📄 小波滤波器构造和消噪程序 - dinga's blog.htm
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<H1 class=ContentTitle><STRONG>小波滤波器构造和消噪程序</STRONG></H1>
<H2 class=ContentAuthor>作者:dinga 日期:2007-05-11</H2></DIV>
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<DIV class=Content-body id=logPanel>1．重构 <BR>
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<DIV class=UBBTitle><IMG style="MARGIN: 0px 2px -3px 0px" alt=程序代码
src="小波滤波器构造和消噪程序 - Dinga's Blog.files/code.gif"> 程序代码</DIV>
<DIV
class=UBBContent><BR>% mallet_wavelet.m <BR>% 此函数用于研究Mallet算法及滤波器设计 <BR>% 此函数仅用于消噪 <BR><BR>a=pi/8; %角度赋初值 <BR><BR>b=pi/8; <BR><BR>%低通重构FIR滤波器h0(n)冲激响应赋值 <BR>h0=cos(a)*cos(b); <BR>h1=sin(a)*cos(b); <BR>h2=-sin(a)*sin(b); <BR>h3=cos(a)*sin(b); <BR><BR>low_construct=[h0,h1,h2,h3]; <BR><BR>L_fre=4; %滤波器长度 <BR>low_decompose=low_construct(end:-1:1); %确定h0(-n)，低通分解滤波器 <BR>for i_high=1:L_fre; %确定h1(n)=(-1)^n,高通重建滤波器 <BR> if(mod(i_high,2)==0); <BR> coefficient=-1; <BR> else <BR> coefficient=1; <BR> end <BR><BR> high_construct(1,i_high)=low_decompose(1,i_high)*coefficient; <BR><BR>end <BR><BR>high_decompose=high_construct(end:-1:1); %高通分解滤波器h1(-n) <BR><BR>L_signal=100; %信号长度 <BR><BR>n=1:L_signal; %信号赋值 <BR><BR>f=10; <BR>t=0.001; <BR>y=10*cos(2*pi*50*n*t).*exp(-20*n*t); <BR><BR>figure(1); <BR>plot(y); <BR>title('原信号'); <BR>check1=sum(high_decompose); %h0(n)性质校验 <BR>check2=sum(low_decompose); <BR>check3=norm(high_decompose); <BR>check4=norm(low_decompose); <BR><BR>l_fre=conv(y,low_decompose); %卷积 <BR><BR>l_fre_down=dyaddown(l_fre); %抽取,得低频细节 <BR><BR>h_fre=conv(y,high_decompose); <BR><BR>h_fre_down=dyaddown(h_fre); %信号高频细节 <BR><BR>figure(2); <BR>subplot(2,1,1) <BR>plot(l_fre_down); <BR>title('小波分解的低频系数'); <BR><BR>subplot(2,1,2); <BR>plot(h_fre_down); <BR>title('小波分解的高频系数'); <BR><BR>l_fre_pull=dyadup(l_fre_down); %0差值 <BR><BR>h_fre_pull=dyadup(h_fre_down); <BR><BR>l_fre_denoise=conv(low_construct,l_fre_pull); <BR><BR>h_fre_denoise=conv(high_construct,h_fre_pull); <BR><BR><BR>l_fre_keep=wkeep(l_fre_denoise,L_signal); %取结果的中心部分,消除卷积影响 <BR><BR>h_fre_keep=wkeep(h_fre_denoise,L_signal); <BR><BR>sig_denoise=l_fre_keep+h_fre_keep; %信号重构 <BR><BR>compare=sig_denoise-y; %与原信号比较 <BR>figure(3); <BR><BR> <BR><BR>subplot(3,1,1) <BR><BR>plot(y); <BR><BR>ylabel('y'); %原信号 <BR><BR> <BR><BR>subplot(3,1,2); <BR><BR>plot(sig_denoise); <BR><BR>ylabel('sig\_denoise'); %重构信号 <BR><BR> <BR><BR>subplot(3,1,3); <BR><BR>plot(compare); <BR><BR>ylabel('compare'); %原信号与消噪后信号的比较 <BR><BR></DIV></DIV><BR><BR><SPAN
style="COLOR: red">2．消噪</SPAN><BR>
<DIV class=UBBPanel>
<DIV class=UBBTitle><IMG style="MARGIN: 0px 2px -3px 0px" alt=程序代码
src="小波滤波器构造和消噪程序 - Dinga's Blog.files/code.gif"> 程序代码</DIV>
<DIV
