FastFourierTransform.cpp

/*
 GRT MIT License
 Copyright (c) <2012> <Nicholas Gillian, Media Lab, MIT>
 
 Permission is hereby granted, free of charge, to any person obtaining a copy of this software
 and associated documentation files (the "Software"), to deal in the Software without restriction,
 including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense,
 and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so,
 subject to the following conditions:
 
 The above copyright notice and this permission notice shall be included in all copies or substantial
 portions of the Software.
 
 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
 LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
 IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
 WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
 SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 */

/*
 This code is based on Dominic Mazzoni's c++ wrapper, which is based on a free implementation of an FFT
 by Don Cross (http://www.intersrv.com/~dcross/fft.html) and the FFT algorithms from Numerical Recipes.
 */

#include "FastFourierTransform.h" 

GRT_BEGIN_NAMESPACE

FastFourierTransform::FastFourierTransform(){
 initialized = false;
 computeMagnitude = true;
 computePhase = true;
 enableZeroPadding = true;
 windowSize = 0;
 windowFunction = RECTANGULAR_WINDOW;
 averagePower = 0;
 
 infoLog.setProceedingText("[FastFourierTransform]");
 warningLog.setProceedingText("[WARNING FastFourierTransform]");
 errorLog.setProceedingText("[ERROR FastFourierTransform]");
 
 initFFT();
}
 
FastFourierTransform::FastFourierTransform(const FastFourierTransform &rhs){

 this->initialized = rhs.initialized;
 this->computeMagnitude = rhs.computeMagnitude;
 this->computePhase = rhs.computePhase;
 this->enableZeroPadding = rhs.enableZeroPadding;
 this->windowSize = rhs.windowSize;
 this->windowFunction = rhs.windowFunction;
 this->averagePower = 0;
 this->initFFT();
 this->infoLog = rhs.infoLog;
 this->warningLog = rhs.warningLog;
 this->errorLog = rhs.errorLog;
 
 if( rhs.initialized ){
 this->init(rhs.windowSize,rhs.windowFunction,rhs.computeMagnitude,rhs.computePhase);
 
 //Copy the fft results
 for(UINT i=0; i<this->windowSize; i++){
 this->fftReal[i] = rhs.fftReal[i];
 this->fftImag[i] = rhs.fftImag[i];
 this->magnitude[i] = rhs.magnitude[i];
 this->phase[i] = rhs.phase[i];
 this->power[i] = rhs.power[i];
 }
 }
}

FastFourierTransform::~FastFourierTransform() {

}
 
FastFourierTransform& FastFourierTransform::operator=(const FastFourierTransform &rhs){
 
 if( this != &rhs ){
 this->initialized = rhs.initialized;
 this->computeMagnitude = rhs.computeMagnitude;
 this->computePhase = rhs.computePhase;
 this->enableZeroPadding = rhs.enableZeroPadding;
 this->windowSize = rhs.windowSize;
 this->windowFunction = rhs.windowFunction;
 this->averagePower = 0;
 this->initFFT();
 
 if( rhs.initialized ){
 this->init(rhs.windowSize,rhs.windowFunction,rhs.computeMagnitude,rhs.computePhase);
 
 //Copy the fft results
 for(UINT i=0; i<this->windowSize; i++){
 this->fftReal[i] = rhs.fftReal[i];
 this->fftImag[i] = rhs.fftImag[i];
 this->magnitude[i] = rhs.magnitude[i];
 this->phase[i] = rhs.phase[i];
 this->power[i] = rhs.power[i];
 }
 }
 }
 return *this;
}
 
bool FastFourierTransform::init(const unsigned int windowSize,const unsigned int windowFunction,const bool computeMagnitude,const bool computePhase,const bool enableZeroPadding){
 
 initialized = false;
 averagePower = 0;
 
