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arduinoFFT/src/arduinoFFT.cpp

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C++
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/*
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
}
}
// The computation result at position 0 should be as close to 0 as possible.
// The DC offset on the signal produces a spike on position 0 that should be
// eliminated to avoid issues.
vReal[0] = 0;
}
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[11] = {
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
// This is added as a precaution, since this index should never be
// accessed under normal conditions
1.0 // Custom, precompiled value.
};
template class ArduinoFFT<double>;
template class ArduinoFFT<float>;
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