fft.c

fft.c code composer studio v 3.01 by steven

/*
 *
 * 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;
   }
}

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,
         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;
    }
}