kopia lustrzana https://github.com/kosme/arduinoFFT
510 wiersze
16 KiB
C++
510 wiersze
16 KiB
C++
/*
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FFT library
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Copyright (C) 2010 Didier Longueville
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Copyright (C) 2014 Enrique Condes
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "arduinoFFT.h"
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arduinoFFT::arduinoFFT(void)
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{ // Constructor
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#warning("This method is deprecated and may be removed on future revisions.")
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}
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arduinoFFT::arduinoFFT(double *vReal, double *vImag, uint16_t samples, double samplingFrequency)
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{// Constructor
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this->_vReal = vReal;
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this->_vImag = vImag;
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this->_samples = samples;
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this->_samplingFrequency = samplingFrequency;
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this->_power = Exponent(samples);
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}
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arduinoFFT::~arduinoFFT(void)
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{
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// Destructor
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}
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uint8_t arduinoFFT::Revision(void)
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{
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return(FFT_LIB_REV);
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}
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void arduinoFFT::Compute(double *vReal, double *vImag, uint16_t samples, uint8_t dir)
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{
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#warning("This method is deprecated and may be removed on future revisions.")
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Compute(vReal, vImag, samples, Exponent(samples), dir);
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}
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void arduinoFFT::Compute(uint8_t dir)
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{// Computes in-place complex-to-complex FFT /
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// Reverse bits /
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uint16_t j = 0;
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for (uint16_t i = 0; i < (this->_samples - 1); i++) {
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if (i < j) {
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Swap(&this->_vReal[i], &this->_vReal[j]);
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if(dir==FFT_REVERSE)
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Swap(&this->_vImag[i], &this->_vImag[j]);
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}
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uint16_t k = (this->_samples >> 1);
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while (k <= j) {
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j -= k;
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k >>= 1;
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}
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j += k;
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}
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// Compute the FFT /
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#ifdef __AVR__
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uint8_t index = 0;
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#endif
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double c1 = -1.0;
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double c2 = 0.0;
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uint16_t l2 = 1;
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for (uint8_t l = 0; (l < this->_power); l++) {
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uint16_t l1 = l2;
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l2 <<= 1;
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double u1 = 1.0;
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double u2 = 0.0;
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for (j = 0; j < l1; j++) {
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for (uint16_t i = j; i < this->_samples; i += l2) {
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uint16_t i1 = i + l1;
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double t1 = u1 * this->_vReal[i1] - u2 * this->_vImag[i1];
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double t2 = u1 * this->_vImag[i1] + u2 * this->_vReal[i1];
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this->_vReal[i1] = this->_vReal[i] - t1;
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this->_vImag[i1] = this->_vImag[i] - t2;
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this->_vReal[i] += t1;
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this->_vImag[i] += t2;
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}
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double z = ((u1 * c1) - (u2 * c2));
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u2 = ((u1 * c2) + (u2 * c1));
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u1 = z;
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}
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#ifdef __AVR__
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c2 = pgm_read_float_near(&(_c2[index]));
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c1 = pgm_read_float_near(&(_c1[index]));
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index++;
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#else
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c2 = sqrt((1.0 - c1) / 2.0);
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c1 = sqrt((1.0 + c1) / 2.0);
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#endif
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if (dir == FFT_FORWARD) {
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c2 = -c2;
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}
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}
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// Scaling for reverse transform /
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if (dir != FFT_FORWARD) {
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for (uint16_t i = 0; i < this->_samples; i++) {
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this->_vReal[i] /= this->_samples;
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this->_vImag[i] /= this->_samples;
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}
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}
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}
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void arduinoFFT::Compute(double *vReal, double *vImag, uint16_t samples, uint8_t power, uint8_t dir)
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{ // Computes in-place complex-to-complex FFT
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// Reverse bits
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#warning("This method is deprecated and may be removed on future revisions.")
