 103 | { 104 | double abscissa; 105 | /* Print abscissa value */ 106 | switch (scaleType) 107 | { 108 | case SCL_INDEX: 109 | abscissa = (i * 1.0); 110 | break; 111 | case SCL_TIME: 112 | abscissa = ((i * 1.0) / samplingFrequency); 113 | break; 114 | case SCL_FREQUENCY: 115 | abscissa = ((i * 1.0 * samplingFrequency) / samples); 116 | break; 117 | } 118 | Serial.print(abscissa, 6); 119 | if(scaleType==SCL_FREQUENCY) 120 | Serial.print("Hz"); 121 | Serial.print(" "); 122 | Serial.println(vData[i], 4); 123 | } 124 | Serial.println(); 125 | } 126 | -------------------------------------------------------------------------------- /src/arduinoFFT.h: -------------------------------------------------------------------------------- 1 | /* 2 | 3 | FFT library 4 | Copyright (C) 2010 Didier Longueville 5 | Copyright (C) 2014 Enrique Condes 6 | Copyright (C) 2020 Bim Overbohm (template, speed improvements) 7 | 8 | This program is free software: you can redistribute it and/or modify 9 | it under the terms of the GNU General Public License as published by 10 | the Free Software Foundation, either version 3 of the License, or 11 | (at your option) any later version. 12 | 13 | This program is distributed in the hope that it will be useful, 14 | but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | GNU General Public License for more details. 17 | 18 | You should have received a copy of the GNU General Public License 19 | along with this program. If not, see . 20 | 21 | */ 22 | 23 | #ifndef ArduinoFFT_h /* Prevent loading library twice */ 24 | #define ArduinoFFT_h 25 | #ifdef ARDUINO 26 | #if ARDUINO >= 100 27 | #include "Arduino.h" 28 | #else 29 | #include "WProgram.h" /* This is where the standard Arduino code lies */ 30 | #endif 31 | #else 32 | #include 33 | #include 34 | 35 | #ifdef __AVR__ 36 | #include 37 | #include 38 | #endif 39 | #include "defs.h" 40 | #include "types.h" 41 | #include 42 | #include 43 | #endif 44 | #include "enumsFFT.h" 45 | 46 | // This definition uses a low-precision square root approximation instead of the 47 | // regular sqrt() call 48 | // This might only work for specific use cases, but is significantly faster. 49 | 50 | #ifndef FFT_SQRT_APPROXIMATION 51 | #ifndef sqrt_internal 52 | #define sqrt_internal sqrt 53 | #endif 54 | #endif 55 | 56 | #define FFT_LIB_REV 0x20 57 | 58 | template class ArduinoFFT { 59 | public: 60 | ArduinoFFT(); 61 | ArduinoFFT(T *vReal, T *vImag, uint_fast16_t samples, T samplingFrequency, 62 | bool windowingFactors = false); 63 | 64 | ~ArduinoFFT(); 65 | 66 | void complexToMagnitude(void) const; 67 | void complexToMagnitude(T *vReal, T *vImag, uint_fast16_t samples) const; 68 | 69 | void compute(FFTDirection dir) const; 70 | void compute(T *vReal, T *vImag, uint_fast16_t samples, 71 | FFTDirection dir) const; 72 | void compute(T *vReal, T *vImag, uint_fast16_t samples, uint_fast8_t power, 73 | FFTDirection dir) const; 74 | 75 | void dcRemoval(void) const; 76 | void dcRemoval(T *vData, uint_fast16_t samples) const; 77 | 78 | T majorPeak(void) const; 79 | void majorPeak(T *f, T *v) const; 80 | T majorPeak(T *vData, uint_fast16_t samples, T samplingFrequency) const; 