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Version 2.0

pull/91/head
Enrique Condes 2024-03-06 13:56:17 +08:00
rodzic 419d7b044e
commit a9f64fb886
13 zmienionych plików z 688 dodań i 628 usunięć
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8
Examples/FFT_01/FFT_01.ino
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@ -3,7 +3,7 @@
Example of use of the FFT libray
Copyright (C) 2014 Enrique Condes
Copyright (C) 2020 Bim Overbohm (header-only, template, speed improvements)
Copyright (C) 2020 Bim Overbohm (template, speed improvements)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
@ -64,11 +64,11 @@ void setup()
void loop()
{
/* Build raw data */
double cycles = (((samples-1) * signalFrequency) / samplingFrequency); //Number of signal cycles that the sampling will read
double ratio = twoPi * signalFrequency / samplingFrequency; // Fraction of a complete cycle stored at each sample (in radians)
for (uint16_t i = 0; i < samples; i++)
{
vReal[i] = int8_t((amplitude * (sin((i * (TWO_PI * cycles)) / samples))) / 2.0);/* Build data with positive and negative values*/
//vReal[i] = uint8_t((amplitude * (sin((i * (twoPi * cycles)) / samples) + 1.0)) / 2.0);/* Build data displaced on the Y axis to include only positive values*/
vReal[i] = int8_t(amplitude * sin(i * ratio) / 2.0);/* Build data with positive and negative values*/
//vReal[i] = uint8_t((amplitude * (sin(i * ratio) + 1.0)) / 2.0);/* Build data displaced on the Y axis to include only positive values*/
vImag[i] = 0.0; //Imaginary part must be zeroed in case of looping to avoid wrong calculations and overflows
}
/* Print the results of the simulated sampling according to time */

6
Examples/FFT_02/FFT_02.ino
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@ -6,7 +6,7 @@
The sketch shows the time that the computing is taking.
Copyright (C) 2014 Enrique Condes
Copyright (C) 2020 Bim Overbohm (header-only, template, speed improvements)
Copyright (C) 2020 Bim Overbohm (template, speed improvements)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
@ -65,10 +65,10 @@ void loop()
for(double frequency = startFrequency; frequency<=stopFrequency; frequency+=step_size)
{
/* Build raw data */
double cycles = (((samples-1) * frequency) / sampling);
double ratio = twoPi * frequency / sampling; // Fraction of a complete cycle stored at each sample (in radians)
for (uint16_t i = 0; i < samples; i++)
{
vReal[i] = int8_t((amplitude * (sin((i * (TWO_PI * cycles)) / samples))) / 2.0);
vReal[i] = int8_t(amplitude * sin(i * ratio) / 2.0);/* Build data with positive and negative values*/
vImag[i] = 0; //Reset the imaginary values vector for each new frequency
}
/*Serial.println("Data:");

2
Examples/FFT_03/FFT_03.ino
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@ -3,7 +3,7 @@
Example of use of the FFT libray to compute FFT for a signal sampled through the ADC.
Copyright (C) 2018 Enrique Condés and Ragnar Ranøyen Homb
Copyright (C) 2020 Bim Overbohm (header-only, template, speed improvements)
Copyright (C) 2020 Bim Overbohm (template, speed improvements)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by

8
Examples/FFT_04/FFT_04.ino
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@ -3,7 +3,7 @@
Example of use of the FFT libray
Copyright (C) 2018 Enrique Condes
Copyright (C) 2020 Bim Overbohm (header-only, template, speed improvements)
Copyright (C) 2020 Bim Overbohm (template, speed improvements)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
@ -63,11 +63,11 @@ void setup()
void loop()
{
/* Build raw data */
double cycles = (((samples-1) * signalFrequency) / samplingFrequency); //Number of signal cycles that the sampling will read
double ratio = twoPi * signalFrequency / samplingFrequency; // Fraction of a complete cycle stored at each sample (in radians)
for (uint16_t i = 0; i < samples; i++)
{
vReal[i] = int8_t((amplitude * (sin((i * (TWO_PI * cycles)) / samples))) / 2.0);/* Build data with positive and negative values*/
//vReal[i] = uint8_t((amplitude * (sin((i * (twoPi * cycles)) / samples) + 1.0)) / 2.0);/* Build data displaced on the Y axis to include only positive values*/
vReal[i] = int8_t(amplitude * sin(i * ratio) / 2.0);/* Build data with positive and negative values*/
//vReal[i] = uint8_t((amplitude * (sin(i * ratio) + 1.0)) / 2.0);/* Build data displaced on the Y axis to include only positive values*/
vImag[i] = 0.0; //Imaginary part must be zeroed in case of looping to avoid wrong calculations and overflows
}
FFT.windowing(FFTWindow::Hamming, FFTDirection::Forward); /* Weigh data */

8
Examples/FFT_05/FFT_05.ino
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@ -3,7 +3,7 @@
Example of use of the FFT libray
Copyright (C) 2014 Enrique Condes
Copyright (C) 2020 Bim Overbohm (header-only, template, speed improvements)
Copyright (C) 2020 Bim Overbohm (template, speed improvements)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
@ -65,11 +65,11 @@ void setup()
void loop()
{
/* Build raw data */
double cycles = (((samples-1) * signalFrequency) / samplingFrequency); //Number of signal cycles that the sampling will read
double ratio = twoPi * signalFrequency / samplingFrequency; // Fraction of a complete cycle stored at each sample (in radians)
for (uint16_t i = 0; i < samples; i++)
{
vReal[i] = int8_t((amplitude * (sin((i * (TWO_PI * cycles)) / samples))) / 2.0);/* Build data with positive and negative values*/
//vReal[i] = uint8_t((amplitude * (sin((i * (twoPi * cycles)) / samples) + 1.0)) / 2.0);/* Build data displaced on the Y axis to include only positive values*/
vReal[i] = int8_t(amplitude * sin(i * ratio) / 2.0);/* Build data with positive and negative values*/
//vReal[i] = uint8_t((amplitude * (sin(i * ratio) + 1.0)) / 2.0);/* Build data displaced on the Y axis to include only positive values*/
vImag[i] = 0.0; //Imaginary part must be zeroed in case of looping to avoid wrong calculations and overflows
}
/* Print the results of the simulated sampling according to time */

10
Examples/FFT_speedup/FFT_speedup.ino
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@ -3,7 +3,7 @@
Example of use of the FFT libray to compute FFT for a signal sampled through the ADC
with speedup through different arduinoFFT options. Based on examples/FFT_03/FFT_03.ino
Copyright (C) 2020 Bim Overbohm (header-only, template, speed improvements)
Copyright (C) 2020 Bim Overbohm (template, speed improvements)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
@ -47,14 +47,8 @@ Input vectors receive computed results from FFT
float vReal[samples];
float vImag[samples];
/*
Allocate space for FFT window weighing factors, so they are calculated only the first time windowing() is called.
If you don't do this, a lot of calculations are necessary, depending on the window function.
