/**********************************************************************
fft.cpp
This class is a C++ wrapper for original code
written by Dominic Mazzoni in September 2000
This file contains a few FFT routines, including a real-FFT
routine that is almost twice as fast as a normal complex FFT,
and a power spectrum routine which is more convenient when
you know you don't care about phase information. It now also
contains a few basic windowing functions.
Some of this code was based on a free implementation of an FFT
by Don Cross, available on the web at:
http://www.intersrv.com/~dcross/fft.html
The basic algorithm for his code was based on Numerical Recipes
in Fortran. I optimized his code further by reducing array
accesses, caching the bit reversal table, and eliminating
float-to-double conversions, and I added the routines to
calculate a real FFT and a real power spectrum.
Note: all of these routines use single-precision floats.
I have found that in practice, floats work well until you
get above 8192 samples. If you need to do a larger FFT,
you need to use doubles.
**********************************************************************/
#include "fft.h"
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
int **gFFTBitTable = NULL;
const int MaxFastBits = 16;
int IsPowerOfTwo(int x)
{
if (x < 2)
return false;
if (x & (x - 1)) /* Thanks to 'byang' for this cute trick! */
return false;
return true;
}
int NumberOfBitsNeeded(int PowerOfTwo)
{
int i;
if (PowerOfTwo < 2) {
fprintf(stderr, "Error: FFT called with size %d\n", PowerOfTwo);
exit(1);
}
for (i = 0;; i++)
if (PowerOfTwo & (1 << i))
return i;
}
int 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 InitFFT()
{
gFFTBitTable = new int *[MaxFastBits];
int len = 2;
for (int b = 1; b <= MaxFastBits; b++) {
gFFTBitTable[b - 1] = new int[len];
for (int i = 0; i < len; i++)
gFFTBitTable[b - 1][i] = ReverseBits(i, b);
len <<= 1;
}
}
inline int FastReverseBits(int i, int NumBits)
{
if (NumBits <= MaxFastBits)
return gFFTBitTable[NumBits - 1][i];
else
return ReverseBits(i, NumBits);
}
/*
* Complex Fast Fourier Transform
*/
void 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;
double angle_numerator = 2.0 * M_PI;
float tr, ti; /* temp real, temp imaginary */
if (!IsPowerOfTwo(NumSamples)) {
fprintf(stderr, "%d is not a power of two\n", NumSamples);
exit(1);
}
if (!gFFTBitTable)
InitFFT();
if (InverseTransform)
angle_numerator = -angle_numerator;
NumBits = NumberOfBitsNeeded(NumSamples);
/*
** Do simultaneous 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 itself...
*/
BlockEnd = 1;
for (BlockSize = 2; BlockSize <= NumSamples; BlockSize <<= 1) {
double delta_angle = angle_numerator / (double) 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 if inverse transform...
*/
if (InverseTransform) {
float denom = (float) NumSamples;
for (i = 0; i < NumSamples; i++) {
RealOut[i] /= denom;
ImagOut[i] /= denom;
}
}
}
/*
* 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]
*/
void RealFFT(int NumSamples, float *RealIn, float *RealOut, float *ImagOut)
{
int Half = NumSamples / 2;
int i;
float theta = M_PI / Half;
float *tmpReal = new float[Half];
float *tmpImag = new float[Half];
for (i = 0; i < Half; i++) {
tmpReal[i] = RealIn[2 * i];
tmpImag[i] = RealIn[2 * i + 1];
}
FFT(Half, 0, tmpReal, tmpImag, RealOut, ImagOut);
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];
delete[]tmpReal;
delete[]tmpImag;
}
/*
* PowerSpectrum
*
* This function computes the same as RealFFT, above, but
* adds the squares of the real and imaginary part of each
* coefficient, extracting the power and throwing away the
* phase.
*
* For speed, it does not call RealFFT, but duplicates some
* of its code.
