Fft.cpp

#include "stdafx.h"

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

#include "fft.h"

float PI ;
float TWOPI ;

/*
 * If forward is true, rfft replaces 2*N real data points in x with
 * N complex values representing the positive frequency half of their
 * Fourier spectrum, with x[1] replaced with the real part of the Nyquist
 * frequency value.  If forward is false, rfft expects x to contain a
 * positive frequency spectrum arranged as before, and replaces it with
 * 2*N real values.  N MUST be a power of 2.
 */
void rfft( float *x, long N, int forward )
{
 float c1, c2, h1r, h1i, h2r, h2i, wr, wi, wpr, wpi, temp, theta ;
 float xr, xi ;
 long i, i1, i2, i3, i4, N2p1 ;
 static int first = 1 ;
    
	if ( first ) 
	{
        PI = (float) (4.*atan( 1. )) ;
        TWOPI = (float) (8.*atan( 1. )) ;
        first = 0 ;
    }
    
	theta = PI/N ;
    wr = 1. ;
    wi = 0. ;
    c1 = 0.5 ;
    
	if ( forward ) 
	{
        c2 = -0.5 ;
        cfft( x, N, forward ) ;
        xr = x[0] ;
        xi = x[1] ;
    }else {
			c2 = 0.5 ;
			theta = -theta ;
			xr = x[1] ;
			xi = 0. ;
			x[1] = 0. ;
		}

    wpr = (float) (-2.*pow( sin( 0.5*theta ), 2. )) ;
    wpi = (float) sin( theta ) ;
    N2p1 = (N<<1) + 1 ;
    
	for ( i = 0 ; i <= N>>1 ; i++ ) 
	{
        i1 = i<<1 ;
        i2 = i1 + 1 ;
        i3 = N2p1 - i2 ;
        i4 = i3 + 1 ;
        if ( i == 0 ) 
		{
            h1r =  c1*(x[i1] + xr ) ;
            h1i =  c1*(x[i2] - xi ) ;
            h2r = -c2*(x[i2] + xi ) ;
            h2i =  c2*(x[i1] - xr ) ;
            x[i1] =  h1r + wr*h2r - wi*h2i ;
            x[i2] =  h1i + wr*h2i + wi*h2r ;
            xr =  h1r - wr*h2r + wi*h2i ;
            xi = -h1i + wr*h2i + wi*h2r ;
        } else {
					h1r =  c1*(x[i1] + x[i3] ) ;
					h1i =  c1*(x[i2] - x[i4] ) ;
					h2r = -c2*(x[i2] + x[i4] ) ;
					h2i =  c2*(x[i1] - x[i3] ) ;
					x[i1] =  h1r + wr*h2r - wi*h2i ;
					x[i2] =  h1i + wr*h2i + wi*h2r ;
					x[i3] =  h1r - wr*h2r + wi*h2i ;
					x[i4] = -h1i + wr*h2i + wi*h2r ;
				}
        
		wr = (temp = wr)*wpr - wi*wpi + wr ;
        wi = wi*wpr + temp*wpi + wi ;
    }
    
	if ( forward )
        x[1] = xr ;
    else
        cfft( x, N, forward ) ;
}

/*
 * cfft replaces float array x containing NC complex values
 * (2*NC float values alternating real, imagininary, etc.)
 * by its Fourier transform if forward is true, or by its
 * inverse Fourier transform if forward is false, using a
 * recursive Fast Fourier transform method due to Danielson
 * and Lanczos.  NC MUST be a power of 2.
 */
void cfft( float *x, long NC, int forward )
{
 float wr, wi, wpr, wpi, theta, scale ;
 long mmax, ND, m, i, j, delta ;
    ND = NC<<1 ;
    bitreverse( x, ND ) ;
    for ( mmax = 2 ; mmax < ND ; mmax = delta ) 
	{
        delta = mmax<<1 ;
        theta = TWOPI/( forward? mmax : -mmax ) ;
        wpr = (float) (-2.*pow( sin( 0.5*theta ), 2. )) ;
        wpi = (float) sin( theta ) ;
        wr = 1. ;
        wi = 0. ;
        for ( m = 0 ; m < mmax ; m += 2 ) 
		{
			register float rtemp, itemp ;
			for ( i = m ; i < ND ; i += delta ) 
			{
                j = i + mmax ;
                rtemp = wr*x[j] - wi*x[j+1] ;
                itemp = wr*x[j+1] + wi*x[j] ;
                x[j] = x[i] - rtemp ;
                x[j+1] = x[i+1] - itemp ;
                x[i] += rtemp ;
                x[i+1] += itemp ;
            }
            wr = (rtemp = wr)*wpr - wi*wpi + wr ;
            wi = wi*wpr + rtemp*wpi + wi ;
        }
    }
/*
 * scale output
 */
    scale = forward ? 6./ND : 2. ; //    scale = forward ? 1./ND : 2. ;
    {							   //6.0 is the optimized value fot Cool Edit FFT view	
		register float *xi=x, *xe=x+ND ;
        while ( xi < xe )
            *xi++ *= scale ;
    }
}
/*
 * bitreverse places float array x containing N/2 complex values
 * into bit-reversed order
 */
void bitreverse( float *x, long N )
{
 float rtemp, itemp ;
 long i, j, m ;
    for ( i = j = 0 ; i < N ; i += 2, j += m ) {
        if ( j > i ) {
            rtemp = x[j] ; itemp = x[j+1] ; /* complex exchange */
            x[j] = x[i] ; x[j+1] = x[i+1] ;
            x[i] = rtemp ; x[i+1] = itemp ;
        }
        for ( m = N>>1 ; m >= 2 && j >= m ; m >>= 1 )
            j -= m ;
    }
}