*/
float weighingFactors[samples];
/* Create FFT object with weighing factor storage */
ArduinoFFT<float> FFT = ArduinoFFT<float>(vReal, vImag, samples, samplingFrequency, weighingFactors);
ArduinoFFT<float> FFT = ArduinoFFT<float>(vReal, vImag, samples, samplingFrequency, true);
#define SCL_INDEX 0x00
#define SCL_TIME 0x01

101
README.md
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@ -4,8 +4,10 @@ arduinoFFT
# Fast Fourier Transform for Arduino
This is a fork from https://code.google.com/p/makefurt/ which has been abandoned since 2011.
~~This is a C++ library for Arduino for computing FFT.~~ Now it works both on Arduino and C projects. This is version 2.0 of the library, which has a different [API](#api). See here [how to migrate from 1.x to 2.x](#migrating-from-1x-to-2x).
Tested on Arduino 1.6.11 and 1.8.10.
This is version 2.0 of the library, which has a different [API](#api).
Tested on Arduino 1.8.19 and 2.3.2.
## Installation on Arduino
@ -33,97 +35,4 @@ select arduinoFTT. This will add a corresponding line to the top of your sketch
## API
* ```ArduinoFFT(T *vReal, T *vImag, uint_fast16_t samples, T samplingFrequency, T * weighingFactors = nullptr);```
Constructor.
The type `T` can be `float` or `double`. `vReal` and `vImag` are pointers to arrays of real and imaginary data and have to be allocated outside of ArduinoFFT. `samples` is the number of samples in `vReal` and `vImag` and `weighingFactors` (if specified). `samplingFrequency` is the sample frequency of the data. `weighingFactors` can optionally be specified to cache weighing factors for the windowing function. This speeds up repeated calls to **windowing()** significantly. You can deallocate `vReal` and `vImag` after you are done using the library, or only use specific library functions that only need one of those arrays.
```C++
const uint32_t nrOfSamples = 1024;
auto real = new float[nrOfSamples];
auto imag = new float[nrOfSamples];
auto fft = ArduinoFFT<float>(real, imag, nrOfSamples, 10000);
// ... fill real + imag and use it ...
fft.compute();
fft.complexToMagnitude();
delete [] imag;
// ... continue using real and only functions that use real ...
auto peak = fft.majorPeak();
```
* ```~ArduinoFFT()```
Destructor.
* ```void complexToMagnitude() const;```
Convert complex values to their magnitude and store in vReal. Uses vReal and vImag.
* ```void compute(FFTDirection dir) const;```
Calcuates the Fast Fourier Transform. Uses vReal and vImag.
* ```void dcRemoval() const;```
Removes the DC component from the sample data. Uses vReal.
* ```T majorPeak() const;```
Returns the frequency of the biggest spike in the analyzed signal. Uses vReal.
* ```void majorPeak(T &frequency, T &value) const;```
Returns the frequency and the value of the biggest spike in the analyzed signal. Uses vReal.
* ```uint8_t revision() const;```
Returns the library revision.
* ```void setArrays(T *vReal, T *vImag);```
Replace the data array pointers.
* ```void windowing(FFTWindow windowType, FFTDirection dir, bool withCompensation = false);```
Performs a windowing function on the values array. Uses vReal. The possible windowing options are:
* Rectangle
* Hamming
* Hann
* Triangle
* Nuttall
* Blackman
* Blackman_Nuttall
* Blackman_Harris
* Flat_top
* Welch
If `withCompensation` == true, the following compensation factors are used:
* Rectangle: 1.0 * 2.0
* Hamming: 1.8549343278 * 2.0
* Hann: 1.8554726898 * 2.0
* Triangle: 2.0039186079 * 2.0
* Nuttall: 2.8163172034 * 2.0
* Blackman: 2.3673474360 * 2.0
* Blackman Nuttall: 2.7557840395 * 2.0
* Blackman Harris: 2.7929062517 * 2.0
* Flat top: 3.5659039231 * 2.0
* Welch: 1.5029392863 * 2.0
## Special flags
You can define these before including arduinoFFT.h:
* #define FFT_SPEED_OVER_PRECISION
Define this to use reciprocal multiplication for division and some more speedups that might decrease precision.
* #define FFT_SQRT_APPROXIMATION
Define this to use a low-precision square root approximation instead of the regular sqrt() call. This might only work for specific use cases, but is significantly faster. Only works if `T == float`.
See the `FFT_speedup.ino` example in `Examples/FFT_speedup/FFT_speedup.ino`.
# Migrating from 1.x to 2.x
* The function signatures where you could pass in pointers were deprecated and have been removed. Pass in pointers to your real / imaginary array in the ArduinoFFT() constructor. If you have the need to replace those pointers during usage of the library (e.g. to free memory) you can do the following:
```C++
const uint32_t nrOfSamples = 1024;
auto real = new float[nrOfSamples];
auto imag = new float[nrOfSamples];
auto fft = ArduinoFFT<float>(real, imag, nrOfSamples, 10000);
// ... fill real + imag and use it ...
fft.compute();
fft.complexToMagnitude();
delete [] real;
// ... replace vReal in library with imag ...
fft.setArrays(imag, nullptr);
// ... keep doing whatever ...
```
* All function names are camelCase case now (start with lower-case character), e.g. "windowing()" instead of "Windowing()".
## TODO
* Ratio table for windowing function.
* Document windowing functions advantages and disadvantages.
* Optimize usage and arguments.
* Add new windowing functions.
* ~~Spectrum table?~~
Documentation was moved to the project's [wiki](https://github.com/kosme/arduinoFFT/wiki).

40
changeLog.txt
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@ -1,40 +0,0 @@
02/22/20 v1.9.2
Fix compilation on AVR systems.
02/22/20 v1.9.1
Add setArrays() function because of issue #32.
Add API migration info to README and improve README.
Use better sqrtf() approximation.
02/19/20 v1.9.0
Remove deprecated API. Consistent renaming of functions to lowercase.
Make template to be able to use float or double type (float brings a ~70% speed increase on ESP32).
Add option to provide cache for window function weighing factors (~50% speed increase on ESP32).
Add some #defines to enable math approximisations to further speed up code (~40% speed increase on ESP32).
01/27/20 v1.5.5
Lookup table for constants c1 and c2 used during FFT comupting. This increases the FFT computing speed in around 5%.
02/10/18 v1.4
Transition version. Minor optimization to functions. New API. Deprecation of old functions.
12/06/18 v1.3
Add support for mbed development boards.
09/04/17 v1.2.3
Finally solves the issue of Arduino IDE not correctly detecting and highlighting the keywords.
09/03/17 v1.2.2
Solves a format issue in keywords.txt that prevented keywords from being detected.
08/28/17 v1.2.1
Fix to issues 6 and 7. Not cleaning the imaginary vector after each cycle leaded to erroneous calculations and could cause buffer overflows.
08/04/17 v1.2
Fix to bug preventing the number of samples to be greater than 128. New logical limit is 32768 samples but it is bound to the RAM on the chip.
05/12/17 v1.1
Fix issue that prevented installation through the Arduino Library Manager interface.
05/11/17 v1.0
Initial commit to Arduino Library Manager.