*/
void PowerSpectrum(int NumSamples, float *In, float *Out)
{
int Half = NumSamples / 2;
int i;
float theta = M_PI / Half;
float *tmpReal = new float[Half];
float *tmpImag = new float[Half];
float *RealOut = new float[Half];
float *ImagOut = new float[Half];
for (i = 0; i < Half; i++) {
tmpReal[i] = In[2 * i];
tmpImag[i] = In[2 * i + 1];
}
FFT(Half, 0, tmpReal, tmpImag, RealOut, ImagOut);
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, rt, it;
//float total=0;
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]);
rt = h1r + wr * h2r - wi * h2i; //printf("Realout%i = %f",i,rt);total+=fabs(rt);
it = h1i + wr * h2i + wi * h2r; // printf(" Imageout%i = %f\n",i,it);
Out[i] = rt * rt + it * it;
rt = h1r - wr * h2r + wi * h2i;
it = -h1i + wr * h2i + wi * h2r;
Out[i3] = rt * rt + it * it;
wr = (wtemp = wr) * wpr - wi * wpi + wr;
wi = wi * wpr + wtemp * wpi + wi;
}
//printf("total = %f\n",total);
rt = (h1r = RealOut[0]) + ImagOut[0];
it = h1r - ImagOut[0];
Out[0] = rt * rt + it * it;
rt = RealOut[Half / 2];
it = ImagOut[Half / 2];
Out[Half / 2] = rt * rt + it * it;
delete[]tmpReal;
delete[]tmpImag;
delete[]RealOut;
delete[]ImagOut;
}
/*
* Windowing Functions
*/
int NumWindowFuncs()
{
return 4;
}
char *WindowFuncName(int whichFunction)
{
switch (whichFunction) {
default:
case 0:
return "Rectangular";
case 1:
return "Bartlett";
case 2:
return "Hamming";
case 3:
return "Hanning";
}
}
void WindowFunc(int whichFunction, int NumSamples, float *in)
{
int i;
if (whichFunction == 1) {
// Bartlett (triangular) window
for (i = 0; i < NumSamples / 2; i++) {
in[i] *= (i / (float) (NumSamples / 2));
in[i + (NumSamples / 2)] *=
(1.0 - (i / (float) (NumSamples / 2)));
}
}
if (whichFunction == 2) {
// Hamming
for (i = 0; i < NumSamples; i++)
in[i] *= 0.54 - 0.46 * cos(2 * M_PI * i / (NumSamples - 1));
}
if (whichFunction == 3) {
// Hanning
for (i = 0; i < NumSamples; i++)
in[i] *= 0.50 - 0.50 * cos(2 * M_PI * i / (NumSamples - 1));
}
}
/* constructor */
fft::fft() {
}
/* destructor */
fft::~fft() {
}
/* Calculate the power spectrum */
void fft::powerSpectrum(int start, int half, float *data, int windowSize,float *magnitude,float *phase, float *power, float *avg_power) {
int i;
int windowFunc = 3;
float total_power = 0.0f;
/* processing variables*/
float *in_real = new float[windowSize];
float *in_img = new float[windowSize];
float *out_real = new float[windowSize];
float *out_img = new float[windowSize];
for (i = 0; i < windowSize; i++) {
in_real[i] = data[start + i];
}
WindowFunc(windowFunc, windowSize, in_real);
RealFFT(windowSize, in_real, out_real, out_img);
for (i = 0; i < half; i++) {
/* compute power */
power[i] = out_real[i]*out_real[i] + out_img[i]*out_img[i];
total_power += power[i];
/* compute magnitude and phase */
magnitude[i] = 2.0*sqrt(power[i]);
phase[i] = atan2(out_img[i],out_real[i]);
}
/* calculate average power */
*(avg_power) = total_power / (float) half;
delete[]in_real;
delete[]in_img;
delete[]out_real;
delete[]out_img;
}
void fft::inversePowerSpectrum(int start, int half, int windowSize, float *finalOut,float *magnitude,float *phase) {
int i;
int windowFunc = 3;
/* processing variables*/
float *in_real = new float[windowSize];
float *in_img = new float[windowSize];
float *out_real = new float[windowSize];
float *out_img = new float[windowSize];
/* get real and imag part */
for (i = 0; i < half; i++) {
in_real[i] = magnitude[i]*cos(phase[i]);
in_img[i] = magnitude[i]*sin(phase[i]);
}
/* zero negative frequencies */
for (i = half; i < windowSize; i++) {
in_real[i] = 0.0;
in_img[i] = 0.0;
}
FFT(windowSize, 1, in_real, in_img, out_real, out_img); // second parameter indicates inverse transform
WindowFunc(windowFunc, windowSize, out_real);
for (i = 0; i < windowSize; i++) {
finalOut[start + i] += out_real[i];
}
delete[]in_real;
delete[]in_img;
delete[]out_real;
delete[]out_img;
}
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