帮我写个1000点FFT的c语言算法

当然，我很乐意帮你！这里是一个简单的C语言实现，以帮助你实现1000点FFT算法：

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

#define PI 3.141592653589793238462643383279502884197

typedef struct {
    double real, imag;
} Complex;

void FFT(Complex *X, int N)
{
    if (N == 1) {
        return;
    }
    Complex X_even[N/2], X_odd[N/2];
    int i;
    for (i = 0; i < N/2; ++i) {
        X_even[i] = X[2*i];
        X_odd[i] = X[2*i+1];
    }
    FFT(X_even, N/2);
    FFT(X_odd, N/2);
    for (i = 0; i < N/2; ++i) {
        Complex temp = {
            X_odd[i].real * cos(2 * PI * i / (double)N) + X_odd[i].imag * sin(2 * PI * i / (double)N),
            -X_odd[i].real * sin(2 * PI * i / (double)N) + X_odd[i].imag * cos(2 * PI * i / (double)N)
        };
        X[2*i] = (Complex){X_even[i].real + temp.real, X_even[i].imag + temp.imag};
        X[2*i+1] = (Complex){X_even[i].real - temp.real, X_even[i].imag - temp.imag};
    }
}

int main()
{
    int n = 1000;
    Complex x[n];
    int i;
    for (i = 0; i < n; ++i) {
        x[i] = (Complex){sin(2 * PI * i / n), 0};
    }
    FFT(x, n);
    for (i = 0; i < n; ++i) {
        printf("%f %f\n", x[i].real, x[i].imag);
    }
    return 0;
}

这个算法的时间复杂度为O(NlogN)，对于N=1000是非常快的。