19
keywords.txt
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@ -17,11 +17,11 @@ FFTWindow KEYWORD1
complexToMagnitude KEYWORD2
compute KEYWORD2
dcRemoval KEYWORD2
windowing KEYWORD2
exponent KEYWORD2
revision KEYWORD2
majorPeak KEYWORD2
majorPeakParabola KEYWORD2
revision KEYWORD2
setArrays KEYWORD2
windowing KEYWORD2
#######################################
# Constants (LITERAL1)
@ -29,13 +29,14 @@ setArrays KEYWORD2
Forward LITERAL1
Reverse LITERAL1
Rectangle LITERAL1
Blackman LITERAL1
Blackman_Harris LITERAL1
Blackman_Nuttall LITERAL1
Flat_top LITERAL1
Hamming LITERAL1
Hann LITERAL1
Triangle LITERAL1
Nuttall LITERAL1
Blackman LITERAL1
Blackman_Nuttall LITERAL1
Blackman_Harris LITERAL1
Flat_top LITERAL1
Rectangle LITERAL1
Triangle LITERAL1
Welch LITERAL1

2
library.json
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@ -25,7 +25,7 @@
"email": "bim.overbohm@googlemail.com"
}
],
"version": "1.9.2",
"version": "2.0",
"frameworks": ["arduino","mbed","espidf"],
"platforms": "*"
}

2
library.properties
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@ -1,5 +1,5 @@
name=arduinoFFT
version=1.9.2
version=2.0
author=Enrique Condes <enrique@shapeoko.com>
maintainer=Enrique Condes <enrique@shapeoko.com>
sentence=A library for implementing floating point Fast Fourier Transform calculations on Arduino.

518
src/arduinoFFT.cpp 100644
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@ -0,0 +1,518 @@
/*
FFT library
Copyright (C) 2010 Didier Longueville
Copyright (C) 2014 Enrique Condes
Copyright (C) 2020 Bim Overbohm (template, speed improvements)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include "arduinoFFT.h"
template <typename T> ArduinoFFT<T>::ArduinoFFT() {}
template <typename T>
ArduinoFFT<T>::ArduinoFFT(T *vReal, T *vImag, uint_fast16_t samples,
T samplingFrequency, bool windowingFactors)
: _samples(samples), _samplingFrequency(samplingFrequency), _vImag(vImag),
_vReal(vReal) {
if (windowingFactors) {
_precompiledWindowingFactors = new T[samples / 2];
}
_power = exponent(samples);
#ifdef FFT_SPEED_OVER_PRECISION
_oneOverSamples = 1.0 / samples;
#endif
}
template <typename T> ArduinoFFT<T>::~ArduinoFFT(void) {
// Destructor
if (_precompiledWindowingFactors) {
delete [] _precompiledWindowingFactors;
}
}
template <typename T> void ArduinoFFT<T>::complexToMagnitude(void) const {
complexToMagnitude(this->_vReal, this->_vImag, this->_samples);
}
template <typename T>
void ArduinoFFT<T>::complexToMagnitude(T *vReal, T *vImag,
uint_fast16_t samples) const {
// vM is half the size of vReal and vImag
for (uint_fast16_t i = 0; i < samples; i++) {
vReal[i] = sqrt_internal(sq(vReal[i]) + sq(vImag[i]));
}
}
template <typename T> void ArduinoFFT<T>::compute(FFTDirection dir) const {
compute(this->_vReal, this->_vImag, this->_samples, exponent(this->_samples),
dir);
}
template <typename T>
void ArduinoFFT<T>::compute(T *vReal, T *vImag, uint_fast16_t samples,
FFTDirection dir) const {
compute(vReal, vImag, samples, exponent(samples), dir);
}
// Computes in-place complex-to-complex FFT
template <typename T>
void ArduinoFFT<T>::compute(T *vReal, T *vImag, uint_fast16_t samples,
uint_fast8_t power, FFTDirection dir) const {
#ifdef FFT_SPEED_OVER_PRECISION
T oneOverSamples = this->_oneOverSamples;
if (!this->_oneOverSamples)
oneOverSamples = 1.0 / samples;
#endif
// Reverse bits
uint_fast16_t j = 0;
for (uint_fast16_t i = 0; i < (samples - 1); i++) {
if (i < j) {
swap(&vReal[i], &vReal[j]);
if (dir == FFTDirection::Reverse)
swap(&vImag[i], &vImag[j]);
}
uint_fast16_t k = (samples >> 1);
while (k <= j) {
j -= k;
k >>= 1;
}
j += k;
}
// Compute the FFT
T c1 = -1.0;
T c2 = 0.0;
uint_fast16_t l2 = 1;
for (uint_fast8_t l = 0; (l < power); l++) {
uint_fast16_t l1 = l2;
l2 <<= 1;
T u1 = 1.0;
T u2 = 0.0;
for (j = 0; j < l1; j++) {
for (uint_fast16_t i = j; i < samples; i += l2) {
uint_fast16_t i1 = i + l1;
T t1 = u1 * vReal[i1] - u2 * vImag[i1];
T t2 = u1 * vImag[i1] + u2 * vReal[i1];
vReal[i1] = vReal[i] - t1;
vImag[i1] = vImag[i] - t2;
vReal[i] += t1;
vImag[i] += t2;
}
T z = ((u1 * c1) - (u2 * c2));
u2 = ((u1 * c2) + (u2 * c1));
u1 = z;
}
#if defined(__AVR__) && defined(USE_AVR_PROGMEM)
c2 = pgm_read_float_near(&(_c2[l]));
c1 = pgm_read_float_near(&(_c1[l]));
#else
T cTemp = 0.5 * c1;
c2 = sqrt_internal(0.5 - cTemp);
c1 = sqrt_internal(0.5 + cTemp);
#endif
if (dir == FFTDirection::Forward) {
c2 = -c2;
}
}
// Scaling for reverse transform
if (dir == FFTDirection::Reverse) {
for (uint_fast16_t i = 0; i < samples; i++) {
#ifdef FFT_SPEED_OVER_PRECISION
vReal[i] *= oneOverSamples;
vImag[i] *= oneOverSamples;
#else
vReal[i] /= samples;
vImag[i] /= samples;
#endif
}
}
}
template <typename T> void ArduinoFFT<T>::dcRemoval(void) const {
dcRemoval(this->_vReal, this->_samples);
}
template <typename T>
void ArduinoFFT<T>::dcRemoval(T *vData, uint_fast16_t samples) const {
// calculate the mean of vData
T mean = 0;
for (uint_fast16_t i = 0; i < samples; i++) {
mean += vData[i];
}
mean /= samples;
// Subtract the mean from vData
for (uint_fast16_t i = 0; i < samples; i++) {
vData[i] -= mean;
}
}
template <typename T> T ArduinoFFT<T>::majorPeak(void) const {
return majorPeak(this->_vReal, this->_samples, this->_samplingFrequency);
}
template <typename T> void ArduinoFFT<T>::majorPeak(T *f, T *v) const {
majorPeak(this->_vReal, this->_samples, this->_samplingFrequency, f, v);
}
template <typename T>
T ArduinoFFT<T>::majorPeak(T *vData, uint_fast16_t samples,
T samplingFrequency) const {
T frequency;
majorPeak(vData, samples, samplingFrequency, &frequency, nullptr);
return frequency;
}
template <typename T>
