%生成正弦信號
N=1000;
t=1:N;
sig1=sin(0.3*t);
%生成三角波信號
sig2(1:500)=((1:500)-1)/500;
sig2(501:N)=(1000-(501:1000))/500;
figure(1);
subplot(2,1,1);plot(t,sig1,'LineWidth',2);
xlabel('時間 t/s');ylabel('幅值 A');
subplot(2,1,2);plot(t,sig2,'LineWidth',2);
xlabel('時間 t/s');ylabel('幅值 A');
%疊加信號
x=sig1+sig2+randn(1,N);
x1=wextend(1,'ppd',x,20);  %信號周期延拓
N1=N+2*20;
t1=1:N1;
figure(2)
subplot(211);plot(t,x,'LineWidth',2);title('原始信號');xlabel('時間 t/s');ylabel('幅值 A');
subplot(212);plot(t1,x1,'linewidth',2);title('延拓信號');xlabel('時間 t/s');ylabel('幅值 A');
%一維小波分解
[c,l] = wavedec(x1,7,'sym4');
%重構第1～7層逼近系數
a7 = wrcoef('a',c,l,'sym4',7);
a6 = wrcoef('a',c,l,'sym4',6);
a5 = wrcoef('a',c,l,'sym4',5);
a4 = wrcoef('a',c,l,'sym4',4);
a3 = wrcoef('a',c,l,'sym4',3);
a2 = wrcoef('a',c,l,'sym4',2);
a1 = wrcoef('a',c,l,'sym4',1);
%顯示逼近系數
figure(3);
subplot(7,1,1);plot(a7,'LineWidth',2);ylabel('a7');
subplot(7,1,2);plot(a6,'LineWidth',2);ylabel('a6');
subplot(7,1,3);plot(a5,'LineWidth',2);ylabel('a5');
subplot(7,1,4);plot(a4,'LineWidth',2);ylabel('a4');
subplot(7,1,5);plot(a3,'LineWidth',2);ylabel('a3');
subplot(7,1,6);plot(a2,'LineWidth',2);ylabel('a2');
subplot(7,1,7);plot(a1,'LineWidth',2);ylabel('a1');
xlabel('時間 t/s');
%重構第1～7層細節系數
d7 = wrcoef('d',c,l,'sym4',7);
d6 = wrcoef('d',c,l,'sym4',6);
d5 = wrcoef('d',c,l,'sym4',5);
d4 = wrcoef('d',c,l,'sym4',4);
d3 = wrcoef('d',c,l,'sym4',3);
d2 = wrcoef('d',c,l,'sym4',2);
d1 = wrcoef('d',c,l,'sym4',1);
%顯示細節系數
figure(4)
subplot(7,1,1);plot(d7,'LineWidth',2);ylabel('d7');
subplot(7,1,2);plot(d6,'LineWidth',2);ylabel('d6');
subplot(7,1,3);plot(d5,'LineWidth',2);ylabel('d5');
subplot(7,1,4);plot(d4,'LineWidth',2);ylabel('d4');
subplot(7,1,5);plot(d3,'LineWidth',2);ylabel('d3');
subplot(7,1,6);plot(d2,'LineWidth',2);ylabel('d2');
subplot(7,1,7);plot(d1,'LineWidth',2);ylabel('d1');
xlabel('時間 t/s');