第二代小波变换降噪算法C代码

由于第二代小波变换降噪算法的实现方式有很多种，因此这里提供一种基于MATLAB的实现思路，将其转化为C语言代码如下：

#include <math.h>

#define MAX(x,y) ((x)>(y)?(x):(y)) // 宏定义求最大值 #define MIN(x,y) ((x)<(y)?(x):(y)) // 宏定义求最小值

// 定义小波函数 double Wavelet(int n, int m, double x) { double s; if (n == 0) s = 1; else if (n == 1) s = x; else if (n == 2) s = 2 * x * x - 1; else if (n == 3) s = 4 * x * x * x - 3 * x; else if (n == 4) s = 8 * x * x * x * x - 8 * x * x + 1; else if (n == 5) s = 16 * x * x * x * x * x - 20 * x * x * x + 5 * x; else if (n == 6) s = 32 * x * x * x * x * x * x - 48 * x * x * x * x + 18 * x * x - 1; else if (n == 7) s = 64 * x * x * x * x * x * x * x - 112 * x * x * x * x * x + 56 * x * x * x - 7 * x; else s = 0; if (m == 0) return s; else if (m == 1) return s * exp(-x * x / 2); else return s * pow(x, m) * exp(-x * x / 2); }

// 定义小波函数的导数 double WaveletDer(int n, int m, double x) { if (n == 0) return 0; else if (m == 0) return -Wavelet(n - 1, 0, x); else return Wavelet(n - 1, m - 1, x) - x * Wavelet(n - 1, m, x); }

// 定义小波变换 void WaveletTransform(double *a, int n) { double *tmp = (double *)malloc(n * sizeof(double)); for (int i = 0; i < n; i++) tmp[i] = a[i]; int nh = n / 2; for (int i = 0; i < nh; i++) { a[i] = a[i * 2] * Wavelet(0, 0, 0.5) + a[i * 2 + 1] * Wavelet(0, 0, -0.5); a[i + nh] = a[i * 2] * Wavelet(0, 0, -0.5) + a[i * 2 + 1] * Wavelet(0, 0, 0.5); } for (int i = 0; i < n; i++) tmp[i] = a[i]; for (int i = 0; i < nh; i++) { a[i] = tmp[i * 2] * Wavelet(0, 0, 0.5) + tmp[i * 2 + 1] * Wavelet(0, 0, -0.5); a[i + nh] = tmp[i * 2] * Wavelet(0, 0, -0.5) + tmp[i * 2 + 1] * Wavelet(0, 0, 0.5); } }

// 定义小波逆变换 void WaveletInverseTransform(double *a, int n) { double *tmp = (double *)malloc(n * sizeof(double)); for (int i = 0; i < n; i++) tmp[i] = a[i]; int nh = n / 2; for (int i = 0; i < nh; i++) { a[i * 2] = (tmp[i] * Wavelet(0, 0, 0.5) + tmp[i + nh] * Wavelet(0, 0, -0.5)) / Wavelet(0, 0, 0.5); a[i * 2 + 1] = (tmp[i] * Wavelet(0, 0, -0.5) + tmp[i + nh] * Wavelet(0, 0, 0.5)) / Wavelet(0, 0, -0.5); } for (int i = 0; i < n; i++) tmp[i] = a[i]; for (int i = 0; i < nh; i++) { a[i * 2] = (tmp[i] * Wavelet(0, 0, 0.5) + tmp[i + nh] * Wavelet(0, 0, -0.5)) / Wavelet(0, 0, 0.5); a[i * 2 + 1] = (tmp[i] * Wavelet(0, 0, -0.5) + tmp[i + nh] * Wavelet(0, 0, 0.5)) / Wavelet(0, 0, -0.5); } }

// 定义小波阈值处理函数 void WaveletThreshold(double *a, int n, double thres) { int N = (int)log2(n); for (int i = N; i >= 1; i--) { int nh = n / pow(2, i); for (int j = 0; j < nh; j++) { double sum = 0.0; for (int k = 0; k < pow(2, i - 1); k++) sum += fabs(a[j * pow(2, i - 1) + k]); if (sum < thres) for (int k = 0; k < pow(2, i - 1); k++) a[j * pow(2, i - 1) + k] = 0.0; } } }

// 定义小波降噪函数 void WaveletDenoise(double *a, int n, double thres) { WaveletTransform(a, n); WaveletThreshold(a, n, thres); WaveletInverseTransform(a, n); }

// 定义主函数 int main() { int n = 256; // 数据长度 double *a = (double *)malloc(n * sizeof(double)); // 数据数组 double thres = 0.5; // 阈值 // 初始化数据 for (int i = 0; i < n; i++) a[i] = sin(2 * M_PI * i / n) + 0.5 * sin(4 * M_PI * i / n) + 0.2 * sin(8 * M_PI * i / n); // 对数据进行小波降噪处理 WaveletDenoise(a, n, thres); // 输出结果 for (int i = 0; i < n; i++) printf("%f ", a[i]); return 0;