小波学习之一（单层一维离散小波变换DWT的Mallat算法C++和MATLAB实现） ---转载

好的，你的第一个问题是关于单层一维离散小波变换DWT的Mallat算法的实现。以下是C++和MATLAB实现的代码：

C++代码：

#include <iostream>
#include <cmath>
#include <cstdlib>
#include <cstdio>

using namespace std;

const int MAXN = 1024;

double h0 = (1 + sqrt(3)) / (4 * sqrt(2));
double h1 = (3 + sqrt(3)) / (4 * sqrt(2));
double g0 = (1 - sqrt(3)) / (4 * sqrt(2));
double g1 = (3 - sqrt(3)) / (4 * sqrt(2));

void dwt(double *a, int n, double *c, double *d)
{
    int i, j, k;
    double tmp[MAXN];
    for (i = 0; i < n; i += 2) {
        tmp[i / 2] = a[i] * h0 + a[i + 1] * h1;
        tmp[(i + n) / 2] = a[i] * g0 + a[i + 1] * g1;
    }
    for (i = 0; i < n; ++i) {
        a[i] = tmp[i];
    }
    for (i = 0; i < n / 2; ++i) {
        c[i] = tmp[i];
        d[i] = tmp[i + n / 2];
    }
}

int main()
{
    int i, n = 8;
    double a[MAXN], c[MAXN], d[MAXN];
    for (i = 0; i < n; ++i) {
        a[i] = i + 1;
    }
    dwt(a, n, c, d);
    printf("Input:\n");
    for (i = 0; i < n; ++i) {
        printf("%.2lf ", a[i]);
    }
    printf("\n");
    printf("Low-pass filter output:\n");
    for (i = 0; i < n / 2; ++i) {
        printf("%.2lf ", c[i]);
    }
    printf("\n");
    printf("High-pass filter output:\n");
    for (i = 0; i < n / 2; ++i) {
        printf("%.2lf ", d[i]);
    }
    printf("\n");
    return 0;
}

MATLAB代码：

function [c, d] = dwt(a)
n = length(a);
h0 = (1 + sqrt(3)) / (4 * sqrt(2));
h1 = (3 + sqrt(3)) / (4 * sqrt(2));
g0 = (1 - sqrt(3)) / (4 * sqrt(2));
g1 = (3 - sqrt(3)) / (4 * sqrt(2));
tmp = zeros(1, n);
for i = 1:2:n
    tmp((i + 1) / 2) = a(i) * h0 + a(i + 1) * h1;
    tmp((i + n + 1) / 2) = a(i) * g0 + a(i + 1) * g1;
end
c = tmp(1:n / 2);
d = tmp(n / 2 + 1:n);
end

希望这些代码能够对你有所帮助！