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uint16_t j = 0;
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for (uint16_t i = 0; i < (samples - 1); i++) {
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if (i < j) {
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Swap(&vReal[i], &vReal[j]);
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if(dir==FFT_REVERSE)
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Swap(&vImag[i], &vImag[j]);
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}
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uint16_t k = (samples >> 1);
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while (k <= j) {
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j -= k;
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k >>= 1;
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}
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j += k;
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}
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// Compute the FFT
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#ifdef __AVR__
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uint8_t index = 0;
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#endif
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double c1 = -1.0;
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double c2 = 0.0;
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uint16_t l2 = 1;
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for (uint8_t l = 0; (l < power); l++) {
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uint16_t l1 = l2;
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l2 <<= 1;
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double u1 = 1.0;
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double u2 = 0.0;
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for (j = 0; j < l1; j++) {
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for (uint16_t i = j; i < samples; i += l2) {
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uint16_t i1 = i + l1;
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double t1 = u1 * vReal[i1] - u2 * vImag[i1];
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double t2 = u1 * vImag[i1] + u2 * vReal[i1];
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vReal[i1] = vReal[i] - t1;
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vImag[i1] = vImag[i] - t2;
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vReal[i] += t1;
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vImag[i] += t2;
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}
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double z = ((u1 * c1) - (u2 * c2));
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u2 = ((u1 * c2) + (u2 * c1));
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u1 = z;
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}
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#ifdef __AVR__
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c2 = pgm_read_float_near(&(_c2[index]));
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c1 = pgm_read_float_near(&(_c1[index]));
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index++;
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#else
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c2 = sqrt((1.0 - c1) / 2.0);
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c1 = sqrt((1.0 + c1) / 2.0);
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#endif
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if (dir == FFT_FORWARD) {
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c2 = -c2;
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}
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}
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// Scaling for reverse transform
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if (dir != FFT_FORWARD) {
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for (uint16_t i = 0; i < samples; i++) {
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vReal[i] /= samples;
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vImag[i] /= samples;
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}
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}
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}
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void arduinoFFT::ComplexToMagnitude()
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{ // vM is half the size of vReal and vImag
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for (uint16_t i = 0; i < this->_samples; i++) {
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this->_vReal[i] = sqrt(sq(this->_vReal[i]) + sq(this->_vImag[i]));
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}
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}
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void arduinoFFT::ComplexToMagnitude(double *vReal, double *vImag, uint16_t samples)
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{ // vM is half the size of vReal and vImag
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#warning("This method is deprecated and may be removed on future revisions.")
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for (uint16_t i = 0; i < samples; i++) {
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vReal[i] = sqrt(sq(vReal[i]) + sq(vImag[i]));
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}
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}
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void arduinoFFT::DCRemoval()
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{
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// calculate the mean of vData
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double mean = 0;
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for (uint16_t i = 0; i < this->_samples; i++)
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{
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mean += this->_vReal[i];
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}
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mean /= this->_samples;
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// Subtract the mean from vData
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for (uint16_t i = 0; i < this->_samples; i++)
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{
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this->_vReal[i] -= mean;
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}
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}
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void arduinoFFT::DCRemoval(double *vData, uint16_t samples)
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{
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// calculate the mean of vData
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#warning("This method is deprecated and may be removed on future revisions.")
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double mean = 0;
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for (uint16_t i = 0; i < samples; i++)
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{
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mean += vData[i];
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}
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mean /= samples;
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// Subtract the mean from vData
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for (uint16_t i = 0; i < samples; i++)
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{
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vData[i] -= mean;
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}
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}
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void arduinoFFT::Windowing(uint8_t windowType, uint8_t dir)
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{// Weighing factors are computed once before multiple use of FFT
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// The weighing function is symmetric; half the weighs are recorded
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double samplesMinusOne = (double(this->_samples) - 1.0);
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for (uint16_t i = 0; i < (this->_samples >> 1); i++) {
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double indexMinusOne = double(i);
