Mallet算法及滤波器

% mallet_wavelet.m

% 此函数用于研究Mallet算法及滤波器设计

% 此函数用于消噪处理

%角度赋值

%此处赋值使滤波器系数恰为db9

%分解的高频系数采用db9较好,即它的消失矩较大

%分解的有用信号小波高频系数基本趋于零

%对于噪声信号高频分解系数很大，便于阈值消噪处理

clc;

clear;

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); %确定h0(-n)，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h1(-n)

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);

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;

figure(1);

subplot(2,1,1);

plot(y);

title('原信号');

subplot(2,1,2);

plot(y_noise);

title('受噪声污染的信号');

check1=sum(high_decompose); %h0(n),性质校验

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); %抽取,得低频细节

h_fre=conv(y_noise,high_decompose);

h_fre_down=dyaddown(h_fre); %信号高频细节

figure(2);

subplot(2,1,1)

plot(l_fre_down);

title('小波分解的低频系数');

subplot(2,1,2);

plot(h_fre_down);

title('小波分解的高频系数');

% 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;

compare=sig_denoise-y; %与原信号比较

figure(3);

subplot(3,1,1)

plot(y);

ylabel('y'); %原信号

subplot(3,1,2);

plot(sig_denoise);

ylabel('sig\_denoise'); %消噪后信号

subplot(3,1,3);

plot(compare);