 //Validate the window size
 if( !isPowerOfTwo( windowSize ) ){
 return false;
 }
 
 if( windowFunction != RECTANGULAR_WINDOW && windowFunction != BARTLETT_WINDOW && 
 windowFunction != HAMMING_WINDOW && windowFunction != HANNING_WINDOW ){
 return false;
 }
 
 initFFT();
 
 this->windowSize = windowSize;
 this->windowFunction = windowFunction;
 this->computeMagnitude = computeMagnitude;
 this->computePhase = computePhase;
 this->enableZeroPadding = enableZeroPadding;
 
 //Init the memory
 fftReal.resize( windowSize );
 fftImag.resize( windowSize );
 tmpReal.resize( windowSize/2 );
 tmpImag.resize( windowSize/2 );
 magnitude.resize( windowSize );
 phase.resize( windowSize );
 power.resize( windowSize );
 averagePower = 0;
 
 //Zero the memory
 for(UINT i=0; i<windowSize/2; i++){
 tmpReal[i] = 0;
 tmpImag[i] = 0;
 }
 for(UINT i=0; i<windowSize; i++){
 fftReal[i] = 0;
 fftImag[i] = 0;
 magnitude[i] = 0;
 phase[i] = 0;
 power[i] = 0;
 }
 
 //Flag that the FFT has been initialized
 initialized = true;
 
 return true;
}

bool FastFourierTransform::computeFFT( VectorFloat &data ){
 
 if( !initialized ){
 return false;
 }

 //Validate the input Vector 
 if( !enableZeroPadding ){
 if( (unsigned int)data.size() != windowSize ){
 errorLog << "The size of the data Vector (" << data.size() << ") does not match the windowSize: " << windowSize << std::endl;
 return false;
 }
 }else{
 if( (unsigned int)data.size() > windowSize ){
 errorLog << "The size of the data Vector (" << data.size() << ") is greater than the windowSize: " << windowSize << std::endl;
 return false;
 }
 }

 //Window the input data
 if( !windowData( data ) ){
 return false;
 }

 //Zero padd the data if needed
 if( enableZeroPadding ){
 if( ((unsigned int)data.size()) != windowSize ){
 const unsigned int oldSize = (unsigned int)data.size();
 data.resize( windowSize );
 for(unsigned int i=oldSize; i<windowSize; i++){
 data[i] = 0;
 }
 }
 }
 
 //Perform the FFT
 realFFT(data, &fftReal[0], &fftImag[0]);
 
 averagePower = 0;
 
 for(unsigned int i = 0; i<windowSize/2; i++){
 
 if( computeMagnitude ){
 power[i] = fftReal[i]*fftReal[i] + fftImag[i]*fftImag[i];
 averagePower += power[i];
 magnitude[i] = 2.0*sqrt( power[i] );
 }
 
 if( computePhase ){
 phase[i] = atan2(fftImag[i],fftReal[i]);
 }
 }

 //Compute the average power
 averagePower = averagePower / (Float)(windowSize/2);
 
 return true;
}
 
bool FastFourierTransform::windowData( VectorFloat &data ){
 
 const unsigned int N = (unsigned int)data.size();
 const unsigned int K = N/2;

 switch( windowFunction ){
 case RECTANGULAR_WINDOW:
 return true;
 break;
 case BARTLETT_WINDOW:
 for(unsigned int i=0; i<K; i++) {
 data[i] *= (i / (Float) (K));
 data[i + K] *= (1.0 - (i / (Float)K));
 }
 return true;
 break;
 case HAMMING_WINDOW:
 for(unsigned int i=0; i<N; i++)
 data[i] *= 0.54 - 0.46 * cos(2 * PI * i / (N - 1));
 return true;
 break;
 case HANNING_WINDOW:
 for(unsigned int i=0; i <N; i++)
 data[i] *= 0.50 - 0.50 * cos(2 * PI * i / (N - 1));
 return true;
 break;
 default:
 return false;
 break;
 }
 