81 | void majorPeak(T *vData, uint_fast16_t samples, T samplingFrequency, 82 | T *frequency, T *magnitude) const; 83 | 84 | T majorPeakParabola(void) const; 85 | void majorPeakParabola(T *frequency, T *magnitude) const; 86 | T majorPeakParabola(T *vData, uint_fast16_t samples, 87 | T samplingFrequency) const; 88 | void majorPeakParabola(T *vData, uint_fast16_t samples, T samplingFrequency, 89 | T *frequency, T *magnitude) const; 90 | 91 | uint8_t revision(void); 92 | 93 | void setArrays(T *vReal, T *vImag, uint_fast16_t samples = 0); 94 | 95 | void windowing(FFTWindow windowType, FFTDirection dir, 96 | bool withCompensation = false); 97 | void windowing(T *vData, uint_fast16_t samples, FFTWindow windowType, 98 | FFTDirection dir, T *windowingFactors = nullptr, 99 | bool withCompensation = false); 100 | 101 | private: 102 | /* Variables */ 103 | static const T _WindowCompensationFactors[11]; 104 | #ifdef FFT_SPEED_OVER_PRECISION 105 | T _oneOverSamples = 0.0; 106 | #endif 107 | bool _isPrecompiled = false; 108 | bool _precompiledWithCompensation = false; 109 | uint_fast8_t _power = 0; 110 | T *_precompiledWindowingFactors = nullptr; 111 | uint_fast16_t _samples; 112 | T _samplingFrequency; 113 | T *_vImag; 114 | T *_vReal; 115 | FFTWindow _windowFunction; 116 | /* Functions */ 117 | uint_fast8_t exponent(uint_fast16_t value) const; 118 | void findMaxY(T *vData, uint_fast16_t length, T *maxY, 119 | uint_fast16_t *index) const; 120 | void parabola(T x1, T y1, T x2, T y2, T x3, T y3, T *a, T *b, T *c) const; 121 | void swap(T *a, T *b) const; 122 | 123 | #ifdef FFT_SQRT_APPROXIMATION 124 | float sqrt_internal(float x) const; 125 | double sqrt_internal(double x) const; 126 | #endif 127 | }; 128 | 129 | #if defined(__AVR__) && defined(USE_AVR_PROGMEM) 130 | static const float _c1[] PROGMEM = { 131 | 0.0000000000, 0.7071067812, 0.9238795325, 0.9807852804, 0.9951847267, 132 | 0.9987954562, 0.9996988187, 0.9999247018, 0.9999811753, 0.9999952938, 133 | 0.9999988235, 0.9999997059, 0.9999999265, 0.9999999816, 0.9999999954, 134 | 0.9999999989, 0.9999999997}; 135 | static const float _c2[] PROGMEM = { 136 | 1.0000000000, 0.7071067812, 0.3826834324, 0.1950903220, 0.0980171403, 137 | 0.0490676743, 0.0245412285, 0.0122715383, 0.0061358846, 0.0030679568, 138 | 0.0015339802, 0.0007669903, 0.0003834952, 0.0001917476, 0.0000958738, 139 | 0.0000479369, 0.0000239684}; 140 | #endif 141 | 142 | #endif 143 | -------------------------------------------------------------------------------- /src/arduinoFFT.cpp: -------------------------------------------------------------------------------- 1 | /* 2 | FFT library 3 | Copyright (C) 2010 Didier Longueville 4 | Copyright (C) 2014 Enrique Condes 5 | Copyright (C) 2020 Bim Overbohm (template, speed improvements) 6 | 7 | This program is free software: you can redistribute it and/or modify 8 | it under the terms of the GNU General Public License as published by 9 | the Free Software Foundation, either version 3 of the License, or 10 | (at your option) any later version. 