fft.cpp

该程序是用C写的FFT的程序

/**********************************************************************

  FFT.cpp

  Dominic Mazzoni

  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 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.

**********************************************************************/

#include <stdlib.h>
#include <stdio.h>
#include <math.h>

#include "FFT.h"

#ifndef M_PI
#define	M_PI		3.14159265358979323846	/* pi */
#endif

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;

  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;

  delete[] tmpReal;
  delete[] tmpImag;
  delete[] RealOut;
  delete[] ImagOut;
}