% mallet_wavelet.m

% 此函數用于研究Mallet算法及濾波器設計

% 此函數僅用于消噪

a=pi/8; %角度賦初值

b=pi/8;

%低通重構FIR濾波器h0(n)沖激響應賦值

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; %濾波器長度

low_decompose=low_construct(end:-1:1); %確定h0(-n)，低通分解濾波器

for i_high=1:L_fre; %確定h1(n)=(-1)^n,高通重建濾波器

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); %高通分解濾波器h1(-n)

L_signal=100; %信號長度

n=1:L_signal; %信號賦值

f=10;

t=0.001;

y=10*cos(2*pi*50*n*t).*exp(-20*n*t);

figure(1);

plot(y);

title('原信號');

check1=sum(high_decompose); %h0(n)性質校驗

check2=sum(low_decompose);

check3=norm(high_decompose);

check4=norm(low_decompose);

l_fre=conv(y,low_decompose); %卷積

l_fre_down=dyaddown(l_fre); %抽取,得低頻細節

h_fre=conv(y,high_decompose);

h_fre_down=dyaddown(h_fre); %信號高頻細節

figure(2);

subplot(2,1,1)

plot(l_fre_down);

title('小波分解的低頻系數');

subplot(2,1,2);

plot(h_fre_down);

title('小波分解的高頻系數');

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); %取結果的中心部分,消除卷積影響

h_fre_keep=wkeep(h_fre_denoise,L_signal);

sig_denoise=l_fre_keep+h_fre_keep; %信號重構

compare=sig_denoise-y; %與原信號比較

figure(3);

subplot(3,1,1)

plot(y);

ylabel('y'); %原信號

subplot(3,1,2);

plot(sig_denoise);

ylabel('sig\_denoise'); %重構信號

subplot(3,1,3);

plot(compare);

ylabel('compare'); %原信號與消噪后信號的比較