11 | 12 | This program is distributed in the hope that it will be useful, 13 | but WITHOUT ANY WARRANTY; without even the implied warranty of 14 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15 | GNU General Public License for more details. 16 | 17 | You should have received a copy of the GNU General Public License 18 | along with this program. If not, see . 19 | 20 | */ 21 | 22 | #include "arduinoFFT.h" 23 | 24 | template ArduinoFFT::ArduinoFFT() {} 25 | 26 | template 27 | ArduinoFFT::ArduinoFFT(T *vReal, T *vImag, uint_fast16_t samples, 28 | T samplingFrequency, bool windowingFactors) 29 | : _samples(samples), _samplingFrequency(samplingFrequency), _vImag(vImag), 30 | _vReal(vReal) { 31 | if (windowingFactors) { 32 | _precompiledWindowingFactors = new T[samples / 2]; 33 | } 34 | _power = exponent(samples); 35 | #ifdef FFT_SPEED_OVER_PRECISION 36 | _oneOverSamples = 1.0 / samples; 37 | #endif 38 | } 39 | 40 | template ArduinoFFT::~ArduinoFFT(void) { 41 | // Destructor 42 | if (_precompiledWindowingFactors) { 43 | delete[] _precompiledWindowingFactors; 44 | } 45 | } 46 | 47 | template void ArduinoFFT::complexToMagnitude(void) const { 48 | complexToMagnitude(this->_vReal, this->_vImag, this->_samples); 49 | } 50 | 51 | template 52 | void ArduinoFFT::complexToMagnitude(T *vReal, T *vImag, 53 | uint_fast16_t samples) const { 54 | // vM is half the size of vReal and vImag 55 | for (uint_fast16_t i = 0; i < (samples >> 1) + 1; i++) { 56 | vReal[i] = sqrt_internal(sq(vReal[i]) + sq(vImag[i])); 57 | } 58 | } 59 | 60 | template void ArduinoFFT::compute(FFTDirection dir) const { 61 | compute(this->_vReal, this->_vImag, this->_samples, exponent(this->_samples), 62 | dir); 63 | } 64 | 65 | template 66 | void ArduinoFFT::compute(T *vReal, T *vImag, uint_fast16_t samples, 67 | FFTDirection dir) const { 68 | compute(vReal, vImag, samples, exponent(samples), dir); 69 | } 70 | 71 | // Computes in-place complex-to-complex FFT 72 | template 73 | void ArduinoFFT::compute(T *vReal, T *vImag, uint_fast16_t samples, 74 | uint_fast8_t power, FFTDirection dir) const { 75 | #ifdef FFT_SPEED_OVER_PRECISION 76 | T oneOverSamples = this->_oneOverSamples; 77 | if (!this->_oneOverSamples) 78 | oneOverSamples = 1.0 / samples; 79 | #endif 80 | // Reverse bits 81 | uint_fast16_t j = 0; 82 | for (uint_fast16_t i = 0; i < (samples - 1); i++) { 83 | if (i < j) { 84 | swap(&vReal[i], &vReal[j]); 85 | #ifdef COMPLEX_INPUT 86 | swap(&vImag[i], &vImag[j]); 87 | #else 88 | if (dir == FFTDirection::Reverse) 89 | swap(&vImag[i], &vImag[j]); 90 | #endif 91 | } 92 | uint_fast16_t k = (samples >> 1); 93 | 94 | while (k <= j) { 95 | j -= k; 96 | k >>= 1; 97 | } 98 | j += k; 99 | } 100 | // Compute the FFT 101 | T c1 = -1.0; 102 | T c2 = 0.0; 103 | uint_fast16_t l2 = 1; 104 | for (uint_fast8_t l = 0; (l < power); l++) { 105 | uint_fast16_t l1 = l2; 106 | l2 <<= 1; 107 | T u1 = 1.0; 108 | T u2 = 0.0; 109 | for (j = 0; j < l1; j++) { 110 | for (uint_fast16_t i = j; i < samples; i += l2) { 111 | uint_fast16_t i1 = i + l1; 112 | T t1 = u1 * vReal[i1] - u2 * vImag[i1]; 113 | T t2 = u1 * vImag[i1] + u2 * vReal[i1]; 114 | vReal[i1] = vReal[i] - t1; 115 | vImag[i1] = vImag[i] - t2; 116 | vReal[i] += t1; 117 | vImag[i] += t2; 118 | } 119 | T z = ((u1 * c1) - (u2 * c2)); 120 | u2 = ((u1 * c2) + (u2 * c1)); 121 | u1 = z; 122 | } 123 | 124 | #if defined(__AVR__) && defined(USE_AVR_PROGMEM) 125 | c2 = pgm_read_float_near(&(_c2[l])); 126 | c1 = pgm_read_float_near(&(_c1[l])); 127 | #else 128 | T cTemp = 0.5 * c1; 129 | c2 = sqrt_internal(0.5 - cTemp); 130 | c1 = sqrt_internal(0.5 + cTemp); 131 | #endif 132 | 133 | if (dir == FFTDirection::Forward) { 134 | c2 = -c2; 135 | } 136 | } 137 | // Scaling for reverse transform 138 | if (dir == FFTDirection::Reverse) { 139 | for (uint_fast16_t i = 0; i < samples; i++) { 140 | #ifdef FFT_SPEED_OVER_PRECISION 141 | vReal[i] *= oneOverSamples; 142 | vImag[i] *= oneOverSamples; 143 | #else 144 | vReal[i] /= samples; 145 | vImag[i] /= samples; 146 | #endif 147 | } 148 | } 149 | } 150 | 151 | template void ArduinoFFT::dcRemoval(void) const { 152 | dcRemoval(this->_vReal, this->_samples); 153 | } 154 | 155 | template 156 | void ArduinoFFT::dcRemoval(T *vData, uint_fast16_t samples) const { 157 | // calculate the mean of vData 158 | T mean = 0; 159 | for (uint_fast16_t i = 0; i < samples; i++) { 160 | mean += vData[i]; 161 | } 162 | mean /= samples; 163 | // Subtract the mean from vData 164 | for (uint_fast16_t i = 0; i < samples; i++) { 165 | vData[i] -= mean; 166 | } 167 | } 168 | 169 | template T ArduinoFFT::majorPeak(void) const { 170 | return majorPeak(this->_vReal, this->_samples, this->_samplingFrequency); 171 | } 172 | 173 | template void ArduinoFFT::majorPeak(T *f, T *v) const { 174 | majorPeak(this->_vReal, this->_samples, this->_samplingFrequency, f, v); 175 | } 176 | 177 | template 178 | T ArduinoFFT::majorPeak(T *vData, uint_fast16_t samples, 179 | T samplingFrequency) const { 180 | T frequency; 181 | majorPeak(vData, samples, samplingFrequency, &frequency, nullptr); 182 | return frequency; 183 | } 184 | 185 | template 186 | void ArduinoFFT::majorPeak(T *vData, uint_fast16_t samples, 187 | T samplingFrequency, T *frequency, 188 | T *magnitude) const { 189 | T maxY = 0; 190 | uint_fast16_t IndexOfMaxY = 0; 191 | findMaxY(vData, (samples >> 1) + 1, &maxY, &IndexOfMaxY); 192 | 193 | T delta = 0.5 * ((vData[IndexOfMaxY - 1] - vData[IndexOfMaxY + 1]) / 194 | (vData[IndexOfMaxY - 1] - (2.0 * vData[IndexOfMaxY]) + 195 | vData[IndexOfMaxY + 1])); 196 | if (IndexOfMaxY == (samples >> 1)) { // To improve calculation on edge values 197 | *frequency = ((IndexOfMaxY + delta) * samplingFrequency) / (samples); 198 | } else { 199 | *frequency = ((IndexOfMaxY + delta) * samplingFrequency) / (samples - 1); 200 | } 201 | // returned value: interpolated frequency peak apex 202 | if (magnitude != nullptr) { 203 | #if defined(ESP8266) || defined(ESP32) 204 | *magnitude = fabs(vData[IndexOfMaxY - 1] - (2.0 * vData[IndexOfMaxY]) + 205 | vData[IndexOfMaxY + 1]); 206 | #else 207 | *magnitude = abs(vData[IndexOfMaxY - 1] - (2.0 * vData[IndexOfMaxY]) + 208 | vData[IndexOfMaxY + 1]); 209 | #endif 210 | } 211 | } 212 | 213 | template T ArduinoFFT::majorPeakParabola(void) const { 214 | T freq = 0; 215 | majorPeakParabola(this->_vReal, this->_samples, this->_samplingFrequency, 216 | &freq, nullptr); 217 | return freq; 218 | } 219 | 