c语言实现4096个点的FFT程序

由于FFT算法比较复杂，实现4096点的FFT需要一定的数学和编程知识。以下是一个简单的C语言实现4096点FFT的程序：

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

#define N 4096

void fft(double *real, double *imag, int n, int inverse) {
    int i, j, k, m;
    double tempreal, tempimag, wreal, wimag, treal, timag;
    double pi = inverse ? -acos(-1.0) : acos(-1.0);
    
    for (i = 0; i < n; i++) {
        j = 0;
        for (k = 0; k < log2(n); k++) {
            j |= ((i >> k) & 1) << (log2(n) - 1 - k);
        }
        if (j > i) {
            tempreal = real[i];
            real[i] = real[j];
            real[j] = tempreal;
            tempimag = imag[i];
            imag[i] = imag[j];
            imag[j] = tempimag;
        }
    }
    
    for (m = 2; m <= n; m <<= 1) {
        wreal = cos(2.0 * pi / m);
        wimag = sin(2.0 * pi / m);
        for (k = 0; k < n; k += m) {
            treal = 1.0;
            timag = 0.0;
            for (i = k; i < k + (m >> 1); i++) {
                tempreal = treal * real[i + (m >> 1)] - timag * imag[i + (m >> 1)];
                tempimag = treal * imag[i + (m >> 1)] + timag * real[i + (m >> 1)];
                real[i + (m >> 1)] = real[i] - tempreal;
                imag[i + (m >> 1)] = imag[i] - tempimag;
                real[i] += tempreal;
                imag[i] += tempimag;
                tempreal = treal * wreal - timag * wimag;
                timag = treal * wimag + timag * wreal;
                treal = tempreal;
            }
        }
    }
    
    if (inverse) {
        for (i = 0; i < n; i++) {
            real[i] /= n;
            imag[i] /= n;
        }
    }
}

int main() {
    double real[N], imag[N];
    int i;
    
    // 生成输入信号
    for (i = 0; i < N; i++) {
        real[i] = sin(2.0 * acos(-1.0) * i / N);
        imag[i] = 0.0;
    }
    
    // 进行FFT变换
    fft(real, imag, N, 0);
    
    // 输出结果
    for (i = 0; i < N; i++) {
        printf("%f + %fi\n", real[i], imag[i]);
    }
    
    return 0;
}

该程序通过调用fft函数实现了对4096个点进行FFT变换，其中real和imag分别为输入实数和虚数数组，n为变换点数，inverse为0表示正变换，为1表示逆变换。程序中使用了蝴蝶运算和位逆序置换两种常用的实现FFT的方法。最后，程序输出了变换后的实部和虚部。