fft.h

实现快速FFT傅立叶变换算法的Header文件

// FFT.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"
#include"math.h"
#include<stdio.h>
#include<stdlib.h>
#include<complex>
#include<iostream.h>
using namespace std;


/* 
Modification of Paul Bourkes FFT code by Peter Cusack 
to utilise the Microsoft complex type. 

This computes an in-place complex-to-complex FFT 
x and y are the real and imaginary arrays of 2^m points. 
dir = 1 gives forward transform 
dir = -1 gives reverse transform 
*/ 
void FFT(int dir, long m, complex <double> x[]) 
{ 
long i, i1, i2,j, k, l, l1, l2, n; 
complex <double> tx, t1, u, c; 

/*Calculate the number of points */ 
n = 1; 
for(i = 0; i < m; i++) 
n <<= 1; 

/* Do the bit reversal */ 
i2 = n >> 1; 
j = 0; 

for (i = 0; i < n-1 ; i++) 
{ 
if (i < j) 
swap(x[i], x[j]); 

k = i2; 

while (k <= j) 
    { 
j -= k; 
k >>= 1; 
} 

j += k; 
} 

/* Compute the FFT */ 
c.real(-1.0); 
c.imag(0.0); 
l2 = 1; 
for (l = 0; l < m; l++) 
{ 
l1 = l2; 
l2 <<= 1; 
u.real(1.0); 
u.imag(0.0); 

for (j = 0; j < l1; j++) 
    { 
for (i = j; i < n; i += l2) 
        { 
i1 = i + l1; 
t1 = u * x[i1]; 
x[i1] = x[i] - t1; 
x[i] += t1; 
} 

u = u * c; 
} 

c.imag(sqrt((1.0 - c.real()) / 2.0)); 
if (dir == 1) 
c.imag(-c.imag()); 
c.real(sqrt((1.0 + c.real()) / 2.0)); 
} 

/* Scaling for forward transform */ 
if (dir == 1) 
{ 
for (i = 0; i < n; i++) 
x[i] /= n; 
} 
return; 
}