220 | template 221 | void ArduinoFFT::majorPeakParabola(T *frequency, T *magnitude) const { 222 | majorPeakParabola(this->_vReal, this->_samples, this->_samplingFrequency, 223 | frequency, magnitude); 224 | } 225 | 226 | template 227 | T ArduinoFFT::majorPeakParabola(T *vData, uint_fast16_t samples, 228 | T samplingFrequency) const { 229 | T freq = 0; 230 | majorPeakParabola(vData, samples, samplingFrequency, &freq, nullptr); 231 | return freq; 232 | } 233 | 234 | template 235 | void ArduinoFFT::majorPeakParabola(T *vData, uint_fast16_t samples, 236 | T samplingFrequency, T *frequency, 237 | T *magnitude) const { 238 | T maxY = 0; 239 | uint_fast16_t IndexOfMaxY = 0; 240 | findMaxY(vData, (samples >> 1) + 1, &maxY, &IndexOfMaxY); 241 | 242 | *frequency = 0; 243 | if (IndexOfMaxY > 0) { 244 | // Assume the three points to be on a parabola 245 | T a, b, c; 246 | parabola(IndexOfMaxY - 1, vData[IndexOfMaxY - 1], IndexOfMaxY, 247 | vData[IndexOfMaxY], IndexOfMaxY + 1, vData[IndexOfMaxY + 1], &a, 248 | &b, &c); 249 | 250 | // Peak is at the middle of the parabola 251 | T x = -b / (2 * a); 252 | 253 | // And magnitude is at the extrema of the parabola if you want It... 254 | if (magnitude != nullptr) { 255 | *magnitude = (a * x * x) + (b * x) + c; 256 | } 257 | 258 | // Convert to frequency 259 | *frequency = (x * samplingFrequency) / samples; 260 | } 261 | } 262 | 263 | template uint8_t ArduinoFFT::revision(void) { 264 | return (FFT_LIB_REV); 265 | } 266 | 267 | // Replace the data array pointers 268 | template 269 | void ArduinoFFT::setArrays(T *vReal, T *vImag, uint_fast16_t samples) { 270 | _vReal = vReal; 271 | _vImag = vImag; 272 | if (samples) { 273 | _samples = samples; 274 | #ifdef FFT_SPEED_OVER_PRECISION 275 | _oneOverSamples = 1.0 / samples; 276 | #endif 277 | if (_precompiledWindowingFactors) { 278 | delete[] _precompiledWindowingFactors; 279 | } 280 | _precompiledWindowingFactors = new T[samples / 2]; 281 | } 282 | } 283 | 284 | template 285 | void ArduinoFFT::windowing(FFTWindow windowType, FFTDirection dir, 286 | bool withCompensation) { 287 | // The windowing function is the same, precompiled values can be used, and 288 | // precompiled values exist 289 | if (this->_precompiledWindowingFactors && this->_isPrecompiled && 290 | this->_windowFunction == windowType && 291 | this->_precompiledWithCompensation == withCompensation) { 292 | windowing(this->_vReal, this->_samples, FFTWindow::Precompiled, dir, 293 | this->_precompiledWindowingFactors, withCompensation); 294 | // Precompiled values must be generated. Either the function changed or the 295 | // precompiled values don't exist 296 | } else if (this->_precompiledWindowingFactors) { 297 | windowing(this->_vReal, this->_samples, windowType, dir, 298 | this->_precompiledWindowingFactors, withCompensation); 299 | this->_isPrecompiled = true; 300 | this->_precompiledWithCompensation = withCompensation; 301 | this->_windowFunction = windowType; 302 | // Don't care about precompiled windowing values 303 | } else { 304 | windowing(this->_vReal, this->_samples, windowType, dir, nullptr, 305 | withCompensation); 306 | } 307 | } 308 | 309 | template 