void ArduinoFFT<T>::majorPeak(T *vData, uint_fast16_t samples,
T samplingFrequency, T *frequency,
T *magnitude) const {
T maxY = 0;
uint_fast16_t IndexOfMaxY = 0;
findMaxY(vData, (samples >> 1) + 1, &maxY, &IndexOfMaxY);
T delta = 0.5 * ((vData[IndexOfMaxY - 1] - vData[IndexOfMaxY + 1]) /
(vData[IndexOfMaxY - 1] - (2.0 * vData[IndexOfMaxY]) +
vData[IndexOfMaxY + 1]));
T interpolatedX = ((IndexOfMaxY + delta) * samplingFrequency) / (samples - 1);
if (IndexOfMaxY == (samples >> 1)) // To improve calculation on edge values
interpolatedX = ((IndexOfMaxY + delta) * samplingFrequency) / (samples);
// returned value: interpolated frequency peak apex
*frequency = interpolatedX;
if (magnitude != nullptr) {
#if defined(ESP8266) || defined(ESP32)
*magnitude = fabs(vData[IndexOfMaxY - 1] - (2.0 * vData[IndexOfMaxY]) +
vData[IndexOfMaxY + 1]);
#else
*magnitude = abs(vData[IndexOfMaxY - 1] - (2.0 * vData[IndexOfMaxY]) +
vData[IndexOfMaxY + 1]);
#endif
}
}
template <typename T> T ArduinoFFT<T>::majorPeakParabola(void) const {
T freq = 0;
majorPeakParabola(this->_vReal, this->_samples, this->_samplingFrequency,
&freq, nullptr);
return freq;
}
template <typename T>
void ArduinoFFT<T>::majorPeakParabola(T *frequency, T *magnitude) const {
majorPeakParabola(this->_vReal, this->_samples, this->_samplingFrequency,
frequency, magnitude);
}
template <typename T>
T ArduinoFFT<T>::majorPeakParabola(T *vData, uint_fast16_t samples,
T samplingFrequency) const {
T freq = 0;
majorPeakParabola(vData, samples, samplingFrequency, &freq, nullptr);
return freq;
}
template <typename T>
void ArduinoFFT<T>::majorPeakParabola(T *vData, uint_fast16_t samples,
T samplingFrequency, T *frequency,
T *magnitude) const {
T maxY = 0;
uint_fast16_t IndexOfMaxY = 0;
findMaxY(vData, (samples >> 1) + 1, &maxY, &IndexOfMaxY);
*frequency = 0;
if (IndexOfMaxY > 0) {
// Assume the three points to be on a parabola
T a, b, c;
parabola(IndexOfMaxY - 1, vData[IndexOfMaxY - 1], IndexOfMaxY,
vData[IndexOfMaxY], IndexOfMaxY + 1, vData[IndexOfMaxY + 1], &a,
&b, &c);
// Peak is at the middle of the parabola
T x = -b / (2 * a);
// And magnitude is at the extrema of the parabola if you want It...
if (magnitude != nullptr) {
*magnitude = a * x * x + b * x + c;
}
// Convert to frequency
*frequency = (x * samplingFrequency) / samples;
}
}
template <typename T> uint8_t ArduinoFFT<T>::revision(void) {
return (FFT_LIB_REV);
}
// Replace the data array pointers
template <typename T>
void ArduinoFFT<T>::setArrays(T *vReal, T *vImag, uint_fast16_t samples) {
_vReal = vReal;
_vImag = vImag;
if (samples) {
_samples = samples;
#ifdef FFT_SPEED_OVER_PRECISION
_oneOverSamples = 1.0 / samples;
#endif
if (_precompiledWindowingFactors) {
delete [] _precompiledWindowingFactors;
}
_precompiledWindowingFactors = new T[samples / 2];
}
}
template <typename T>
void ArduinoFFT<T>::windowing(FFTWindow windowType, FFTDirection dir,
bool withCompensation) {
// The windowing function is the same, precompiled values can be used, and
// precompiled values exist
if (this->_precompiledWindowingFactors && this->_isPrecompiled &&
this->_windowFunction == windowType &&
this->_precompiledWithCompensation == withCompensation) {
windowing(this->_vReal, this->_samples, FFTWindow::Precompiled, dir,
this->_precompiledWindowingFactors, withCompensation);
// Precompiled values must be generated. Either the function changed or the
// precompiled values don't exist
} else if (this->_precompiledWindowingFactors) {
windowing(this->_vReal, this->_samples, windowType, dir,
this->_precompiledWindowingFactors, withCompensation);
this->_isPrecompiled = true;
this->_precompiledWithCompensation = withCompensation;
this->_windowFunction = windowType;
// Don't care about precompiled windowing values
} else {
windowing(this->_vReal, this->_samples, windowType, dir, nullptr,
withCompensation);
}
}
template <typename T>
void ArduinoFFT<T>::windowing(T *vData, uint_fast16_t samples,
FFTWindow windowType, FFTDirection dir,
T *windowingFactors, bool withCompensation) {
// Weighing factors are computed once before multiple use of FFT
// The weighing function is symmetric; half the weighs are recorded
if (windowingFactors != nullptr && windowType == FFTWindow::Precompiled) {
for (uint_fast16_t i = 0; i < (samples >> 1); i++) {
if (dir == FFTDirection::Forward) {
vData[i] *= windowingFactors[i];
vData[samples - (i + 1)] *= windowingFactors[i];
} else {
#ifdef FFT_SPEED_OVER_PRECISION
T inverse = 1.0 / windowingFactors[i];
vData[i] *= inverse;
vData[samples - (i + 1)] *= inverse;
#else
vData[i] /= windowingFactors[i];
vData[samples - (i + 1)] /= windowingFactors[i];
#endif
}
}
} else {
T samplesMinusOne = (T(samples) - 1.0);
T compensationFactor;
if (withCompensation) {
compensationFactor =
_WindowCompensationFactors[static_cast<uint_fast8_t>(windowType)];
}
for (uint_fast16_t i = 0; i < (samples >> 1); i++) {
T indexMinusOne = T(i);
T ratio = (indexMinusOne / samplesMinusOne);
T weighingFactor = 1.0;
// Compute and record weighting factor
switch (windowType) {
case FFTWindow::Hamming: // hamming
weighingFactor = 0.54 - (0.46 * cos(twoPi * ratio));
break;
case FFTWindow::Hann: // hann
weighingFactor = 0.54 * (1.0 - cos(twoPi * ratio));
break;
case FFTWindow::Triangle: // triangle (Bartlett)
#if defined(ESP8266) || defined(ESP32)
weighingFactor =
1.0 - ((2.0 * fabs(indexMinusOne - (samplesMinusOne / 2.0))) /
samplesMinusOne);
#else
weighingFactor =
1.0 - ((2.0 * abs(indexMinusOne - (samplesMinusOne / 2.0))) /
samplesMinusOne);
#endif
break;
case FFTWindow::Nuttall: // nuttall
weighingFactor = 0.355768 - (0.487396 * (cos(twoPi * ratio))) +
