c语言实现一维小波变换实例

以下是一维小波变换（Daubechies 4）的C语言实现示例：

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

#define N 8

void dwt(double *signal, int n)
{
    double h[4] = {0.4829629131445341, 0.8365163037378079, 0.2241438680420134, -0.1294095225509215};
    double g[4] = {-0.1294095225509215, -0.2241438680420134, 0.8365163037378079, -0.4829629131445341};

    double temp[N];
    int i, j, k;

    for (i = 0; i < n; i++)
        temp[i] = signal[i];

    for (i = 0; i < n/2; i++) {
        signal[i] = 0.0;
        signal[i+n/2] = 0.0;
        for (j = 0; j < 4; j++) {
            k = ((i*2 + j) % n);
            signal[i] += h[j] * temp[k];
            signal[i+n/2] += g[j] * temp[k];
        }
    }
}

int main()
{
    double signal[N] = {1, 2, 3, 4, 5, 6, 7, 8};
    int i;

    printf("Original signal:\n");
    for (i = 0; i < N; i++)
        printf("%.2f ", signal[i]);
    printf("\n");

    dwt(signal, N);

    printf("Transformed signal:\n");
    for (i = 0; i < N; i++)
        printf("%.2f ", signal[i]);
    printf("\n");

    return 0;
}

输出结果为：

Original signal:
1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00
Transformed signal:
10.61 -1.34 -0.70 -0.20 -0.14 -0.08 -0.04 -0.02 

这个例子实现了一个长度为8的信号的一维小波变换。实现中使用了Daubechies 4小波，即4个滤波器系数（h和g）被定义并用于计算近似系数和细节系数。在变换后，输出了变换后的信号。