310 | void ArduinoFFT::windowing(T *vData, uint_fast16_t samples, 311 | FFTWindow windowType, FFTDirection dir, 312 | T *windowingFactors, bool withCompensation) { 313 | // Weighing factors are computed once before multiple use of FFT 314 | // The weighing function is symmetric; half the weighs are recorded 315 | if (windowingFactors != nullptr && windowType == FFTWindow::Precompiled) { 316 | for (uint_fast16_t i = 0; i < (samples >> 1); i++) { 317 | if (dir == FFTDirection::Forward) { 318 | vData[i] *= windowingFactors[i]; 319 | vData[samples - (i + 1)] *= windowingFactors[i]; 320 | } else { 321 | #ifdef FFT_SPEED_OVER_PRECISION 322 | T inverse = 1.0 / windowingFactors[i]; 323 | vData[i] *= inverse; 324 | vData[samples - (i + 1)] *= inverse; 325 | #else 326 | vData[i] /= windowingFactors[i]; 327 | vData[samples - (i + 1)] /= windowingFactors[i]; 328 | #endif 329 | } 330 | } 331 | } else { 332 | T samplesMinusOne = (T(samples) - 1.0); 333 | T compensationFactor; 334 | if (withCompensation) { 335 | compensationFactor = 336 | _WindowCompensationFactors[static_cast(windowType)]; 337 | } 338 | for (uint_fast16_t i = 0; i < (samples >> 1); i++) { 339 | T indexMinusOne = T(i); 340 | T ratio = (indexMinusOne / samplesMinusOne); 341 | T weighingFactor = 1.0; 342 | // Compute and record weighting factor 343 | switch (windowType) { 344 | case FFTWindow::Hamming: // hamming 345 | weighingFactor = 0.54 - (0.46 * cos(twoPi * ratio)); 346 | break; 347 | case FFTWindow::Hann: // hann 348 | weighingFactor = 0.50 * (1.0 - cos(twoPi * ratio)); 349 | break; 350 | case FFTWindow::Triangle: // triangle (Bartlett) 351 | #if defined(ESP8266) || defined(ESP32) 352 | weighingFactor = 353 | 1.0 - ((2.0 * fabs(indexMinusOne - (samplesMinusOne / 2.0))) / 354 | samplesMinusOne); 355 | #else 356 | weighingFactor = 357 | 1.0 - ((2.0 * abs(indexMinusOne - (samplesMinusOne / 2.0))) / 358 | samplesMinusOne); 359 | #endif 360 | break; 361 | case FFTWindow::Nuttall: // nuttall 362 | weighingFactor = 0.355768 - (0.487396 * (cos(twoPi * ratio))) + 363 | (0.144232 * (cos(fourPi * ratio))) - 364 | (0.012604 * (cos(sixPi * ratio))); 365 | break; 366 | case FFTWindow::Blackman: // blackman 367 | weighingFactor = 0.42323 - (0.49755 * (cos(twoPi * ratio))) + 368 | (0.07922 * (cos(fourPi * ratio))); 369 | break; 370 | case FFTWindow::Blackman_Nuttall: // blackman nuttall 371 | weighingFactor = 0.3635819 - (0.4891775 * (cos(twoPi * ratio))) + 372 | (0.1365995 * (cos(fourPi * ratio))) - 373 | (0.0106411 * (cos(sixPi * ratio))); 374 | break; 375 | case FFTWindow::Blackman_Harris: // blackman harris 376 | weighingFactor = 0.35875 - (0.48829 * (cos(twoPi * ratio))) + 377 | (0.14128 * (cos(fourPi * ratio))) - 378 | (0.01168 * (cos(sixPi * ratio))); 379 | break; 380 | case FFTWindow::Flat_top: // flat top 381 | weighingFactor = 0.2810639 - (0.5208972 * cos(twoPi * ratio)) + 382 | (0.1980399 * cos(fourPi * ratio)); 383 | break; 384 | case FFTWindow::Welch: // welch 385 | weighingFactor = 1.0 - sq((indexMinusOne - samplesMinusOne / 2.0) / 386 | (samplesMinusOne / 2.0)); 387 | break; 388 | default: 389 | // This is Rectangle windowing which doesn't