%Zachary Orsoli 40004528
%ELEC 342 Lab2 Part1 Question2
clear all
clc

% b)
n=[0:1];
x1=n;
x2=n;

y1 =x1.^2;
y2 = x2.^2;
%if x3[n] = x1[n] + x2[n]
x3 = x1+x2;
y3 = x3.^2;
y4=y1+y2;
disp(' ') %create line spacing
disp('For the system y[n] = x^2[n] with input x[n]=[0,1] :')
if(y3 == y4)
disp('This function is linear since y3[n] = y4[n]')
else
disp('This function is not linear since y3[n] is not equal to y4[n]')
end
%Checking for Time Invariance
x1 = n;
x2 = x1+1;
y2 =(x2).^2;
y1_shifted = (x1+1).^2;
if(y1_shifted == y2)
disp('This function is Time-Invariant since y1[n+shift] = y2[n] where x2 = x1 +shift')
else
disp('This function is not Time-Invariant since y1[n+shift] is notequal to y2[n]')
end
%part b) (i) with range x[n]=[0:20]
n = [0:20];
x1 = n;
x2 = n;
%if y[n] = x^2[n]
y1 =x1.^2;
y2 = x2.^2;
%if x3[n] = x1[n] + x2[n]
x3 = x1+x2;
y3 = x3.^2;
y4=y1+y2;
disp(' ') %create line spacing
disp('For the system y[n] = x^2[n] with input x[n]=[0:20] :')
if(y3 == y4)
disp('This function is linear since y3[n] = y4[n]')
else
disp('This function is not linear since y3[n] is not equal to y4[n]')
end
%Checking for Time Invariance
x1 = n;
x2 = x1+1;
y2 =(x2).^2;


y1_shifted = (x1+1).^2;
if(y1_shifted == y2)
disp('This function is Time-Invariant since y1[n+shift] = y2[n] where x2 = x1 +shift')
else
disp('This function is not Time-Invariant since y1[n+shift] is not equal to y2[n]')
end



%part b)(i) with range x[n]=[0:1]
n = [0:1];
x1 = n;
x2 = n;
%if y[n] = 2*x[n] + 5*delta[n]
y1 = 2*x1;
y1(1) = y1(1) + 5; % +5*delta[n]
y2 = 2*x2;
y2(1) =y2(1)+ 5; % +5*delta[n]
%if x3[n] = x1[n] + x2[n]
x3 = x1+x2;
y3 = 2*x3;
y3(1) =y3(1)+ 5; % +5*delta[n]
y4=y1+y2;
subplot(2,2,1)
stem(n,x1)
hold
stem(n,y1)
title('x1[n] and y1[n]')
xlabel('n')
ylabel('x1 and y1')
subplot(2,2,2)
stem(n,x2)
hold
stem(n,y2)
title('x2[n] and y2[n]')
xlabel('n')
ylabel('x2 and y2')
subplot(2,2,3)
stem(n,x3)

hold
stem(n,y3)
title('x3[n] and y3[n]')
xlabel('n')
ylabel('x3 and y3')
subplot(2,2,4)
stem(n,y1)
title('x4[n] and y4[n]')
xlabel('n')
ylabel('y4')

disp(' ') %create line spacing
disp('For the system y[n] = 2*x[n] + 5*delta[n] with input x[n]=[0,1] :')
if(y3 == y4)
disp('This function is linear since y3[n] = y4[n]')
else
disp('This function is not linear since y3[n] is not equal to y4[n]')
end
%Checking for Time Invariance
x1 = n;
x2 = x1+1;
y2 =(x2).^2;
y1_shifted = (x1+1).^2;
if(y1_shifted == y2)
disp('This function is Time-Invariant since y1[n+shift] = y2[n] where x2 = x1 +shift')
else
disp('This function is not Time-Invariant since y1[n+shift] is not equal to y2[n]')
end
%part b) (i) with range x[n]=[0:20]
n = [0:20];
x1 = n;
x2 = n;
%if y[n] = 2*x[n]
y1 =x1.^2;
y2 = x2.^2;
%if x3[n] = x1[n] + x2[n]
x3 = x1+x2;
y3 = x3.^2;
y4=y1+y2;
disp(' ') %create line spacing
disp('For the system y[n] = 2*x[n] + 5*delta[n] with input x[n]=[0:20] :')
if(y3 == y4)
disp('This function is linear since y3[n] = y4[n]')
else
disp('This function is not linear since y3[n] is not equal to y4[n]')
end

%Checking for Time Invariance
x1 = n;
x2 = x1+1;
y2 =(x2).^2;
y1_shifted = (x1+1).^2;
if(y1_shifted == y2)
disp('This function is Time-Invariant since y1[n+shift] = y2[n] where x2 = x1 +shift')
else
disp('This function is not Time-Invariant since y1[n+shift] is not equal to y2[n]')
end