C++傅里叶变换

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


#define pi 3.1415926

typedef struct 
{
    float re;// really 
    float im;// imaginary 
}complex, * pcomplex;

complex complexadd(complex a, complex b) //复数加
{ 
    complex rt;
    rt.re = a.re + b.re;
    rt.im = a.im + b.im;
    return rt;
}

complex complexMult(complex a, complex b) //复数乘
{ 
    complex rt;
    rt.re = a.re * b.re - a.im * b.im;
    rt.im = a.im * b.re + a.re * b.im;
    return rt;
}
//离散傅里叶变换
void dft(complex F[], complex x[], int N) //X[]标识变换后频域，x[]为时域采样信号，下同
{ 
    float data_re[10];
    float data_im[10];
    complex temp;
    complex data;
    int k, n;
    for (int k = 0; k < N; k++)
    {
        F[k].re = 0;
        F[k].im = 0;
        for (int n = 0; n < N; n++)
        {
            temp.re = (float)cos(2 * pi * k * n / N);
            temp.im = -(float)sin(2 * pi * k * n / N);
            F[k] = complexadd(F[k], complexMult(x[n], temp));
            data = complexadd(F[k], complexMult(x[n], temp));
            data_re[n] = temp.re;
            data_im[n] = temp.im;
        }
    }
}
//离散傅里叶逆变换
void idft(complex X[], complex x[], int N) 
{
    complex temp;
    int k, n;
    for (int k = 0; k < N; k++)
    {
        x[k].re = 0;
        x[k].im = 0;
        for (int n = 0; n < N; n++)
        {
            temp.re = (float)cos(2 * pi * k * n / N);
            temp.im = (float)sin(2 * pi * k * n / N);
            x[k] = complexadd(x[k], complexMult(X[n], temp));
        }
        x[k].re /= N;
        x[k].im /= N;
    }
}

#define N 10

int main() 
{
    complex samples[N], X[N], x[N]; //samples[]示例

    for (int i = 0; i < N; i++)
    {
        samples[i].re = i;
        samples[i].im = 0;
    }
    dft(X, samples, N);
    printf("DFI:\n");
    for (int i = 0; i < N; i++)
    {
        printf("(%f,%f)\n", X[i].re, X[i].im);
    }

    idft(X, x, N);
    printf("IDFI:\n");
    for (int i = 0; i < N; i++)
    {
        printf("(%f,%f)\n", x[i].re, x[i].im);
    }
}

 运行结果如下