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double ratio = (indexMinusOne / samplesMinusOne);
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double weighingFactor = 1.0;
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// Compute and record weighting factor
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switch (windowType) {
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case FFT_WIN_TYP_RECTANGLE: // rectangle (box car)
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weighingFactor = 1.0;
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break;
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case FFT_WIN_TYP_HAMMING: // hamming
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weighingFactor = 0.54 - (0.46 * cos(twoPi * ratio));
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break;
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case FFT_WIN_TYP_HANN: // hann
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weighingFactor = 0.54 * (1.0 - cos(twoPi * ratio));
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break;
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case FFT_WIN_TYP_TRIANGLE: // triangle (Bartlett)
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#if defined(ESP8266) || defined(ESP32)
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weighingFactor = 1.0 - ((2.0 * fabs(indexMinusOne - (samplesMinusOne / 2.0))) / samplesMinusOne);
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#else
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weighingFactor = 1.0 - ((2.0 * abs(indexMinusOne - (samplesMinusOne / 2.0))) / samplesMinusOne);
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#endif
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break;
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case FFT_WIN_TYP_NUTTALL: // nuttall
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weighingFactor = 0.355768 - (0.487396 * (cos(twoPi * ratio))) + (0.144232 * (cos(fourPi * ratio))) - (0.012604 * (cos(sixPi * ratio)));
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break;
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case FFT_WIN_TYP_BLACKMAN: // blackman
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weighingFactor = 0.42323 - (0.49755 * (cos(twoPi * ratio))) + (0.07922 * (cos(fourPi * ratio)));
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break;
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case FFT_WIN_TYP_BLACKMAN_NUTTALL: // blackman nuttall
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weighingFactor = 0.3635819 - (0.4891775 * (cos(twoPi * ratio))) + (0.1365995 * (cos(fourPi * ratio))) - (0.0106411 * (cos(sixPi * ratio)));
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break;
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case FFT_WIN_TYP_BLACKMAN_HARRIS: // blackman harris
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weighingFactor = 0.35875 - (0.48829 * (cos(twoPi * ratio))) + (0.14128 * (cos(fourPi * ratio))) - (0.01168 * (cos(sixPi * ratio)));
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break;
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case FFT_WIN_TYP_FLT_TOP: // flat top
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weighingFactor = 0.2810639 - (0.5208972 * cos(twoPi * ratio)) + (0.1980399 * cos(fourPi * ratio));
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break;
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case FFT_WIN_TYP_WELCH: // welch
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weighingFactor = 1.0 - sq((indexMinusOne - samplesMinusOne / 2.0) / (samplesMinusOne / 2.0));
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break;
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}
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if (dir == FFT_FORWARD) {
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this->_vReal[i] *= weighingFactor;
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this->_vReal[this->_samples - (i + 1)] *= weighingFactor;
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}
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else {
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this->_vReal[i] /= weighingFactor;
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this->_vReal[this->_samples - (i + 1)] /= weighingFactor;
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}
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}
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}
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void arduinoFFT::Windowing(double *vData, uint16_t samples, uint8_t windowType, uint8_t dir)
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{// Weighing factors are computed once before multiple use of FFT
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// The weighing function is symetric; half the weighs are recorded
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#warning("This method is deprecated and may be removed on future revisions.")
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double samplesMinusOne = (double(samples) - 1.0);
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for (uint16_t i = 0; i < (samples >> 1); i++) {
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double indexMinusOne = double(i);
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double ratio = (indexMinusOne / samplesMinusOne);
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double weighingFactor = 1.0;
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// Compute and record weighting factor
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switch (windowType) {
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case FFT_WIN_TYP_RECTANGLE: // rectangle (box car)
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weighingFactor = 1.0;
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break;
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case FFT_WIN_TYP_HAMMING: // hamming
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weighingFactor = 0.54 - (0.46 * cos(twoPi * ratio));
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break;
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case FFT_WIN_TYP_HANN: // hann
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weighingFactor = 0.54 * (1.0 - cos(twoPi * ratio));
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break;
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case FFT_WIN_TYP_TRIANGLE: // triangle (Bartlett)
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#if defined(ESP8266) || defined(ESP32)
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weighingFactor = 1.0 - ((2.0 * fabs(indexMinusOne - (samplesMinusOne / 2.0))) / samplesMinusOne);
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#else
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weighingFactor = 1.0 - ((2.0 * abs(indexMinusOne - (samplesMinusOne / 2.0))) / samplesMinusOne);
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#endif
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break;
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case FFT_WIN_TYP_NUTTALL: // nuttall
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weighingFactor = 0.355768 - (0.487396 * (cos(twoPi * ratio))) + (0.144232 * (cos(fourPi * ratio))) - (0.012604 * (cos(sixPi * ratio)));
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break;
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case FFT_WIN_TYP_BLACKMAN: // blackman
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weighingFactor = 0.42323 - (0.49755 * (cos(twoPi * ratio))) + (0.07922 * (cos(fourPi * ratio)));
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break;
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case FFT_WIN_TYP_BLACKMAN_NUTTALL: // blackman nuttall
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weighingFactor = 0.3635819 - (0.4891775 * (cos(twoPi * ratio))) + (0.1365995 * (cos(fourPi * ratio))) - (0.0106411 * (cos(sixPi * ratio)));
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break;
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case FFT_WIN_TYP_BLACKMAN_HARRIS: // blackman harris
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weighingFactor = 0.35875 - (0.48829 * (cos(twoPi * ratio))) + (0.14128 * (cos(fourPi * ratio))) - (0.01168 * (cos(sixPi * ratio)));
