% 此函数用于去噪处理
%角度赋值
%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，便于阈值去噪处理
[l,h]=wfilters('db9','d');
low_construct=l;
L_fre=12; %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=sin(2*pi*50*n*t).*exp(-10*n*t);
%信号加噪声信号产生
noise=[zeros(1,L_signal/2),2*(rand(1,20)-0.4),zeros(1,30)];
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');
% 去噪处理
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; %去噪后信号重构
%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'); %去噪后信号
axis tight
subplot(3,1,3);
plot(compare);
ylabel('compare'); %原信号与去噪后信号的比较
axis tight