 return false;
}
 
VectorFloat FastFourierTransform::getMagnitudeData(){
 
 if( !initialized ) return VectorFloat();
 
 const unsigned int N = windowSize/2; 
 VectorFloat magnitudeData(N);
 
 for(unsigned int i=0; i<N; i++){
 magnitudeData[i] = magnitude[i];
 }
 
 return magnitudeData;
}

VectorFloat FastFourierTransform::getPhaseData(){
 if( !initialized ) return VectorFloat();

 const unsigned int N = windowSize/2; 
 VectorFloat phaseData(N);
 
 for(unsigned int i=0; i<N; i++){
 phaseData[i] = phase[i];
 }
 
 return phaseData;
}

VectorFloat FastFourierTransform::getPowerData(){
 if( !initialized ) return VectorFloat();
 
 VectorFloat powerData(windowSize/2);
 
 for(unsigned int i=0; i<windowSize/2; i++){
 powerData[i] = power[i];
 }
 
 return powerData;
}
 
Float FastFourierTransform::getAveragePower(){
 return averagePower;
}
 
Float* FastFourierTransform::getMagnitudeDataPtr(){
 return &magnitude[0];
}

Float* FastFourierTransform::getPhaseDataPtr(){
 return &phase[0];
}

Float* FastFourierTransform::getPowerDataPtr(){
 return &power[0];
}
 
/*
 * Real Fast Fourier Transform
 *
 * This function was based on the code in Numerical Recipes in C.
 * In Num. Rec., the inner loop is based on a single 1-based array
 * of interleaved real and imaginary numbers. Because we have two
 * separate zero-based arrays, our indices are quite different.
 * Here is the correspondence between Num. Rec. indices and our indices:
 *
 * i1 <-> real[i]
 * i2 <-> imag[i]
 * i3 <-> real[n/2-i]
 * i4 <-> imag[n/2-i]
 */

bool FastFourierTransform::realFFT( const VectorFloat &realIn, Float *realOut, Float *imagOut ){
 int NumSamples = (int)windowSize;
 int Half = NumSamples / 2;
 int i;
 
 Float theta = PI / Half;
 
 for (i = 0; i < Half; i++) {
 tmpReal[i] = realIn[2 * i];
 tmpImag[i] = realIn[2 * i + 1];
 }
 
 if( !FFT(Half, 0, &tmpReal[0], &tmpImag[0], realOut, imagOut) ){
 return false;
 }
 
 Float wtemp = Float(sin(0.5 * theta));
 
 Float wpr = -2.0 * wtemp * wtemp;
 Float wpi = Float (sin(theta));
 Float wr = 1.0 + wpr;
 Float wi = wpi;
 
 int i3;
 
 Float h1r, h1i, h2r, h2i;
 
 for (i = 1; i < Half / 2; i++) {
 
 i3 = Half - i;
 
 h1r = 0.5 * (realOut[i] + realOut[i3]);
 h1i = 0.5 * (imagOut[i] - imagOut[i3]);
 h2r = 0.5 * (imagOut[i] + imagOut[i3]);
 h2i = -0.5 * (realOut[i] - realOut[i3]);
 
 realOut[i] = h1r + wr * h2r - wi * h2i;
 imagOut[i] = h1i + wr * h2i + wi * h2r;
 realOut[i3] = h1r - wr * h2r + wi * h2i;
 imagOut[i3] = -h1i + wr * h2i + wi * h2r;
 
 wr = (wtemp = wr) * wpr - wi * wpi + wr;
 wi = wi * wpr + wtemp * wpi + wi;
 }
 
 realOut[0] = (h1r = realOut[0]) + imagOut[0];
 imagOut[0] = h1r - imagOut[0];
 
 return true;
}

bool FastFourierTransform::FFT(int numSamples,bool inverseTransform,Float *realIn, Float *imagIn, Float *realOut, Float *imagOut){
 int NumBits; /* Number of bits needed to store indices */
 int i, j, k, n;
 int BlockSize, BlockEnd;
 
