利用小波消噪对非平稳信号的噪声消除

 精通MATLAB信号处理*沈再阳书中的一段代码p337，官方代码中不包含，自己拿来发现不适用自己要处理的信号，贴出来给需要的人。

clear all
close all

[l,h]=wfilters('db10','d');
low_construct = l;
L_fre = 20;
%滤波器长度
low_decompose = low_construct(end:-1:1);
%低通分解滤波器
for i_high = 1:L_fre  %确定 h1(n) = (-1)^n,
    %高通重建滤波器
    if( mod(i_high,2) == 0 )
        coefficient = -1;
    else
        coefficient = 1;
    end
    high_construct(1,i_high) = low_decompose(1,i_high) * coefficient;
end
high_decompose = high_construct(end:-1:1);
%高通分解滤波器

L_signal = 100;
%信号长度
n = 1:L_signal;
%原始信号赋值
f = 10;
t = 0.001;
y = 10 * cos(2*pi*50*n*t) .* exp(-30 * n *t) + randn(size(t));
zero1 = zeros(1,60);
%信号加噪声信号产生
zero2 = zeros(1,30);
noise = [zero1,3*(randn(1,10)-0.5),zero2];
y_noise = y + noise;
subplot(2,3,1);
plot(y);
title('原信号');
grid on;
subplot(2,3,4);
plot(y_noise);
title('受噪声污染的信号');
grid on;
check1 = sum(high_decompose);
check2 = sum(low_decompose);
check3 = norm(high_decompose);
check4 = norm(low_decompose);
l_fre = conv(y_noise,low_decompose);
%卷积
l_fre_down=dyaddown(l_fre);
%低频细节
h_fre = conv(y_noise,high_decompose);
h_fre_down = dyaddown(h_fre);
%信号高频细节
subplot(2,3,2)
plot(l_fre_down);
title('小波分解的低频系数');
grid on;
subplot(2,3,5);
plot(h_fre_down);
title('小波分解的高频系数');
grid on;
%消噪处理
for i_decrease = 31:44;
    if abs(h_fre_down(1,i_decrease)) >= 0.000001
        h_fre_down(1,i_decrease) = (10^-7);
    end
end
l_fre_pull = dyadup(l_fre_down);
%0差值
h_fre_pull = dyadup(h_fre_down);
l_fre_denoise = conv(low_construct,l_fre_pull);
h_fre_denoise = conv(high_construct,h_fre_pull);
l_fre_keep = wkeep(l_fre_denoise,L_signal);
%取结果的中心部分，消除卷积影响
h_fre_keep = wkeep(h_fre_denoise,L_signal);
sig_denoise = l_fre_keep + h_fre_keep;
%消噪后信号重构
%平滑处理
for j = 1:2
    for i=60:70
        sig_denoise(i) = sig_denoise(i-2)+sig_denoise(i+2)/2;
    end
end
subplot(2,3,3)
plot(y);
title(' 原信号');
grid on;
subplot(2,3,6);
plot(sig_denoise);
title('消噪后的信号');
grid on;