快速傅里叶变换（正/反）

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define  PI 3.141592653589793238462643383279        //这三十位的PI我小学就会背了

void fft_rec(int N,int offset,int delta,double (*x)[2],double (*X)[2],double (*XX)[2])
{
    int N2=N/2;
    int k;
    double cs,sn;
    int k00,k01,k10,k11;
    double tmp0,tmp1;

    if(N != 2)  
    {
        fft_rec(N2, offset, 2*delta, x, XX, X);
        fft_rec(N2, offset+delta, 2*delta, x, XX, X);

        for(k=0; k<N2; k++)
        {
            k00 = offset + k*delta;    k01 = k00 + N2*delta;
            k10 = offset + 2*k*delta;  k11 = k10 + delta;
            cs = cos(2*PI*k/(double)N); sn = sin(2*PI*k/(double)N);
            tmp0 = cs * XX[k11][0] + sn * XX[k11][1];
            tmp1 = cs * XX[k11][1] - sn * XX[k11][0];
            X[k01][0] = XX[k10][0] - tmp0;
            X[k01][1] = XX[k10][1] - tmp1;
            X[k00][0] = XX[k10][0] + tmp0;
            X[k00][1] = XX[k10][1] + tmp1;
        }
    }
    else  
    {
        k00 = offset; k01 = k00 + delta;
        X[k01][0] = x[k00][0] - x[k01][0];
        X[k01][1] = x[k00][1] - x[k01][1];
        X[k00][0] = x[k00][0] + x[k01][0];
        X[k00][1] = x[k00][1] + x[k01][1];
    }
}

void fft(int N,double (*x)[2],double (*X)[2])
{
    double (*XX)[2]=malloc(2*N*sizeof(double));
    fft_rec(N,0,1,x,X,XX);
    free(XX);
}

void ifft(int N, double (*x)[2], double (*X)[2])
{
    int N2 = N/2;       
    int i;             
    double tmp0, tmp1;  

    fft(N, X, x);
    x[0][0] = x[0][0]/N;    
    x[0][1] = x[0][1]/N;
    x[N2][0] = x[N2][0]/N;  
    x[N2][1] = x[N2][1]/N;
    for(i=1; i<N2; i++)
    {
        tmp0 = x[i][0]/N;       
        tmp1 = x[i][1]/N;
        
        x[i][0] = x[N-i][0]/N; 
        x[i][1] = x[N-i][1]/N;

        x[N-i][0] = tmp0;      
        x[N-i][1] = tmp1;
    }
}

int main()
{
    int N;                //N点FFT变换，数据的个数
    int i;                //通用索引变量
    double dummy;        //随便起的名字
    double (*x)[2];        //时域采样，x[i][0]实部，x[i][1]虚部
    double (*X)[2];        //频域采样，X[i][0]实部，X[i][1]虚部
    FILE *fp;            //文件指针
    char *file="C:\\Users\\tc\\Documents\\Visual Studio 2010\\Projects\\fftc\\Debug\\data.txt";    //data.txt文件全路径
    N=0;            

    if (!(fp=fopen(file,"r")))
    {
        printf("file not read data");
        system("pause");
        return 0;
    }
    
    while (fscanf(fp, "%lg%lg",&dummy,&dummy)==2)
        N++;
    printf("N=%d",N);

    if (N>=2)
    {
        i=N;
        while(i==2*(i/2))
            i=i/2;
    }

    if (N<2 || i!=1)
    {
        printf(",must equal 2^n for an integer n>=1");
        system("pause");
        return 0;
    }

    x=malloc(2*N*sizeof(double));
    X=malloc(2*N*sizeof(double));

    rewind(fp);            //重置文件指针

    for (i=0;i<N;i++)
        fscanf(fp,"%lg%lg",&x[i][0],&x[i][1]);        //读取文件数据，赋为时域采样值
    fclose(fp);                    //关闭文件

    printf("\n时域采样数据x(n):\n");        //显示原始数据
    for (i=0;i<N;i++)
    {
        printf("%12f %12f\n",x[i][0],x[i][1]);
    }
    
    fft(N,x,X);        //正变换函数

    printf("\n频域变换数据X(k):\n");        //显示正变换后的数据
    for (i=0;i<N;i++)
    {
        printf("%12f %12f\n",X[i][0],X[i][1]);
        x[i][0]=0;
        x[i][1]=0;
    }

    ifft(N,x,X);        //反变换函数

    printf("\n再反变换后时域数据x(n):\n");    //显示反变换后的数据，理论上和原数据一致
    for (i=0;i<N;i++)
    {
        printf("%12f %12f\n",x[i][0],x[i][1]);
    }
    free(x);
    free(X);

    system("pause");
    return 0;
}

data.txt:

3.6 2.6
2.9 6.3
5.6 4.0
4.8 9.1
3.3 0.4
5.9 4.8
5.0 2.6
4.3 4.1

受朋友所托，写了这样的一个程序，参考了加州理工一个老外的程序。