%%%%%%%mallat algorithm%%%%%
clc;
clear;
%%%%original signal%%%%
f=100;%%frequence
ts=1/800;%%抽樣間隔
N=1:100;%%點數
s=sin(2*ts*pi*f.*N);%%源信號

figure(1)
plot(s);%%%源信號s
title('原信號');
grid on;
%%%%小波濾波器%%%%
ld=wfilters('db1','l');%%低通
hd=wfilters('db1','h');%%高通

figure(2)
stem(ld,'r');%%%低通
grid on;
figure(3)
stem(hd,'b')%%%高通
grid on;
%%%%%
tem=conv(s,ld);%%低通和原信號卷積
ca1=dyaddown(tem);%%抽樣
figure(4)
plot(ca1);
grid on;

tem=conv(s,hd);%%高通和原信號卷積
cb1=dyaddown(tem);%%抽樣
figure(5)
plot(cb1);
grid on;
%%%%%%%%
[ca3,cb3]=dwt(s,'db1');%%小波變換
%%%%%%%%
[lr,hr]=wfilters('db1','r');%%重構濾波器

figure(6)
stem(lr);
figure(7)
stem(hr);

tem=dyadup(cb1);%%插值
tem=conv(tem,hr);%%卷積
d1=wkeep(tem,100);%%去掉兩頭的分量
%%%%%%%%%
tem=dyadup(ca1);%%插值
tem=conv(tem,lr);%%卷積
a1=wkeep(tem,100);%%去掉兩頭的分量

a=a1+d1;%%%重構原信號
%%%%%%%%%
a3=idwt(ca3,cb3,'db1',100);%%%小波逆變換
%%%%%%%%%
figure(8)
plot(a,'.b');
hold on;
plot(s,'r');
grid on;
title('重構信號和原信號的比較');

figure(9)
plot(a3,'.b');
hold on;
plot(s,'r');
grid on;
title('重構信號和原信號的比較');