(0.144232 * (cos(fourPi * ratio))) -
(0.012604 * (cos(sixPi * ratio)));
break;
case FFTWindow::Blackman: // blackman
weighingFactor = 0.42323 - (0.49755 * (cos(twoPi * ratio))) +
(0.07922 * (cos(fourPi * ratio)));
break;
case FFTWindow::Blackman_Nuttall: // blackman nuttall
weighingFactor = 0.3635819 - (0.4891775 * (cos(twoPi * ratio))) +
(0.1365995 * (cos(fourPi * ratio))) -
(0.0106411 * (cos(sixPi * ratio)));
break;
case FFTWindow::Blackman_Harris: // blackman harris
weighingFactor = 0.35875 - (0.48829 * (cos(twoPi * ratio))) +
(0.14128 * (cos(fourPi * ratio))) -
(0.01168 * (cos(sixPi * ratio)));
break;
case FFTWindow::Flat_top: // flat top
weighingFactor = 0.2810639 - (0.5208972 * cos(twoPi * ratio)) +
(0.1980399 * cos(fourPi * ratio));
break;
case FFTWindow::Welch: // welch
weighingFactor = 1.0 - sq((indexMinusOne - samplesMinusOne / 2.0) /
(samplesMinusOne / 2.0));
break;
default:
// This is Rectangle windowing which doesn't do anything
// and Precompiled which shouldn't be selected
break;
}
if (withCompensation) {
weighingFactor *= compensationFactor;
}
if (windowingFactors) {
windowingFactors[i] = weighingFactor;
}
if (dir == FFTDirection::Forward) {
vData[i] *= weighingFactor;
vData[samples - (i + 1)] *= weighingFactor;
} else {
#ifdef FFT_SPEED_OVER_PRECISION
T inverse = 1.0 / weighingFactor;
vData[i] *= inverse;
vData[samples - (i + 1)] *= inverse;
#else
vData[i] /= weighingFactor;
vData[samples - (i + 1)] /= weighingFactor;
#endif
}
}
}
}
// Private functions
template <typename T>
uint_fast8_t ArduinoFFT<T>::exponent(uint_fast16_t value) const {
// Calculates the base 2 logarithm of a value
uint_fast8_t result = 0;
while (value >>= 1)
result++;
return result;
}
template <typename T>
void ArduinoFFT<T>::findMaxY(T *vData, uint_fast16_t length, T *maxY,
uint_fast16_t *index) const {
*maxY = 0;
*index = 0;
// If sampling_frequency = 2 * max_frequency in signal,
// value would be stored at position samples/2
for (uint_fast16_t i = 1; i < length; i++) {
if ((vData[i - 1] < vData[i]) && (vData[i] > vData[i + 1])) {
if (vData[i] > vData[*index]) {
*index = i;
}
}
}
*maxY = vData[*index];
}
template <typename T>
void ArduinoFFT<T>::parabola(T x1, T y1, T x2, T y2, T x3, T y3, T *a, T *b,
T *c) const {
// const T reversed_denom = 1 / ((x1 - x2) * (x1 - x3) * (x2 - x3));
// This is a special case in which the three X coordinates are three positive,
// consecutive integers. Therefore the reverse denominator will always be -0.5
const T reversed_denom = -0.5;
*a = (x3 * (y2 - y1) + x2 * (y1 - y3) + x1 * (y3 - y2)) * reversed_denom;
*b = (x3 * x3 * (y1 - y2) + x2 * x2 * (y3 - y1) + x1 * x1 * (y2 - y3)) *
reversed_denom;
*c = (x2 * x3 * (x2 - x3) * y1 + x3 * x1 * (x3 - x1) * y2 +
x1 * x2 * (x1 - x2) * y3) *
reversed_denom;
}
template <typename T> void ArduinoFFT<T>::swap(T *a, T *b) const {
T temp = *a;
*a = *b;
*b = temp;
}
#ifdef FFT_SQRT_APPROXIMATION
// Fast inverse square root aka "Quake 3 fast inverse square root", multiplied
// by x. Uses one iteration of Halley's method for precision. See:
// https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Iterative_methods_for_reciprocal_square_roots
// And: https://github.com/HorstBaerbel/approx
template <typename T> float ArduinoFFT<T>::sqrt_internal(float x) const {
union // get bits for floating point value
{
float x;
int32_t i;
} u;
u.x = x;
u.i = 0x5f375a86 - (u.i >> 1); // gives initial guess y0.
float xu = x * u.x;
float xu2 = xu * u.x;
// Halley's method, repeating increases accuracy
u.x = (0.125 * 3.0) * xu * (5.0 - xu2 * ((10.0 / 3.0) - xu2));
return u.x;
}
template <typename T> double ArduinoFFT<T>::sqrt_internal(double x) const {
// According to HosrtBaerbel, on the ESP32 the approximation is not faster, so
// we use the standard function
#ifdef ESP32
return sqrt(x);
#else
union // get bits for floating point value
{
double x;
int64_t i;
} u;
u.x = x;
u.i = 0x5fe6ec85e7de30da - (u.i >> 1); // gives initial guess y0.
double xu = x * u.x;
double xu2 = xu * u.x;
// Halley's method, repeating increases accuracy
u.x = (0.125 * 3.0) * xu * (5.0 - xu2 * ((10.0 / 3.0) - xu2));
return u.x;
#endif
}
#endif
template <typename T>
const T ArduinoFFT<T>::_WindowCompensationFactors[10] = {
1.0000000000 * 2.0, // rectangle (Box car)
1.8549343278 * 2.0, // hamming
1.8554726898 * 2.0, // hann
2.0039186079 * 2.0, // triangle (Bartlett)
2.8163172034 * 2.0, // nuttall
2.3673474360 * 2.0, // blackman
2.7557840395 * 2.0, // blackman nuttall
2.7929062517 * 2.0, // blackman harris
3.5659039231 * 2.0, // flat top
1.5029392863 * 2.0 // welch
};
template class ArduinoFFT<double>;
template class ArduinoFFT<float>;

524
src/arduinoFFT.h
Wyświetl plik

@ -3,7 +3,7 @@
FFT library
Copyright (C) 2010 Didier Longueville
Copyright (C) 2014 Enrique Condes
Copyright (C) 2020 Bim Overbohm (header-only, template, speed improvements)
Copyright (C) 2020 Bim Overbohm (template, speed improvements)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
@ -29,40 +29,30 @@
#include "WProgram.h" /* This is where the standard Arduino code lies */
#endif
#else
#include <stdlib.h>
#include <stdio.h>
#include <stdlib.h>
#ifdef __AVR__
#include <avr/io.h>
#include <avr/pgmspace.h>
#endif
#include <math.h>
#include "defs.h"
#include "types.h"
#include <math.h>
#include <stdint.h>
#endif
// Define this to use reciprocal multiplication for division and some more speedups that might decrease precision
//#define FFT_SPEED_OVER_PRECISION
// This definition uses a low-precision square root approximation instead of the
// regular sqrt() call
// This might only work for specific use cases, but is significantly faster.
