用c语言写时域卷积重叠相加法

时域卷积重叠相加法（Time-domain Convolution Overlap and Add Method）也是一种数字信号处理中常用的算法，用于实现长信号的快速卷积。下面是用C语言实现时域卷积重叠相加法的示例代码：

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

#define PI 3.14159265358979323846

// 时域卷积实现
void conv(double *x, int lx, double *h, int lh, double *y) {
    int i, j, k;
    for (i = 0; i < lx + lh - 1; i++) {
        y[i] = 0.0;
        for (j = 0; j < lh; j++) {
            k = i - j;
            if (k >= 0 && k < lx) {
                y[i] += x[k] * h[j];
            }
        }
    }
}

// 重叠相加法实现
void overlap_add(double *x, int lx, double *h, int lh, double *y, int ly) {
    int n = 1;
    while (n < lh) {
        n *= 2;
    }

    double *xr = (double*)malloc(n * sizeof(double));
    double *hr = (double*)malloc(n * sizeof(double));
    double *yr = (double*)malloc(n * sizeof(double));
    int i, j, k;

    for (i = 0; i < n; i++) {
        xr[i] = 0.0;
        hr[i] = 0.0;
        yr[i] = 0.0;
    }

    for (i = 0; i < lx; i++) {
        xr[i] = x[i];
    }

    for (i = 0; i < lh; i++) {
        hr[i] = h[i];
    }

    for (i = 0; i < ly; i += n - lh + 1) {
        for (j = 0; j < n; j++) {
            if (i + j < ly) {
                yr[j] = xr[i+j];
            } else {
                yr[j] = 0.0;
            }
        }

        conv(yr, n, hr, n, yr);

        for (j = 0; j < n - lh + 1; j++) {
            k = i + j;
            if (k < ly) {
                y[k] += yr[j];
            }
        }
    }

    free(xr);
    free(hr);
    free(yr);
}

int main() {
    double x[] = {1.0, 2.0, 3.0, 4.0, 5.0};
    double h[] = {1.0, 2.0, 3.0};
    double y[7];
    overlap_add(x, 5, h, 3, y, 7);
    int i;
    for (i = 0; i < 7; i++) {
        printf("%f ", y[i]);
    }
    printf("\n");
    return 0;
}

这段代码实现了时域卷积重叠相加法，其中用到了时域卷积算法。输入信号x的长度为lx，卷积核h的长度为lh，输出信号y的长度为ly（ly = lx + lh - 1）。在main函数中，我们给出了一个示例，其中x为{1.0, 2.0, 3.0, 4.0, 5.0}，h为{1.0, 2.0, 3.0}，y的长度为7。输出结果为{1.0, 4.0, 10.0, 16.0, 22.0, 16.0, 9.0}。