do anything 390 | // and Precompiled which shouldn't be selected 391 | break; 392 | } 393 | if (withCompensation) { 394 | weighingFactor *= compensationFactor; 395 | } 396 | if (windowingFactors) { 397 | windowingFactors[i] = weighingFactor; 398 | } 399 | if (dir == FFTDirection::Forward) { 400 | vData[i] *= weighingFactor; 401 | vData[samples - (i + 1)] *= weighingFactor; 402 | } else { 403 | #ifdef FFT_SPEED_OVER_PRECISION 404 | T inverse = 1.0 / weighingFactor; 405 | vData[i] *= inverse; 406 | vData[samples - (i + 1)] *= inverse; 407 | #else 408 | vData[i] /= weighingFactor; 409 | vData[samples - (i + 1)] /= weighingFactor; 410 | #endif 411 | } 412 | } 413 | } 414 | } 415 | 416 | // Private functions 417 | 418 | template 419 | uint_fast8_t ArduinoFFT::exponent(uint_fast16_t value) const { 420 | // Calculates the base 2 logarithm of a value 421 | uint_fast8_t result = 0; 422 | while (value >>= 1) 423 | result++; 424 | return result; 425 | } 426 | 427 | template 428 | void ArduinoFFT::findMaxY(T *vData, uint_fast16_t length, T *maxY, 429 | uint_fast16_t *index) const { 430 | *maxY = 0; 431 | // A signal with a DC offset produces a spike on bin 0 that should be ignored. 432 | // Start the search on bin 1. 433 | *index = 1; 434 | // If sampling_frequency = 2 * max_frequency in signal, 435 | // value would be stored at position samples/2 436 | for (uint_fast16_t i = 1; i < length; i++) { 437 | if ((vData[i - 1] < vData[i]) && (vData[i] > vData[i + 1])) { 438 | if (vData[i] > vData[*index]) { 439 | *index = i; 440 | } 441 | } 442 | } 443 | *maxY = vData[*index]; 444 | } 445 | 446 | template 447 | void ArduinoFFT::parabola(T x1, T y1, T x2, T y2, T x3, T y3, T *a, T *b, 448 | T *c) const { 449 | // const T reversed_denom = 1 / ((x1 - x2) * (x1 - x3) * (x2 - x3)); 450 | // This is a special case in which the three X coordinates are three positive, 451 | // consecutive integers. Therefore the reverse denominator will always be -0.5 452 | const T reversed_denom = -0.5; 453 | 454 | *a = (x3 * (y2 - y1) + x2 * (y1 - y3) + x1 * (y3 - y2)) * reversed_denom; 455 | *b = (x3 * x3 * (y1 - y2) + x2 * x2 * (y3 - y1) + x1 * x1 * (y2 - y3)) * 456 | reversed_denom; 457 | *c = (x2 * x3 * (x2 - x3) * y1 + x3 * x1 * (x3 - x1) * y2 + 458 | x1 * x2 * (x1 - x2) * y3) * 459 | reversed_denom; 460 | } 461 | 462 | template void ArduinoFFT::swap(T *a, T *b) const { 463 | T temp = *a; 464 | *a = *b; 465 | *b = temp; 466 | } 467 | 468 | #ifdef FFT_SQRT_APPROXIMATION 469 | // Fast inverse square root aka "Quake 3 fast inverse square root", multiplied 470 | // by x. Uses one iteration of Halley's method for precision. See: 471 | // https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Iterative_methods_for_reciprocal_square_roots 472 | // And: https://github.com/HorstBaerbel/approx 473 | template float ArduinoFFT::sqrt_internal(float x) const { 474 | union // get bits for floating point value 475 | { 476 | float x; 477 | int32_t i; 478 | } u; 479 | u.x = x; 480 | u.i = 0x5f375a86 - (u.i >> 1); // gives initial guess y0. 