// Define this to use a low-precision square root approximation instead of the regular sqrt() call
// This might only work for specific use cases, but is significantly faster. Only works for ArduinoFFT<float>.
//#define FFT_SQRT_APPROXIMATION
#ifdef FFT_SQRT_APPROXIMATION
#include <type_traits>
#else
#ifndef sqrt_internal
#ifndef FFT_SQRT_APPROXIMATION
#define sqrt_internal sqrt
#endif
#endif
enum class FFTDirection
{
Reverse,
Forward
};
enum class FFTDirection { Forward, Reverse };
enum class FFTWindow
{
enum class FFTWindow {
Rectangle, // rectangle (Box car)
Hamming, // hamming
Hann, // hann
@ -72,429 +62,117 @@ enum class FFTWindow
Blackman_Nuttall, // blackman nuttall
Blackman_Harris, // blackman harris
Flat_top, // flat top
Welch // welch
Welch, // welch
Precompiled // Placeholder for using custom or precompiled window values
};
#define FFT_LIB_REV 0x20
/* Custom constants */
/* These defines keep compatibility with pre 2.0 code */
#define FFT_FORWARD FFTDirection::Forward
#define FFT_REVERSE FFTDirection::Reverse
template <typename T>
class ArduinoFFT
{
/* Windowing type */
#define FFT_WIN_TYP_RECTANGLE FFTWindow::Rectangle /* rectangle (Box car) */
#define FFT_WIN_TYP_HAMMING FFTWindow::Hamming /* hamming */
#define FFT_WIN_TYP_HANN FFTWindow::Hann /* hann */
#define FFT_WIN_TYP_TRIANGLE FFTWindow::Triangle /* triangle (Bartlett) */
#define FFT_WIN_TYP_NUTTALL FFTWindow::Nuttall /* nuttall */
#define FFT_WIN_TYP_BLACKMAN FFTWindow::Blackman /* blackman */
#define FFT_WIN_TYP_BLACKMAN_NUTTALL \
FFTWindow::Blackman_Nuttall /* blackman nuttall */
#define FFT_WIN_TYP_BLACKMAN_HARRIS \
FFTWindow::Blackman_Harris /* blackman harris*/
#define FFT_WIN_TYP_FLT_TOP FFTWindow::Flat_top /* flat top */
#define FFT_WIN_TYP_WELCH FFTWindow::Welch /* welch */
/* End of compatibility defines */
/* Mathematial constants */
#define twoPi 6.28318531
#define fourPi 12.56637061
#define sixPi 18.84955593
template <typename T> class ArduinoFFT {
public:
// Constructor
ArduinoFFT(T *vReal, T *vImag, uint_fast16_t samples, T samplingFrequency, T *windowWeighingFactors = nullptr)
: _vReal(vReal)
, _vImag(vImag)
, _samples(samples)
#ifdef FFT_SPEED_OVER_PRECISION
, _oneOverSamples(1.0 / samples)
#endif
, _samplingFrequency(samplingFrequency)
, _windowWeighingFactors(windowWeighingFactors)
{
// Calculates the base 2 logarithm of sample count
_power = 0;
while (((samples >> _power) & 1) != 1)
{
_power++;
}
}
ArduinoFFT();
ArduinoFFT(T *vReal, T *vImag, uint_fast16_t samples, T samplingFrequency,
bool windowingFactors = false);
// Destructor
~ArduinoFFT()
{
}
~ArduinoFFT();
// Get library revision
static uint8_t revision()
{
return 0x19;
}
void complexToMagnitude(void) const;
void complexToMagnitude(T *vReal, T *vImag, uint_fast16_t samples) const;
// Replace the data array pointers
void setArrays(T *vReal, T *vImag)
{
_vReal = vReal;
_vImag = vImag;
}
void compute(FFTDirection dir) const;
void compute(T *vReal, T *vImag, uint_fast16_t samples,
FFTDirection dir) const;
void compute(T *vReal, T *vImag, uint_fast16_t samples, uint_fast8_t power,
FFTDirection dir) const;
// Computes in-place complex-to-complex FFT
void compute(FFTDirection dir) const
{
// Reverse bits /
uint_fast16_t j = 0;
for (uint_fast16_t i = 0; i < (this->_samples - 1); i++)
{
if (i < j)
{
Swap(this->_vReal[i], this->_vReal[j]);
if (dir == FFTDirection::Reverse)
{
Swap(this->_vImag[i], this->_vImag[j]);
}
}
uint_fast16_t k = (this->_samples >> 1);
while (k <= j)
{
j -= k;
k >>= 1;
}
j += k;
}
// Compute the FFT
#ifdef __AVR__
uint_fast8_t index = 0;
#endif
T c1 = -1.0;
T c2 = 0.0;
uint_fast16_t l2 = 1;
for (uint_fast8_t l = 0; (l < this->_power); l++)
{
uint_fast16_t l1 = l2;
l2 <<= 1;
T u1 = 1.0;
T u2 = 0.0;
for (j = 0; j < l1; j++)
{
for (uint_fast16_t i = j; i < this->_samples; i += l2)
{
uint_fast16_t i1 = i + l1;
T t1 = u1 * this->_vReal[i1] - u2 * this->_vImag[i1];
T t2 = u1 * this->_vImag[i1] + u2 * this->_vReal[i1];
this->_vReal[i1] = this->_vReal[i] - t1;
this->_vImag[i1] = this->_vImag[i] - t2;
this->_vReal[i] += t1;
this->_vImag[i] += t2;
}
T z = ((u1 * c1) - (u2 * c2));
u2 = ((u1 * c2) + (u2 * c1));
u1 = z;
}
#ifdef __AVR__
c2 = pgm_read_float_near(&(_c2[index]));
c1 = pgm_read_float_near(&(_c1[index]));
index++;
#else
T cTemp = 0.5 * c1;
c2 = sqrt_internal(0.5 - cTemp);
c1 = sqrt_internal(0.5 + cTemp);
#endif
c2 = dir == FFTDirection::Forward ? -c2 : c2;
}
// Scaling for reverse transform
if (dir != FFTDirection::Forward)
{
for (uint_fast16_t i = 0; i < this->_samples; i++)
{
#ifdef FFT_SPEED_OVER_PRECISION
this->_vReal[i] *= _oneOverSamples;
this->_vImag[i] *= _oneOverSamples;
#else
this->_vReal[i] /= this->_samples;
this->_vImag[i] /= this->_samples;
#endif
}
}
}
void dcRemoval(void) const;
void dcRemoval(T *vData, uint_fast16_t samples) const;
void complexToMagnitude() const
{
// vM is half the size of vReal and vImag
for (uint_fast16_t i = 0; i < this->_samples; i++)
{
this->_vReal[i] = sqrt_internal(sq(this->_vReal[i]) + sq(this->_vImag[i]));
}
}
T majorPeak(void) const;
void majorPeak(T *f, T *v) const;
T majorPeak(T *vData, uint_fast16_t samples, T samplingFrequency) const;
void majorPeak(T *vData, uint_fast16_t samples, T samplingFrequency,
T *frequency, T *magnitude) const;
void dcRemoval() const
{
// calculate the mean of vData
T mean = 0;
for (uint_fast16_t i = 1; i < ((this->_samples >> 1) + 1); i++)
{
mean += this->_vReal[i];
}
mean /= this->_samples;
// Subtract the mean from vData
for (uint_fast16_t i = 1; i < ((this->_samples >> 1) + 1); i++)
{
this->_vReal[i] -= mean;
}
}
T majorPeakParabola(void) const;
void majorPeakParabola(T *frequency, T *magnitude) const;
T majorPeakParabola(T *vData, uint_fast16_t samples,
T samplingFrequency) const;
void majorPeakParabola(T *vData, uint_fast16_t samples, T samplingFrequency,
T *frequency, T *magnitude) const;
void windowing(FFTWindow windowType, FFTDirection dir, bool withCompensation = false)
{
// check if values are already pre-computed for the correct window type and compensation
if (_windowWeighingFactors && _weighingFactorsComputed &&
_weighingFactorsFFTWindow == windowType &&
_weighingFactorsWithCompensation == withCompensation)
{
