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#include "fft.h"
#include <math.h>
#include <stdlib.h>
/* Everything here comes from Audacity 1.3.13
(orignally in C++ and with more genericity and functionnality)
Original Author : Dominic Mazzoni
Licenced under GPL 2.0 (see LICENCE)
*/
#define MaxFastBits 16
int *gFFTBitTable[MaxFastBits]={NULL};
void InitFFT();
int NumberOfBitsNeeded(int PowerOfTwo);
inline int FastReverseBits(int i, int NumBits);
int ReverseBits(int index, int NumBits);
void FFT(int NumSamples,
int 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;
double tr, ti; /* temp real, temp imaginary */
/*
if (!IsPowerOfTwo(NumSamples)) {
fprintf(stderr, "%d is not a power of two\n", NumSamples);
exit(1);
}
*/
if (!gFFTBitTable[0])
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;
double sm2 = sin(-2 * delta_angle);
double sm1 = sin(-delta_angle);
double cm2 = cos(-2 * delta_angle);
double cm1 = cos(-delta_angle);
double w = 2 * cm1;
double 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;
}
}
}
void InitFFT() {
int len=2;
int b, i;
for (b=0; b<MaxFastBits; b++) {
gFFTBitTable[b]=malloc(len*sizeof(int));
for (i=0; i<len; i++)
gFFTBitTable[b][i] = ReverseBits(i, b+1);
len <<= 1;
}
}
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;
}
inline int FastReverseBits(int i, int NumBits)
{
if (NumBits <= MaxFastBits)
return gFFTBitTable[NumBits - 1][i];
else
return ReverseBits(i, NumBits);
}
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;
}
/*
* 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(float In[PSNumS], float Out[PSHalf]) {
int i;
float theta = M_PI / PSHalf;
float tmpReal[PSHalf];
float tmpImag[PSHalf];
float RealOut[PSHalf];
float ImagOut[PSHalf];
for (i=0; i<PSHalf; i++) {
tmpReal[i] = In[2*i];
tmpImag[i] = In[2*i+1];
}
FFT(PSHalf, 0, tmpReal, tmpImag, RealOut, ImagOut);
float wtemp = sin(0.5 * theta);
float wpr = -2.0 * wtemp * wtemp;
float wpi = -1.0 * sin(theta);
float wr = 1.0 + wpr;
float wi = wpi;
int i3;
float h1r, h1i, h2r, h2i, rt, it;
for (i=1; i < PSHalf/2; i++) {
i3 = PSHalf - 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;
it = h1i + wr * h2i + wi * h2r;
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;
}
rt = (h1r = RealOut[0]) + ImagOut[0];
it = h1r - ImagOut[0];
Out[0] = rt * rt + it * it;
rt = RealOut[PSHalf / 2];
it = ImagOut[PSHalf / 2];
Out[PSHalf / 2] = rt * rt + it * it;
}
void DeinitFFT() {
int i;
if (gFFTBitTable[0]) {
for (i=0;i<MaxFastBits;i++) {
free(gFFTBitTable[i]);
}
}
}
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