%Question(1):

%A)1-
n1=[-12:12];
x1=[-2,-1,0,1,2];
x1=[x1 x1 x1 x1 x1];
stem(n1,x1);
title('Plotting five periods');
xlabel('n1');
ylabel('x1');
figure

%A)2-
n2=[0:20];
x2=exp(0.1*n2).*[stepseg(0,0,20)-stepseg(20,0,20)];
x2=[x2 x2 x2];
%n2=[0:62];
n2=[-21:41];
stem(n2,x2);
title('Plotting three periods');
xlabel('n2');
ylabel('x2=e^(0.1*n2)*[u(n)-u(n-20)]');
figure

%A)3-
n3=[0:10];
x3=sin(0.1*pi*n3).*[stepseg(0,0,10)-stepseg(10,0,10)];
x3=[x3 x3 x3 x3];
n3=[-22:21];
stem(n3,x3);
title('Plotting four periods');
ylabel('x3=sin(0.1*pi*n3)*[u(n)-u(n-10)]');
xlabel('n3');
figure

%A)4-
n4=[0:24]
x4a=[1,2,3];
x4b=[1,2,3,4];
x4a=[x4a x4a x4a x4a x4a x4a x4a x4a 1];  %to suits the n[0:24] 25 elements
x4b=[x4b x4b x4b x4b x4b x4b 1];          %to suits the n[0:24] 25 elements
x4=x4a+x4b;
stem(n4,x4);
title('The sum of two periodic signals');
xlabel('n4');
ylabel('x4');
figure
%-------------------------------------------------------------------------------

%B)
x=[2,4,-3,1,-5,4,7];
n=[-3,3];
%B)1-
[x1,n1]=sigshift(x,n,3);                 %x(n-3)
[x2,n2]=sigshift(x,n,-4);                %x(n+4)
[x12,n12]=sigadd(2*x1,n1,3*x2,n2);       %x12=2*x(n-3)+3*x(n+4)
[xfinal,nfinal]=sigadd(x12,n12,-1*x,n);  %xfinal=2*x(n-3)+3*x(n+4)-x(n)
stem(nfinal,xfinal);
xlabel('nfinal');
ylabel('2*x(n-3)+3*x(n+4)-x(n)');
figure

%B)2-
[x1,n1]=sigshift(x,n,-4);                %x1=x(n+4)
[x2,n2]=sigshift(x,n,-5);                %x2=x(n+5)
[x12,n12]=sigadd(4*x1,n1,5*x2,n2);       %x12=4*x(n+4)+5*x(n+5)
[xfinal,nfinal]=sigadd(x12,n12,2*x,n);   %xfinal=4*x(n+4)+5*x(n+5)+2*x(n)
stem(nfinal,xfinal);
xlabel('nfinal');
ylabel('4*x(n+4)+5*x(n+5)+2*x(n)');
figure

%B)3-
[x1,n1]=sigshift(x,n,-3);                %x1=x(n+3)
[x2,n2]=sigshift(x,n,2);                 %x2=x(n-2)
[x3,n3]=sigshift(x,n,-1);                %x3=x(n+1)
[x4,n4]=sigfold(x3,n3)                   %x4=x(1-n)
[x12,n12]=sigmult(x1,n1,x2,n2);          %x12=x(n+3)*x(n-2)
[x34,n34]=sigmult(x3,n3,x4,n4);          %x34=x(n+1)*x(1-n)
[xfinal,nfinal]=sigadd(x12,n12,x34,n34)  %xfinal=x(n+3)*x(n-2)+x(n+1)*x(1-n)
stem(xfinal,nfinal);
xlabel('nfinal');
ylabel('x(n+3)*x(n-2)+x(n+1)*x(1-n)');
figure

%B)4-
x=[zeros(1,7) x zeros(1,7)];
n=[-10:10];
[x1,n1]=sigshift(x,n,-2);                %x1=x(n+2);
[x2,n2]=sigmult(x1,n1,cos(0.1*pi*n),n);  %x2=x(n+2)*cos(2*pi*n)
[x3,n3]=sigmult(x,n,exp(0.5*n),n);       %x3=e^(0.5*n)*x(n)
[xfinal,nfinal]=sigadd(2*x3,n3,x2,n2);   %xfinal=2*e^(0.5*n)*x(n)+x(n+2)*cos(2*pi*n)
stem(xfinal,nfinal)
xlabel('nfinal');
ylabel('2*e^(0.5*n)*x(n)+x(n+2)*cos(2*pi*n)');
figure
%-------------------------------------------------------------------------------

%Question(2):

%i)
x1=[1,2,4];
nx=[0:2];
h1=[1,1,1,1,1];
nh=[-2:2];
[y,ny]=conv_m(x1,nx,h1,nh);
stem(ny,y);
title('Convolution');
xlabel('ny');
ylabel('y=x1*h1');
figure

%ii)
x2=[0,1,-2,3,-4];
nx=[0:4];
h2=[0.5,1,2,1,0.5];
nh=[-2:2];
[y1,ny1]=conv_m(x2,nx,h2,nh);
stem(ny1,y1);
title('Convolution');
xlabel('ny');
ylabel('y=x1*h1');
figure

%iii)
x3=[1,2,3,4];
nx=[0:3];
h3=[4,3,2,1];
nh=[0:3];
[y3,ny3]=conv_m(x3,nx,h3,nh)
stem(ny3,y3);
title('convolution');
xlabel('ny3');
ylabel('y=x*h');
figure

%iv)
x4=[1,2,3,4];
h4=[1,2,3,4];
n4=[0:3];
[y4,ny4]=conv_m(x4,n4,h4,n4);
stem(ny4,y4);
title('convolution');
xlabel('ny3');
ylabel('y=x*h');
figure

%------------------------------------------------------------------------------
%Question(3):