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break;
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case FFT_WIN_TYP_FLT_TOP: // flat top
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weighingFactor = 0.2810639 - (0.5208972 * cos(twoPi * ratio)) + (0.1980399 * cos(fourPi * ratio));
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break;
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case FFT_WIN_TYP_WELCH: // welch
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weighingFactor = 1.0 - sq((indexMinusOne - samplesMinusOne / 2.0) / (samplesMinusOne / 2.0));
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break;
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}
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if (dir == FFT_FORWARD) {
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vData[i] *= weighingFactor;
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vData[samples - (i + 1)] *= weighingFactor;
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}
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else {
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vData[i] /= weighingFactor;
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vData[samples - (i + 1)] /= weighingFactor;
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}
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}
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}
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double arduinoFFT::MajorPeak()
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{
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double maxY = 0;
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uint16_t IndexOfMaxY = 0;
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//If sampling_frequency = 2 * max_frequency in signal,
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//value would be stored at position samples/2
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for (uint16_t i = 1; i < ((this->_samples >> 1) + 1); i++) {
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if ((this->_vReal[i-1] < this->_vReal[i]) && (this->_vReal[i] > this->_vReal[i+1])) {
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if (this->_vReal[i] > maxY) {
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maxY = this->_vReal[i];
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IndexOfMaxY = i;
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}
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}
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}
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double delta = 0.5 * ((this->_vReal[IndexOfMaxY-1] - this->_vReal[IndexOfMaxY+1]) / (this->_vReal[IndexOfMaxY-1] - (2.0 * this->_vReal[IndexOfMaxY]) + this->_vReal[IndexOfMaxY+1]));
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double interpolatedX = ((IndexOfMaxY + delta) * this->_samplingFrequency) / (this->_samples-1);
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if(IndexOfMaxY==(this->_samples >> 1)) //To improve calculation on edge values
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interpolatedX = ((IndexOfMaxY + delta) * this->_samplingFrequency) / (this->_samples);
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// returned value: interpolated frequency peak apex
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return(interpolatedX);
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}
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void arduinoFFT::MajorPeak(double *f, double *v)
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{
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double maxY = 0;
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uint16_t IndexOfMaxY = 0;
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//If sampling_frequency = 2 * max_frequency in signal,
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//value would be stored at position samples/2
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for (uint16_t i = 1; i < ((this->_samples >> 1) + 1); i++) {
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if ((this->_vReal[i - 1] < this->_vReal[i]) && (this->_vReal[i] > this->_vReal[i + 1])) {
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if (this->_vReal[i] > maxY) {
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maxY = this->_vReal[i];
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IndexOfMaxY = i;
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}
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}
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}
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double delta = 0.5 * ((this->_vReal[IndexOfMaxY - 1] - this->_vReal[IndexOfMaxY + 1]) / (this->_vReal[IndexOfMaxY - 1] - (2.0 * this->_vReal[IndexOfMaxY]) + this->_vReal[IndexOfMaxY + 1]));
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double interpolatedX = ((IndexOfMaxY + delta) * this->_samplingFrequency) / (this->_samples - 1);
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if (IndexOfMaxY == (this->_samples >> 1)) //To improve calculation on edge values
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interpolatedX = ((IndexOfMaxY + delta) * this->_samplingFrequency) / (this->_samples);
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// returned value: interpolated frequency peak apex
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*f = interpolatedX;
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#if defined(ESP8266) || defined(ESP32)
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*v = fabs(this->_vReal[IndexOfMaxY - 1] - (2.0 * this->_vReal[IndexOfMaxY]) + this->_vReal[IndexOfMaxY + 1]);
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#else
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*v = abs(this->_vReal[IndexOfMaxY - 1] - (2.0 * this->_vReal[IndexOfMaxY]) + this->_vReal[IndexOfMaxY + 1]);
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#endif
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}
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double arduinoFFT::MajorPeak(double *vD, uint16_t samples, double samplingFrequency)
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{
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#warning("This method is deprecated and may be removed on future revisions.")
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double maxY = 0;
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uint16_t IndexOfMaxY = 0;
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//If sampling_frequency = 2 * max_frequency in signal,
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//value would be stored at position samples/2
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for (uint16_t i = 1; i < ((samples >> 1) + 1); i++) {
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if ((vD[i-1] < vD[i]) && (vD[i] > vD[i+1])) {
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if (vD[i] > maxY) {
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maxY = vD[i];
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IndexOfMaxY = i;
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}
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}
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}
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double delta = 0.5 * ((vD[IndexOfMaxY-1] - vD[IndexOfMaxY+1]) / (vD[IndexOfMaxY-1] - (2.0 * vD[IndexOfMaxY]) + vD[IndexOfMaxY+1]));
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double interpolatedX = ((IndexOfMaxY + delta) * samplingFrequency) / (samples-1);
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if(IndexOfMaxY==(samples >> 1)) //To improve calculation on edge values
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interpolatedX = ((IndexOfMaxY + delta) * samplingFrequency) / (samples);
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// returned value: interpolated frequency peak apex
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return(interpolatedX);
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}
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void arduinoFFT::MajorPeak(double *vD, uint16_t samples, double samplingFrequency, double *f, double *v)
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{
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#warning("This method is deprecated and may be removed on future revisions.")