// yes. values are precomputed
if (dir == FFTDirection::Forward)
{
for (uint_fast16_t i = 0; i < (this->_samples >> 1); i++)
{
this->_vReal[i] *= _windowWeighingFactors[i];
this->_vReal[this->_samples - (i + 1)] *= _windowWeighingFactors[i];
}
}
else
{
for (uint_fast16_t i = 0; i < (this->_samples >> 1); i++)
{
#ifdef FFT_SPEED_OVER_PRECISION
// on many architectures reciprocals and multiplying are much faster than division
T oneOverFactor = 1.0 / _windowWeighingFactors[i];
this->_vReal[i] *= oneOverFactor;
this->_vReal[this->_samples - (i + 1)] *= oneOverFactor;
#else
this->_vReal[i] /= _windowWeighingFactors[i];
this->_vReal[this->_samples - (i + 1)] /= _windowWeighingFactors[i];
#endif
}
}
}
else
{
// no. values need to be pre-computed or applied
T samplesMinusOne = (T(this->_samples) - 1.0);
T compensationFactor = _WindowCompensationFactors[static_cast<uint_fast8_t>(windowType)];
for (uint_fast16_t i = 0; i < (this->_samples >> 1); i++)
{
T indexMinusOne = T(i);
T ratio = (indexMinusOne / samplesMinusOne);
T weighingFactor = 1.0;
// Compute and record weighting factor
switch (windowType)
{
case FFTWindow::Rectangle: // rectangle (box car)
weighingFactor = 1.0;
break;
case FFTWindow::Hamming: // hamming
weighingFactor = 0.54 - (0.46 * cos(TWO_PI * ratio));
break;
case FFTWindow::Hann: // hann
weighingFactor = 0.54 * (1.0 - cos(TWO_PI * ratio));
break;
case FFTWindow::Triangle: // triangle (Bartlett)
weighingFactor = 1.0 - ((2.0 * abs(indexMinusOne - (samplesMinusOne / 2.0))) / samplesMinusOne);
break;
case FFTWindow::Nuttall: // nuttall
weighingFactor = 0.355768 - (0.487396 * (cos(TWO_PI * ratio))) + (0.144232 * (cos(FOUR_PI * ratio))) - (0.012604 * (cos(SIX_PI * ratio)));
break;
case FFTWindow::Blackman: // blackman
weighingFactor = 0.42323 - (0.49755 * (cos(TWO_PI * ratio))) + (0.07922 * (cos(FOUR_PI * ratio)));
break;
case FFTWindow::Blackman_Nuttall: // blackman nuttall
weighingFactor = 0.3635819 - (0.4891775 * (cos(TWO_PI * ratio))) + (0.1365995 * (cos(FOUR_PI * ratio))) - (0.0106411 * (cos(SIX_PI * ratio)));
break;
case FFTWindow::Blackman_Harris: // blackman harris
weighingFactor = 0.35875 - (0.48829 * (cos(TWO_PI * ratio))) + (0.14128 * (cos(FOUR_PI * ratio))) - (0.01168 * (cos(SIX_PI * ratio)));
break;
case FFTWindow::Flat_top: // flat top
weighingFactor = 0.2810639 - (0.5208972 * cos(TWO_PI * ratio)) + (0.1980399 * cos(FOUR_PI * ratio));
break;
case FFTWindow::Welch: // welch
weighingFactor = 1.0 - sq((indexMinusOne - samplesMinusOne / 2.0) / (samplesMinusOne / 2.0));
break;
}
if (withCompensation)
{
weighingFactor *= compensationFactor;
}
if (_windowWeighingFactors)
{
_windowWeighingFactors[i] = weighingFactor;
}
if (dir == FFTDirection::Forward)
{
this->_vReal[i] *= weighingFactor;
this->_vReal[this->_samples - (i + 1)] *= weighingFactor;
}
else
{
#ifdef FFT_SPEED_OVER_PRECISION
// on many architectures reciprocals and multiplying are much faster than division
T oneOverFactor = 1.0 / weighingFactor;
this->_vReal[i] *= oneOverFactor;
this->_vReal[this->_samples - (i + 1)] *= oneOverFactor;
#else
this->_vReal[i] /= weighingFactor;
this->_vReal[this->_samples - (i + 1)] /= weighingFactor;
#endif
}
}
// mark cached values as pre-computed
_weighingFactorsFFTWindow = windowType;
_weighingFactorsWithCompensation = withCompensation;
_weighingFactorsComputed = true;
}
}
uint8_t revision(void);
T majorPeak() const
{
T maxY = 0;
uint_fast16_t IndexOfMaxY = 0;
//If sampling_frequency = 2 * max_frequency in signal,
//value would be stored at position samples/2
for (uint_fast16_t i = 1; i < ((this->_samples >> 1) + 1); i++)
{
if ((this->_vReal[i - 1] < this->_vReal[i]) && (this->_vReal[i] > this->_vReal[i + 1]))
{
if (this->_vReal[i] > maxY)
{
maxY = this->_vReal[i];
IndexOfMaxY = i;
}
}
}
T delta = 0.5 * ((this->_vReal[IndexOfMaxY - 1] - this->_vReal[IndexOfMaxY + 1]) / (this->_vReal[IndexOfMaxY - 1] - (2.0 * this->_vReal[IndexOfMaxY]) + this->_vReal[IndexOfMaxY + 1]));
T interpolatedX = ((IndexOfMaxY + delta) * this->_samplingFrequency) / (this->_samples - 1);
if (IndexOfMaxY == (this->_samples >> 1))
{
//To improve calculation on edge values
interpolatedX = ((IndexOfMaxY + delta) * this->_samplingFrequency) / (this->_samples);
}
// returned value: interpolated frequency peak apex
return interpolatedX;
}
void setArrays(T *vReal, T *vImag, uint_fast16_t samples = 0);
void majorPeak(T &frequency, T &value) const
{
T maxY = 0;
uint_fast16_t IndexOfMaxY = 0;
//If sampling_frequency = 2 * max_frequency in signal,
//value would be stored at position samples/2
for (uint_fast16_t i = 1; i < ((this->_samples >> 1) + 1); i++)
{
if ((this->_vReal[i - 1] < this->_vReal[i]) && (this->_vReal[i] > this->_vReal[i + 1]))
{
if (this->_vReal[i] > maxY)
{
maxY = this->_vReal[i];
IndexOfMaxY = i;
}
}
}
T delta = 0.5 * ((this->_vReal[IndexOfMaxY - 1] - this->_vReal[IndexOfMaxY + 1]) / (this->_vReal[IndexOfMaxY - 1] - (2.0 * this->_vReal[IndexOfMaxY]) + this->_vReal[IndexOfMaxY + 1]));
T interpolatedX = ((IndexOfMaxY + delta) * this->_samplingFrequency) / (this->_samples - 1);
if (IndexOfMaxY == (this->_samples >> 1))
{
//To improve calculation on edge values
interpolatedX = ((IndexOfMaxY + delta) * this->_samplingFrequency) / (this->_samples);
}
// returned value: interpolated frequency peak apex
frequency = interpolatedX;
value = abs(this->_vReal[IndexOfMaxY - 1] - (2.0 * this->_vReal[IndexOfMaxY]) + this->_vReal[IndexOfMaxY + 1]);
}
void windowing(FFTWindow windowType, FFTDirection dir,
bool withCompensation = false);
void windowing(T *vData, uint_fast16_t samples, FFTWindow windowType,
FFTDirection dir, T *windowingFactors = nullptr,
bool withCompensation = false);
private:
#ifdef __AVR__
static const float _c1[] PROGMEM;
static const float _c2[] PROGMEM;
#endif
static const T _WindowCompensationFactors[10];
// Mathematial constants
#ifndef TWO_PI
static constexpr T TWO_PI = 6.28318531; // might already be defined in Arduino.h
#endif
static constexpr T FOUR_PI = 12.56637061;
static constexpr T SIX_PI = 18.84955593;
static inline void Swap(T &x, T &y)
{
T temp = x;
x = y;
y = temp;
}
#ifdef FFT_SQRT_APPROXIMATION
// Fast inverse square root aka "Quake 3 fast inverse square root", multiplied by x.
