1、小波滤波器构造和消噪程序（2 个）1重构% mallet_wavelet.m% 此函数用于研究 Mallet 算法及滤波器设计% 此函数仅用于消噪a=pi/8; %角度赋初值b=pi/8;%低通重构 FIR 滤波器 h0(n)冲激响应赋值h0=cos(a)*cos(b);h1=sin(a)*cos(b);h2=-sin(a)*sin(b);h3=cos(a)*sin(b);low_construct=h0,h1,h2,h3;L_fre=4; %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
2、_fre; %确定 h1(n)=(-1)n,高通重建滤波器if(mod(i_high,2)=0);coefficient=-1;elsecoefficient=1;endhigh_construct(1,i_high)=low_decompose(1,i_high)*coefficient;endhigh_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; %信号赋值f=10;t=0.001;y=10*cos(2*pi*50*n*t).*exp(-20*n*t);figure(1
3、);plot(y);title(原信号);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,low_decompose); %卷积l_fre_down=dyaddown(l_fre); %抽取,得低频细节h_fre=conv(y,high_decompose);h_fre_down=dyaddown(h_fre); %信号高频细节figure(2);subplot(2,1,1)plo
4、t(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);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
5、_keep=wkeep(h_fre_denoise,L_signal);sig_denoise=l_fre_keep+h_fre_keep; %信号重构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); %重构信号subplot(3,1,3);plot(compare);ylabel(compare); %原信号与消噪后信号的比较2消噪% mallet_wavelet.m% 此函数用
6、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);coeffi
7、cient=-1;elsecoefficient=1;endhigh_construct(1,i_high)=low_decompose(1,i_high)*coefficient;endhigh_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*
8、(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=dy
9、addown(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)=0.000001h_fre_down(1,i_decrease)=(10-7);
10、endendl_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=1:2for 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
