ref: 080b6c7cb5a24ae80477e441b75ba6f3bdfc2cab
dir: /src/FFT.c/
/*
*
* FFT.c
*
* Based on FFT.cpp from Audacity, which contained the following text:
*
* 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 when you know you don't care
* about phase information.
*
* 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 Numerican 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.
*
* This file is now part of SoX, and is copyright Ian Turner and others.
*
* SoX 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 2 of the License, or
* (at your option) any later version.
*
* Foobar 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 SoX; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <assert.h>
#include "FFT.h"
int **gFFTBitTable = NULL;
const int MaxFastBits = 16;
/* Declare Static functions */
static int IsPowerOfTwo(int x);
static int NumberOfBitsNeeded(int PowerOfTwo);
static int ReverseBits(int index, int NumBits);
static void InitFFT();
int IsPowerOfTwo(int x)
{
if (x < 2)
return 0;
return !(x & (x-1)); /* Thanks to 'byang' for this cute trick! */
}
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;
}
/* This function allocates about 250k (actually (2**16)-2 ints) which is never
* freed, to use as a lookup table for bit-reversal. The good news is that
* we bascially need this until the very end, so the fact that it's not freed
* is OK. */
void InitFFT()
{
int len, b;
gFFTBitTable = (int**)calloc(MaxFastBits, sizeof(*gFFTBitTable));
len = 2;
for (b = 1; b <= MaxFastBits; b++) {
int i;
gFFTBitTable[b - 1] = (int*)calloc(len, sizeof(**gFFTBitTable));
for (i = 0; i < len; i++) {
gFFTBitTable[b - 1][i] = ReverseBits(i, b);
}
len <<= 1;
}
}
#define FastReverseBits(i, NumBits) \
(NumBits <= MaxFastBits) ? gFFTBitTable[NumBits - 1][i] : ReverseBits(i, NumBits)
/*
* Complex Fast Fourier Transform
*/
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;
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 for 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 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;
float *tmpReal = (float*)calloc(Half, sizeof(float));
float *tmpImag = (float*)calloc(Half, sizeof(float));
for (i = 0; i < Half; i++) {
tmpReal[i] = RealIn[2 * i];
tmpImag[i] = RealIn[2 * i + 1];
}
FFT(Half, 0, tmpReal, tmpImag, RealOut, ImagOut);
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];
free(tmpReal);
free(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, i, i3;
float theta, wtemp, wpr, wpi, wr, wi;
float h1r, h1i, h2r, h2i, rt, it;
float *tmpReal;
float *tmpImag;
float *RealOut;
float *ImagOut;
Half = NumSamples / 2;
theta = M_PI / Half;
tmpReal = (float*)calloc(Half, sizeof(float));
tmpImag = (float*)calloc(Half, sizeof(float));
RealOut = (float*)calloc(Half, sizeof(float));
ImagOut = (float*)calloc(Half, sizeof(float));
for (i = 0; i < Half; i++) {
tmpReal[i] = In[2 * i];
tmpImag[i] = In[2 * i + 1];
}
FFT(Half, 0, tmpReal, tmpImag, RealOut, ImagOut);
wtemp = (float) sin(0.5 * theta);
wpr = -2.0 * wtemp * wtemp;
wpi = (float) sin(theta);
wr = 1.0 + wpr;
wi = wpi;
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;
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[Half / 2];
it = ImagOut[Half / 2];
Out[Half / 2] = rt * rt + it * it;
free(tmpReal);
free(tmpImag);
free(RealOut);
free(ImagOut);
}
/*
* Windowing Functions
*/
void WindowFunc(windowfunc_t whichFunction, int NumSamples, float *in)
{
int i;
switch (whichFunction) {
case BARTLETT:
for (i = 0; i < NumSamples / 2; i++) {
in[i] *= (i / (float) (NumSamples / 2));
in[i + (NumSamples / 2)] *=
(1.0 - (i / (float) (NumSamples / 2)));
}
break;
case HAMMING:
for (i = 0; i < NumSamples; i++)
in[i] *= 0.54 - 0.46 * cos(2 * M_PI * i / (NumSamples - 1));
break;
case HANNING:
for (i = 0; i < NumSamples; i++)
in[i] *= 0.50 - 0.50 * cos(2 * M_PI * i / (NumSamples - 1));
break;
case RECTANGULAR:
break;
}
}