/*

* This file contains codes realize Fast Fourier Transform;

* Created By Suzm 2015.06.10.

* Finised 2015.06.10.

* Copyright reserved.

* Compiled with gcc `gcc fft.c -std=c99 -lm -o fft`.

*

*/

#include <stdio.h>

#include <complex.h>

#include <math.h>

#include <string.h>

#include <stdlib.h>

#define PI 3.1415926

#define FORWARD 1

#define BACKWARD 0

unsigned reversebit(unsigned a,unsigned char );

void fft(double _Complex *in, double _Complex *out, unsigned char N,short sign);

void cdprintf(double _Complex *, unsigned );

int main(int argc, char const *argv[])

{

double _Complex *in, *out;

double real,imag;

unsigned short N;

printf("Please input sequence lenth: ");

scanf("%hu",&N);

unsigned listlenth = pow(2,N);

in = (double _Complex *)malloc(sizeof(double _Complex)*pow(2,N));

for(int i=0;i<pow(2,N);i++){

scanf("%lf %lf",&real,&imag);

in[i]=real+imag*I;

}

out = (double _Complex *)malloc(sizeof(double _Complex)*pow(2,N));

printf("\nFORWARD fft");

fft(in, out, N,FORWARD);

cdprintf(out,listlenth);

printf("\nBACKWARD fft");

fft(out,in,N,BACKWARD);

cdprintf(in,listlenth);

putchar('\n');

free(out);

free(in);

return 0;

}

void fft(double _Complex *in, double _Complex *out,unsigned char N, short sign)

{

double _Complex *mid;

unsigned temp, temp1,rank;

unsigned listlenth = pow(2,N);

mid=(double _Complex *)malloc(sizeof(double _Complex)*listlenth);

for(unsigned i=0;i<listlenth;i++)

mid[i]=in[reversebit(i,(unsigned char)N)];

unsigned j, t, interval;

double _Complex exponent, exponent_unit;

interval = 1;

for(unsigned i=1;i<=N;i++){

j=0;

while(j<listlenth){

exponent_unit = (sign<=0)? cexp(I*PI/interval):cexp(-I*PI/interval);

exponent= 1;

for(t=0;t<interval*2;t++){

out[t+j]=mid[t%interval+j]+exponent*mid[t%interval+interval+ j];

exponent *= exponent_unit;

}

j=j+interval*2;

}

interval *= 2;

memcpy(mid,out,listlenth*sizeof(double _Complex));

}

if (sign <=0){

for(j = 0;j <listlenth;j++)

out[j] /= listlenth;

}

free(mid);

}

unsigned reversebit(unsigned a, unsigned char N)

{

/*

This function is used to reverse number bit:

For Example : 6 in binary is 110, it's reverse bit is 011 which is 3(Oct) .

so, 3=reversebit(6, 3);

*/

unsigned b=0, c=1;

for(unsigned char i=1;i<=N;i++)

{

b=b<<1;

b = b+(c&a) ;

a=a>>1;

}

return b;

}

void cdprintf(double _Complex * in,unsigned N)

{

putchar('\n');

for(unsigned i=0;i<N;i++)

printf("%lf%+lf*I%c",creal(in[i]),cimag(in[i]),i%5==4?'\n':'\t' );

}