 Float angle_numerator = 2.0 * PI;
 Float tr, ti; /* temp real, temp imaginary */
 
 if( !isPowerOfTwo(numSamples) ) {
 fprintf(stderr, "%d is not a power of two\n", numSamples);
 return false;
 }
 
 if( bitTable.size() == 0 ) initFFT();
 
 if( inverseTransform ) angle_numerator = -angle_numerator;
 
 NumBits = numberOfBitsNeeded(numSamples);
 
 //Simultaneously data copy and bit-reversal ordering into outputs...
 for(i = 0; i < numSamples; i++) {
 j = fastReverseBits(i, NumBits);
 realOut[j] = realIn[i];
 imagOut[j] = (imagIn == NULL) ? 0.0 : imagIn[i];
 }
 
 //Do the FFT
 BlockEnd = 1;
 for (BlockSize = 2; BlockSize <= numSamples; BlockSize <<= 1) {
 
 Float delta_angle = angle_numerator / (Float) BlockSize;
 
 Float sm2 = sin(-2 * delta_angle);
 Float sm1 = sin(-delta_angle);
 Float cm2 = cos(-2 * delta_angle);
 Float cm1 = cos(-delta_angle);
 Float w = 2 * cm1;
 Float ar0, ar1, ar2, ai0, ai1, ai2;
 
 for (i = 0; i < numSamples; i += BlockSize) {
 ar2 = cm2;
 ar1 = cm1;
 
 ai2 = sm2;
 ai1 = sm1;
 
 for (j = i, n = 0; n < BlockEnd; j++, n++) {
 ar0 = w * ar1 - ar2;
 ar2 = ar1;
 ar1 = ar0;
 
 ai0 = w * ai1 - ai2;
 ai2 = ai1;
 ai1 = ai0;
 
 k = j + BlockEnd;
 tr = ar0 * realOut[k] - ai0 * imagOut[k];
 ti = ar0 * imagOut[k] + ai0 * realOut[k];
 
 realOut[k] = realOut[j] - tr;
 imagOut[k] = imagOut[j] - ti;
 
 realOut[j] += tr;
 imagOut[j] += ti;
 }
 }
 
 BlockEnd = BlockSize;
 }
 
 //Need to normalize the results if we are computing the inverse transform
 if( inverseTransform ){
 Float denom = (Float) numSamples;
 
 for(i = 0; i < numSamples; i++) {
 realOut[i] /= denom;
 imagOut[i] /= denom;
 }
 }
 
 return true;
}
 
int FastFourierTransform::numberOfBitsNeeded(int powerOfTwo)
{
 for (int i = 0;; i++){
 if (powerOfTwo & (1 << i)){
 return i;
 }
 }
 return 0;
}

int FastFourierTransform::reverseBits(int index, int numBits)
{
 int i, rev;
 
 for (i = rev = 0; i < numBits; i++) {
 rev = (rev << 1) | (index & 1);
 index >>= 1;
 }
 
 return rev;
}

void FastFourierTransform::initFFT()
{
 bitTable.resize( MAX_FAST_BITS );
 
 int len = 2;
 for (int b = 1; b <= MAX_FAST_BITS; b++) {
 
 bitTable[b - 1].resize(len);
 
 for (int i = 0; i < len; i++)
 bitTable[b - 1][i] = reverseBits(i, b);
 
 len <<= 1;
 }
}

inline int FastFourierTransform::fastReverseBits(const int i, const int numBits)
{
 if (numBits <= MAX_FAST_BITS)
 return bitTable[numBits - 1][i];
 else
 return reverseBits(i, numBits);
}
 
inline bool FastFourierTransform::isPowerOfTwo(const unsigned int x){
 if (x < 2) return false;
 if (x & (x - 1)) return false;
 return true;
}

GRT_END_NAMESPACE