class=UBBContent>% mallet_wavelet.m <BR><BR>% 此函数用于研究Mallet算法及滤波器设计 <BR><BR>% 此函数用于消噪处理 <BR><BR> <BR><BR>%角度赋值 <BR><BR>%此处赋值使滤波器系数恰为db9 <BR><BR> <BR><BR>%分解的高频系数采用db9较好,即它的消失矩较大 <BR><BR>%分解的有用信号小波高频系数基本趋于零 <BR><BR>%对于噪声信号高频分解系数很大，便于阈值消噪处理 <BR><BR> <BR><BR>[l,h]=wfilters('db10','d'); <BR><BR> <BR><BR>low_construct=l; <BR><BR> <BR><BR>L_fre=20; %滤波器长度 <BR><BR> <BR><BR> <BR><BR>low_decompose=low_construct(end:-1:1); %确定h0(-n)，低通分解滤波器 <BR><BR> <BR><BR>for i_high=1:L_fre; %确定h1(n)=(-1)^n,高通重建滤波器 <BR><BR> <BR><BR> if(mod(i_high,2)==0); <BR><BR> coefficient=-1; <BR><BR> else <BR><BR> coefficient=1; <BR><BR> end <BR><BR> <BR><BR> high_construct(1,i_high)=low_decompose(1,i_high)*coefficient; <BR><BR>end <BR><BR> <BR><BR>high_decompose=high_construct(end:-1:1); %高通分解滤波器h1(-n) <BR><BR> <BR><BR> <BR><BR> <BR><BR>L_signal=100; %信号长度 <BR><BR> <BR><BR>n=1:L_signal; %原始信号赋值 <BR><BR>f=10; <BR><BR>t=0.001; <BR><BR>y=10*cos(2*pi*50*n*t).*exp(-30*n*t); <BR><BR> <BR><BR>zero1=zeros(1,60); %信号加噪声信号产生 <BR><BR>zero2=zeros(1,30); <BR><BR>noise=[zero1,3*(randn(1,10)-0.5),zero2]; <BR><BR>y_noise=y+noise; <BR><BR> <BR><BR>figure(1); <BR><BR>subplot(2,1,1); <BR><BR>plot(y); <BR><BR>title('原信号'); <BR><BR> <BR><BR>subplot(2,1,2); <BR><BR>plot(y_noise); <BR><BR>title('受噪声污染的信号'); <BR><BR> <BR><BR>check1=sum(high_decompose); %h0(n),性质校验 <BR><BR>check2=sum(low_decompose); <BR><BR>check3=norm(high_decompose); <BR><BR>check4=norm(low_decompose); <BR><BR> <BR><BR>l_fre=conv(y_noise,low_decompose); %卷积 <BR><BR>l_fre_down=dyaddown(l_fre); %抽取,得低频细节 <BR><BR> <BR><BR>h_fre=conv(y_noise,high_decompose); <BR><BR>h_fre_down=dyaddown(h_fre); %信号高频细节 <BR><BR> <BR><BR> <BR><BR>figure(2); <BR><BR>subplot(2,1,1) <BR><BR>plot(l_fre_down); <BR><BR>title('小波分解的低频系数'); <BR><BR> <BR><BR>subplot(2,1,2); <BR><BR>plot(h_fre_down); <BR><BR>title('小波分解的高频系数'); <BR><BR> <BR><BR> <BR><BR>% 消噪处理 <BR><BR> for i_decrease=31:44; <BR><BR> <BR><BR> if abs(h_fre_down(1,i_decrease))>=0.000001 <BR><BR> h_fre_down(1,i_decrease)=(10^-7); <BR><BR> end <BR><BR> <BR><BR> end <BR><BR> <BR><BR> <BR><BR>l_fre_pull=dyadup(l_fre_down); %0差值 <BR><BR>h_fre_pull=dyadup(h_fre_down); <BR><BR> <BR><BR> <BR><BR> <BR><BR>l_fre_denoise=conv(low_construct,l_fre_pull); <BR><BR>h_fre_denoise=conv(high_construct,h_fre_pull); <BR><BR> <BR><BR>l_fre_keep=wkeep(l_fre_denoise,L_signal); %取结果的中心部分,消除卷积影响 <BR><BR>h_fre_keep=wkeep(h_fre_denoise,L_signal); <BR><BR> <BR><BR>sig_denoise=l_fre_keep+h_fre_keep; %消噪后信号重构 <BR><BR> <BR><BR>%平滑处理 <BR><BR> <BR><BR>for j=1:2 <BR><BR>for i=60:70; <BR><BR> sig_denoise(i)=sig_denoise(i-2)+sig_denoise(i+2)/2; <BR><BR>end; <BR><BR>end; <BR><BR> <BR><BR>compare=sig_denoise-y; %与原信号比较 <BR><BR> <BR><BR>figure(3); <BR><BR> <BR><BR>subplot(3,1,1) <BR><BR>plot(y); <BR><BR>ylabel('y'); %原信号 <BR><BR> <BR><BR>subplot(3,1,2); <BR><BR>plot(sig_denoise); <BR><BR>ylabel('sig\_denoise'); %消噪后信号 <BR><BR> <BR><BR>subplot(3,1,3); <BR><BR>plot(compare);ylabel('compare'); %原信号与消噪后信号的比较<BR></DIV></DIV><BR><BR></DIV>
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