1. function[y,n]=sigadd(x1,n1,x2,n2)
%n1:index vector for x1
%n2:index vector for x2
n=min(min(n1),min(n2)):max(max(n1),max(n2));%duration of y(n)
y1=zeros(1,length(n)); y2=y1; %initialization
y1(find((n>=min(n1))&(n<=max(n1))))=x1; %x1 with duration of y
y2(find((n>=min(n2))&(n<=max(n2))))=x2; %x2 with duration of y
y=y1+y2;

2. >> x1=[1 1 1];
>> n1=[2 3 4];
>> x2=[2 2 2];
>> n2=[4 5 6];
>> [y,n]=sigadd(x1,n1,x2,n2)
y =
n =

3. function[y,n]=sigmult(x1,n1,x2,n2)
%n1:index vector for x1
%n2:index vector for x2
n=min(min(n1),min(n2)):max(max(n1),max(n2));%duration of y(n)
y1=zeros(1,length(n)); y2=y1; %initialization
y1(find((n>=min(n1))&(n<=max(n1))))=x1; %x1 with duration of y
y2(find((n>=min(n2))&(n<=max(n2))))=x2; %x2 with duration of y
y=y1.*y2;

4. >> [y,n]=sigmult(x1,n1,x2,n2)
n =

5. function [y,n]=sigshift(x,m,k)
%implements y(n)=x(n-k)
%m: index vector for x
n=m+k;y=x;
>> xn=0:20;x=stepseq(0,0,20);
>> [y,yn]=sigshift(x,xn,5);
>> subplot(2,1,1),stem(xn,x),title('u(n)'),axis([0 30,0,1])
>> subplot(2,1,2),stem(yn,y),title('u(n-5)'),axis([0 30,0,1])

6. function [y,n]=sigfold(x,n)
%implements y(n)=x(-n)
y=fliplr(x); n=-fliplr(n);
>> xn=0:6;x=rampseq(0,0,6);
>> [y,yn]=sigfold(x,xn);
>> subplot(2,1,1),stem(xn,x),title('ur(n)'),axis([-10,10 ,0,6])
>> subplot(2,1,2),stem(yn,y),title('ur(-n)'),axis([-10,10 ,0,6])

7. >> n=-2:10;x=[1:7, 6:-1:1];
>> [x11,n11]=sigfold(x,n);[x11,n11]=sigshift(x11,n11,3);
>>[x12,n12]=sigshift(x,n,2);[x12,n12]=sigmult(x,n,x12,n12);
>> [x1,n1]=sigadd(x11,n11,x12,n12);
>> stem(n1,x1)

8. N=7
>> x=[ ];
>> n=-6:14;
>> stem(n,[x x x])

9. function [xe,xo,l]=evenodd(x,n)
%Real signal decomposition into even and odd parts
if any(imag(x)~=0)
error('x is not a real signal')
end
[y,m]=sigfold(x,n);
[xe,l]=sigadd(x,n,y,m);xe=xe/2;
[xo]=sigadd(x,n,-y,m);xo=xo/2;

10. >> n=[0:10];x=stepseq(0,0,10)-stepseq(10,0,10);
>> [xe,xo,m]=evenodd(x,n);
>> subplot(2,2,1); stem(n,x);title('X(n)'); axis([-10,10,0,1.2])
>> subplot(2,2,2); stem(m,xe);title('Xe(n)'); axis([-10,10,0,1.2])
>> subplot(2,2,4); stem(m,xo);title('Xo(n)'); axis([-10,10,-0.6,0.6])

11. >> nx=-3:3;X=[1:7];[Y,ny]=sigfold(X,nx);
>> [Y1,ny1]=sigshift(Y,ny,1);
>> [X1,nx1]=sigshift(X,nx,1);[Y2,ny2]=sigfold(X1,nx1);
>> subplot(2,1,1); stem(ny1,Y1); title('y(n-1)');axis([-4,4,0,8])
>> subplot(2,1,2); stem(ny2,Y2); title('y(n,1)');axis([-4,4,0,8])
y(n)=x(-n) is TIME VARIANT