c语言实现傅里叶变换，并翻译成MATLAB

C语言实现傅里叶变换：

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

#define PI 3.14159265358979323846

typedef struct {
    double re;
    double im;
} complex;

void fft(complex *x, int N) {
    if (N <= 1) return;
    complex *even = (complex *)malloc(N/2 * sizeof(complex));
    complex *odd = (complex *)malloc(N/2 * sizeof(complex));
    for (int i = 0; i < N/2; i++) {
        even[i] = x[2*i];
        odd[i] = x[2*i+1];
    }
    fft(even, N/2);
    fft(odd, N/2);
    for (int k = 0; k < N/2; k++) {
        complex t = {cos(2*PI*k/N), -sin(2*PI*k/N)};
        t.re *= odd[k].re;
        t.im *= odd[k].im;
        odd[k].re = even[k].re - t.re;
        odd[k].im = even[k].im - t.im;
        even[k].re += t.re;
        even[k].im += t.im;
        x[2*k] = even[k];
        x[2*k+1] = odd[k];
    }
    free(even);
    free(odd);
}

int main() {
    int N = 8;  // 8个采样点
    double x[] = {1, 1, 1, 1, 0, 0, 0, 0};  // 4个正弦波的采样值
    complex *X = (complex *)malloc(N * sizeof(complex));
    for (int i = 0; i < N; i++) {
        X[i].re = x[i];
        X[i].im = 0;
    }
    fft(X, N);
    for (int i = 0; i < N; i++) {
        printf("X[%d] = (%f, %f)\n", i, X[i].re, X[i].im);
    }
    free(X);
    return 0;
}

MATLAB实现傅里叶变换：

N = 8;  % 8个采样点
x = [1 1 1 1 0 0 0 0];  % 4个正弦波的采样值
X = fft(x, N);
for i = 1:N
    fprintf('X[%d] = (%f, %f)\n', i-1, real(X(i)), imag(X(i)));
end