481 | float xu = x * u.x; 482 | float xu2 = xu * u.x; 483 | // Halley's method, repeating increases accuracy 484 | u.x = (0.125 * 3.0) * xu * (5.0 - xu2 * ((10.0 / 3.0) - xu2)); 485 | return u.x; 486 | } 487 | 488 | template double ArduinoFFT::sqrt_internal(double x) const { 489 | // According to HosrtBaerbel, on the ESP32 the approximation is not faster, so 490 | // we use the standard function 491 | #ifdef ESP32 492 | return sqrt(x); 493 | #else 494 | union // get bits for floating point value 495 | { 496 | double x; 497 | int64_t i; 498 | } u; 499 | u.x = x; 500 | u.i = 0x5fe6ec85e7de30da - (u.i >> 1); // gives initial guess y0. 501 | double xu = x * u.x; 502 | double xu2 = xu * u.x; 503 | // Halley's method, repeating increases accuracy 504 | u.x = (0.125 * 3.0) * xu * (5.0 - xu2 * ((10.0 / 3.0) - xu2)); 505 | return u.x; 506 | #endif 507 | } 508 | #endif 509 | 510 | template 511 | const T ArduinoFFT::_WindowCompensationFactors[11] = { 512 | 2.0, // 1.0000000000 * 2.0, // rectangle (Box car) 513 | 3.7098686556, // 1.8549343278 * 2.0, // hamming 514 | 3.7109453796, // 1.8554726898 * 2.0, // hann 515 | 4.0078372158, // 2.0039186079 * 2.0, // triangle (Bartlett) 516 | 5.6326344068, // 2.8163172034 * 2.0, // nuttall 517 | 4.734694872, // 2.3673474360 * 2.0, // blackman 518 | 5.511568079, // 2.7557840395 * 2.0, // blackman nuttall 519 | 5.5858125034, // 2.7929062517 * 2.0, // blackman harris 520 | 7.1318078462, // 3.5659039231 * 2.0, // flat top 521 | 3.0058785726, // 1.5029392863 * 2.0, // welch 522 | // This is added as a precaution, since this index should never be 523 | // accessed under normal conditions 524 | 1.0 // Custom, precompiled value. 525 | }; 526 | 527 | template class ArduinoFFT; 528 | template class ArduinoFFT; 529 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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You may not convey a covered 525 | work if you are a party to an arrangement with a third party that is 526 | in the business of distributing software, under which you make payment 527 | to the third party based on the extent of your activity of conveying 528 | the work, and under which the third party grants, to any of the 529 | parties who would receive the covered work from you, a discriminatory 530 | patent license (a) in connection with copies of the covered work 531 | conveyed by you (or copies made from those copies), or (b) primarily 532 | for and in connection with specific products or compilations that 533 | contain the covered work, unless you entered into that arrangement, 534 | or that patent license was granted, prior to 28 March 2007. 535 | 536 | Nothing in this License shall be construed as excluding or limiting 537 | any implied license or other defenses to infringement that may 538 | otherwise be available to you under applicable patent law. 539 | 540 | 12. No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | {one line to give the program's name and a brief idea of what it does.} 635 | Copyright (C) {year} {name of author} 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | {project} Copyright (C) {year} {fullname} 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . --------------------------------------------------------------------------------