提供C语言代码和matlab代码，实现长序列数据分段的级联FFT功能

以下是C语言代码实现长序列数据分段的级联FFT功能：

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

#define PI 3.14159265358979323846

typedef struct {
    double real;
    double imag;
} Complex;

// FFT变换
void fft(Complex *x, int n) {
    if (n == 1) {
        return;
    }

    Complex *xeven = (Complex *)malloc(n / 2 * sizeof(Complex));
    Complex *xodd = (Complex *)malloc(n / 2 * sizeof(Complex));

    for (int i = 0; i < n / 2; i++) {
        xeven[i] = x[2 * i];
        xodd[i] = x[2 * i + 1];
    }

    fft(xeven, n / 2);
    fft(xodd, n / 2);

    for (int k = 0; k < n / 2; k++) {
        Complex t = {cos(2 * PI * k / n), -sin(2 * PI * k / n)};
        t.real *= xodd[k].real;
        t.imag *= xodd[k].imag;

        x[k].real = xeven[k].real + t.real;
        x[k].imag = xeven[k].imag + t.imag;

        x[k + n / 2].real = xeven[k].real - t.real;
        x[k + n / 2].imag = xeven[k].imag - t.imag;
    }

    free(xeven);
    free(xodd);
}

// 长序列数据分段的级联FFT
void cascade_fft(double *x, int n, int m) {
    Complex *X = (Complex *)malloc(n * sizeof(Complex));

    for (int k = 0; k < m; k++) {
        for (int i = 0; i < n; i++) {
            X[i].real = x[k * n + i];
            X[i].imag = 0;
        }

        fft(X, n);

        for (int i = 0; i < n; i++) {
            x[k * n + i] = X[i].real * X[i].real + X[i].imag * X[i].imag;
        }
    }

    free(X);
}

int main() {
    int n = 8;
    int m = 4;

    double *x = (double *)malloc(n * m * sizeof(double));

    for (int i = 0; i < m; i++) {
        for (int j = 0; j < n; j++) {
            x[i * n + j] = sin(2 * PI * i * j / n);
        }
    }

    cascade_fft(x, n, m);

    for (int i = 0; i < m; i++) {
        for (int j = 0; j < n; j++) {
            printf("%lf ", x[i * n + j]);
        }
        printf("\n");
    }

    free(x);

    return 0;
}

以下是MATLAB代码实现长序列数据分段的级联FFT功能：

n = 8;
m = 4;
x = zeros(n, m);

for i = 1:m
    for j = 1:n
        x(j, i) = sin(2 * pi * (i - 1) * (j - 1) / n);
    end
end

for k = 1:m
    X = fft(x(:, k));
    x(:, k) = abs(X).^2;
end

disp(x);