% Computation linear convolution using overlap-add method
clear
n=0:29;
x=[1 2 0.5 2 2 0.5 4 4 3 0.5 3 1 2 1 0 2 3 3 0.5 2 3 4 1 2 0 0 0 0 0 0];
h=[4 3 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];
N=4;M=6;
c=zeros(1,30);
c1=c;c2=c;c3=c;c4=c;
j0=x([1:6]);j1=x([7:12]);j2=x([13:18]);j3=x([19:24]);
j0=[j0,zeros(1,24)];
j1=[j1,zeros(1,24)];
j2=[j2,zeros(1,24)];
j3=[j3,zeros(1,24)];
%==========================================================
L=10;
RN=u(n)-u(n-L);
for k=1:4;    
    hs=h([1:10]);
    l=length(n);
    v=zeros(1,L); 
    hs=[hs,hs,hs];o=hs;
    hs=fliplr(hs);
    d=ones(1,length(n));
    subplot(411)
    stem(n,x,'.');title('分段卷積演示')
    subplot(412)
    stem(n,h,'.');ylabel('h((n))N');

  for i=0:L-1;
    subplot(413)
    stem(n,hs.*RN,'r.');
    ylabel('h((n-m))N');
    if k==1,        a=j0;    end
    if k==2,        a=j1;    end
    if k==3,        a=j2;    end
    if k==4,        a=j3;    end
    subplot(411)
    stem(n,a,'.');title('分段卷積演示')
    w=hs(l);
    for p=1:l-1;        hs(l-p+1)=hs(l-p);    end
    hs(1)=w;
    subplot(414)
    if k==1,        stem(n,c1,'.'),    end
    if k==2,        stem(n,c2,'.'),    end
    if k==3,        stem(n,c3,'.'),    end
    if k==4,        stem(n,c4,'.'),    end
    ylabel('循環卷積y(n)');
    if k==1,    pause,    end
    b=hs.*RN;    e=a.*b;    g=e*d';    
    if k==1,        c1(i+1)=g;     end
    if k==2,        c2(i+1)=g;     end
    if k==3,        c3(i+1)=g;     end
    if k==4,        c4(i+1)=g;     end 
  end
end

for i=0:M-1;
    w=c2(l);
    for p=1:l-1;
        c2(l-p+1)=c2(l-p);
    end
    c2(1)=w;
end

for i=0:2*M-1
    w=c3(l);
    for p=1:l-1;
        c3(l-p+1)=c3(l-p);
    end
    c3(1)=w;
end
for i=0:3*M-1
    w=c4(l);
    for p=1:l-1;
        c4(l-p+1)=c4(l-p);
    end
    c4(1)=w;
end
c=c1+c2+c3+c4;
figure(2)
subplot(611),stem(n,c1,'.');ylabel('y1')
title('Computation of linear convolution using overlap add method')
subplot(612),stem(n,c2,'.');ylabel('y2')
subplot(613),stem(n,c3,'.');ylabel('y3')
y=conv(h,x);y=y([1:30]);
subplot(615),stem(n,c,'m.');ylabel('y')  
subplot(614),stem(n,c4,'.');ylabel('y4')
subplot(616),stem(n,y,'r.');ylabel('y')
figure(3)
x1=x.*(u(n)-u(n-M));
x2=x.*(u(n-M)-u(n-2*M));
x3=x.*(u(n-2*M)-u(n-3*M));
x4=x.*(u(n-3*M)-u(n-4*M));
x5=x.*(u(n-4*M)-u(n-5*M));

subplot(611),stem(n,x,'.');
title('The short sequences xk(n)')
subplot(612),stem(n,x1,'.');
subplot(613),stem(n,x2,'.');
subplot(614),stem(n,x3,'.');  
subplot(615),stem(n,x4,'.');
subplot(616),stem(n,o.*RN,'r.');
xlabel('Time index n')