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double maxY = 0;
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uint16_t IndexOfMaxY = 0;
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//If sampling_frequency = 2 * max_frequency in signal,
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//value would be stored at position samples/2
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for (uint16_t i = 1; i < ((samples >> 1) + 1); i++) {
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if ((vD[i - 1] < vD[i]) && (vD[i] > vD[i + 1])) {
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if (vD[i] > maxY) {
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maxY = vD[i];
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IndexOfMaxY = i;
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}
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}
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}
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double delta = 0.5 * ((vD[IndexOfMaxY - 1] - vD[IndexOfMaxY + 1]) / (vD[IndexOfMaxY - 1] - (2.0 * vD[IndexOfMaxY]) + vD[IndexOfMaxY + 1]));
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double interpolatedX = ((IndexOfMaxY + delta) * samplingFrequency) / (samples - 1);
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//double popo =
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if (IndexOfMaxY == (samples >> 1)) //To improve calculation on edge values
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interpolatedX = ((IndexOfMaxY + delta) * samplingFrequency) / (samples);
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// returned value: interpolated frequency peak apex
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*f = interpolatedX;
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#if defined(ESP8266) || defined(ESP32)
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*v = fabs(vD[IndexOfMaxY - 1] - (2.0 * vD[IndexOfMaxY]) + vD[IndexOfMaxY + 1]);
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#else
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*v = abs(vD[IndexOfMaxY - 1] - (2.0 * vD[IndexOfMaxY]) + vD[IndexOfMaxY + 1]);
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#endif
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}
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double arduinoFFT::MajorPeakParabola()
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{
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double maxY = 0;
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uint16_t IndexOfMaxY = 0;
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//If sampling_frequency = 2 * max_frequency in signal,
|
|
//value would be stored at position samples/2
|
|
for (uint16_t i = 1; i < ((this->_samples >> 1) + 1); i++)
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{
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if ((this->_vReal[i-1] < this->_vReal[i]) && (this->_vReal[i] > this->_vReal[i+1]))
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{
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|
if (this->_vReal[i] > maxY)
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|
{
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|
maxY = this->_vReal[i];
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IndexOfMaxY = i;
|
|
}
|
|
}
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|
}
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|
|
|
double freq = 0;
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|
if( IndexOfMaxY>0 )
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|
{
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|
// Assume the three points to be on a parabola
|
|
double a,b,c;
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|
Parabola(IndexOfMaxY-1, this->_vReal[IndexOfMaxY-1], IndexOfMaxY, this->_vReal[IndexOfMaxY], IndexOfMaxY+1, this->_vReal[IndexOfMaxY+1], &a, &b, &c);
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|
|
|
// Peak is at the middle of the parabola
|
|
double x = -b/(2*a);
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|
|
|
// And magnitude is at the extrema of the parabola if you want It...
|
|
// double y = a*x*x+b*x+c;
|
|
|
|
// Convert to frequency
|
|
freq = (x * this->_samplingFrequency) / (this->_samples);
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|
}
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|
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return freq;
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|
}
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void arduinoFFT::Parabola(double x1, double y1, double x2, double y2, double x3, double y3, double *a, double *b, double *c)
|
|
{
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|
double reversed_denom = 1/((x1 - x2) * (x1 - x3) * (x2 - x3));
|
|
|
|
*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;
|
|
}
|
|
|
|
uint8_t arduinoFFT::Exponent(uint16_t value)
|
|
{
|
|
#warning("This method may not be accessible on future revisions.")
|
|
// Calculates the base 2 logarithm of a value
|
|
uint8_t result = 0;
|
|
while (((value >> result) & 1) != 1) result++;
|
|
return(result);
|
|
}
|
|
|
|
// Private functions
|
|
|
|
void arduinoFFT::Swap(double *x, double *y)
|
|
{
|
|
double temp = *x;
|
|
*x = *y;
|
|
*y = temp;
|
|
}
|