clear all
close all
clc
%% Experiment 3.... LTI System
n=-10:10;
x1=int32(n>0 & n<=5);
x2=int32(n>-2 & n<=1);
a=2;b=3;
% Linearity check for y(n)=x^2(n)
y1=x1.^2; % . needed for indivisual operation on each element of array
y2=x2.^2;
lhs=(a*x1+b*x2).^2;
rhs=a*y1+b*y2;
if y1==y2
    display("System is Linear");
else
    display("System is non linear");
subplot(5,2,1);
stem(n,lhs);
title("LHS: (a*x1 + b*x2)^2");
subplot(5,2,2);
stem(n,rhs);
title("RHS: a*x1 + b*x2");
% Time Invariance check for y(n)=x^2(n)
n0=3; % Shift amount
x_shift=circshift(x1,n0);
y_shift__input=x_shift.^2;
y_shift__output=circshift(y1,n0);
if (y_shift__output==y_shift__input)
    display("System is Time Invariant")
else
    display("System is Time Variant")
end
subplot(5,2,3);
stem(n,y_shift__input);
title("Output for shifted input")
subplot(5,2,4);
stem(n,y_shift__output);
title("Shifted output of original");
end
% Time shifting
l=length(n);
x=zeros(1,l);
for i=1:l
    if(n(i)>0 && n(i)<=5)
        x(i)=n(i);
    else
        x(i)=0;
    end
end
disp("x(n):");disp(x)
for i=1:l
    if(n(i)>0 && n(i)<=5)
        x(i-2)=n(i);
    elseif (n(i)>5)
        x(i-2)=0;
    else
        x(i)=0;
    end
end
disp("x(n+2):");disp(x)
for i=1:l
    if((n(i)-2)>0 && (n(i)-2)<=5)
        x(i)=n(i)-2;
    else
        x(i)=0;
    end
end
disp("x(n-2)");disp(x)
for i=1:l
    if(-n(i)>0 && -n(i)<=5)
        x(i)=-n(i);
    elseif (-n(i)>5)
        x(i)=0;
    else
        x(i)=0;
    end
end
disp("x(-n)");disp(x)
for i=1:l
    if(-n(i)+2>0 && -n(i)+2<=5)
        x(i)=-n(i-2);
    elseif (n(i)>1)
        x(i)=0;
    else
        x(i)=0;
    end
end
disp("x(-n-2)");disp(x)
for i=1:l
    if(-n(i)-2>0 && -n(i)-2<=5)
        x(i)=-n(i+2);
    elseif (n(i)>1)
        x(i)=0;
    else
        x(i)=0;
    end
end
disp("x(n+2):");disp(x)
subplot(5,2,5);
stem(n,x);
title("Original Signal : x(n)");
xlabel("n");ylabel("x(n)")
subplot(5,2,6);
stem(n,x);
title("Shifted Signal : x(n+2)");
xlabel("n");ylabel("x(n+2)");
subplot(5,2,7);
stem(n,x);
title("Shifted Signal : x(n-2)");
xlabel("n");ylabel("x(n+2)");
subplot(5,2,8);
stem(-n,x);
title("Shifted Signal : x(-n)");
xlabel("n");ylabel("x(-n)");
subplot(5,2,9);
stem(-n,x);
title("Shifted Signal : x(-n-2)");
xlabel("n");ylabel("x(-n-2)");
subplot(5,2,10);
stem(-n,x);
title("Shifted Signal : x(-n+2)");
xlabel("n");ylabel("x(-n+2)");