// Uses one iteration of Halley's method for precision.
// See: https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Iterative_methods_for_reciprocal_square_roots
// And: https://github.com/HorstBaerbel/approx
template <typename V = T>
static inline V sqrt_internal(typename std::enable_if<std::is_same<V, float>::value, V>::type x)
{
union // get bits for float value
{
float x;
int32_t i;
} u;
u.x = x;
u.i = 0x5f375a86 - (u.i >> 1); // gives initial guess y0.
float xu = x * u.x;
float xu2 = xu * u.x;
u.x = (0.125 * 3.0) * xu * (5.0 - xu2 * ((10.0 / 3.0) - xu2)); // Halley's method, repeating increases accuracy
return u.x;
}
template <typename V = T>
static inline V sqrt_internal(typename std::enable_if<std::is_same<V, double>::value, V>::type x)
{
// According to HosrtBaerbel, on the ESP32 the approximation is not faster, so we use the standard function
#ifdef ESP32
return sqrt(x);
#else
union // get bits for float value
{
double x;
int64_t i;
} u;
u.x = x;
u.i = 0x5fe6ec85e7de30da - (u.i >> 1); // gives initial guess y0.
double xu = x * u.x;
double xu2 = xu * u.x;
u.x = (0.125 * 3.0) * xu * (5.0 - xu2 * ((10.0 / 3.0) - xu2)); // Halley's method, repeating increases accuracy
return u.x;
#endif
}
#endif
/* Variables */
T *_vReal = nullptr;
T *_vImag = nullptr;
uint_fast16_t _samples = 0;
static const T _WindowCompensationFactors[10];
#ifdef FFT_SPEED_OVER_PRECISION
T _oneOverSamples = 0.0;
#endif
T _samplingFrequency = 0;
T *_windowWeighingFactors = nullptr;
FFTWindow _weighingFactorsFFTWindow;
bool _weighingFactorsWithCompensation = false;
bool _weighingFactorsComputed = false;
bool _isPrecompiled = false;
bool _precompiledWithCompensation = false;
uint_fast8_t _power = 0;
T *_precompiledWindowingFactors;
uint_fast16_t _samples;
T _samplingFrequency;
T *_vImag;
T *_vReal;
FFTWindow _windowFunction;
/* Functions */
uint_fast8_t exponent(uint_fast16_t value) const;
void findMaxY(T *vData, uint_fast16_t length, T *maxY,
uint_fast16_t *index) const;
void parabola(T x1, T y1, T x2, T y2, T x3, T y3, T *a, T *b, T *c) const;
void swap(T *a, T *b) const;
#ifdef FFT_SQRT_APPROXIMATION
float sqrt_internal(float x) const;
double sqrt_internal(double x) const;
#endif
};
#ifdef __AVR__
template <typename T>
const float ArduinoFFT<T>::_c1[] PROGMEM = {
0.0000000000, 0.7071067812, 0.9238795325, 0.9807852804,
0.9951847267, 0.9987954562, 0.9996988187, 0.9999247018,
0.9999811753, 0.9999952938, 0.9999988235, 0.9999997059,
0.9999999265, 0.9999999816, 0.9999999954, 0.9999999989,
0.9999999997};
template <typename T>
const float ArduinoFFT<T>::_c2[] PROGMEM = {
1.0000000000, 0.7071067812, 0.3826834324, 0.1950903220,
0.0980171403, 0.0490676743, 0.0245412285, 0.0122715383,
0.0061358846, 0.0030679568, 0.0015339802, 0.0007669903,
0.0003834952, 0.0001917476, 0.0000958738, 0.0000479369,
0.0000239684};
#if defined(__AVR__) && defined(USE_AVR_PROGMEM)
static const float _c1[] PROGMEM = {
0.0000000000, 0.7071067812, 0.9238795325, 0.9807852804, 0.9951847267,
0.9987954562, 0.9996988187, 0.9999247018, 0.9999811753, 0.9999952938,
0.9999988235, 0.9999997059, 0.9999999265, 0.9999999816, 0.9999999954,
0.9999999989, 0.9999999997};
static const float _c2[] PROGMEM = {
1.0000000000, 0.7071067812, 0.3826834324, 0.1950903220, 0.0980171403,
0.0490676743, 0.0245412285, 0.0122715383, 0.0061358846, 0.0030679568,
0.0015339802, 0.0007669903, 0.0003834952, 0.0001917476, 0.0000958738,
0.0000479369, 0.0000239684};
#endif
template <typename T>
const T ArduinoFFT<T>::_WindowCompensationFactors[10] = {
1.0000000000 * 2.0, // rectangle (Box car)
1.8549343278 * 2.0, // hamming
1.8554726898 * 2.0, // hann
2.0039186079 * 2.0, // triangle (Bartlett)
2.8163172034 * 2.0, // nuttall
2.3673474360 * 2.0, // blackman
2.7557840395 * 2.0, // blackman nuttall
2.7929062517 * 2.0, // blackman harris
3.5659039231 * 2.0, // flat top
1.5029392863 * 2.0 // welch
};
#endif