MATLAB: Verification of system characteristics

home worklab work

% FOR CHECKING SYSTEM IS TIME VARIANT OR INVARIANT (1ST BIT)
clc
clear all
close all
t=-5:0.001:5
l=length(t)
for i=1:l
    if t(i)>=0
        x1(i)=1;
        
    else x1(i)=0;
    end
end
x2=cos(pi*t)
x3=cos(pi*(t-1))
y1=x1.*x2
y2=x1.*x3
subplot(4,1,1)
plot(t,x1)
xlabel('t')
ylabel('x1')
title('for x1')
grid on
gtext('1841014009')
subplot(4,1,2)
plot(t,y1)
xlabel('t')
ylabel('y1')
title('for y1')
grid on
gtext('1841014009')
subplot(4,1,3)
plot(t,x2)
xlabel('t')
ylabel('x2')
title('for x2')
grid on
gtext('1841014009')
subplot(4,1,4)
plot(t,y2)
xlabel('t')
ylabel('y2')
title('for y2')
grid on
gtext('1841014009')
if round(y1)==round(y2)
    disp('time invariant');
    
else disp('time variant');
end
This is what i have done.
please help me.

Best Answer

% FOR TIME VARITANT OR INVARIANT
clc
clear all
close all
t=-5:0.001:5
l=length(t)
for i=1:l
    if t(i)>=0
        x1(i)=1;
        
    else x1(i)=0;
    end
end
x2=cos(pi*t)
x3=cos(pi*(t-2))
y1=x1.*x2
y2=x1.*x3
subplot(4,1,1)
plot(t,x1)
xlabel('t')
ylabel('x1')
title('for x1')
grid on
gtext('1841014009')
subplot(4,1,2)
plot(t,y1)
xlabel('t')
ylabel('y1')
title('for y1')
grid on
gtext('1841014009')
subplot(4,1,3)
plot(t,x2)
xlabel('t')
ylabel('x2')
title('for x2')
grid on
gtext('1841014009')
subplot(4,1,4)
plot(t,y2)
xlabel('t')
ylabel('y2')
title('for y2')
grid on
gtext('1841014009')
if round(y1)==round(y2)
    disp('time invariant');text(-2,-0.5, ('System Is Time Invariant'));
    
else disp('time variant');text(-2,-0.5, ('System Is Time Variant'))
end
% FOR LINEARITY TEST
clc
clear all
close all
t=-4:0.001:5
l=length(t)
for i=1:l
    if t(i)>=0
        x1(i)=1;
        
    else x1(i)=0;
    end
end
 
for i=1:l
if t(i)>=1
    x2(i)=1;
    
else x2(i)=0;
end
end
 
a1=2
a2=3
 
y1=a1.*x1.*cos(pi*t)
y2=a2.*x2.*cos(pi*(t-1))
 
y=((a1.*x1)+(a2.*x2)).*cos(pi*t)
 
y3=y1+y2;
 
subplot(4,1,1)
plot(t,y)
title('for y')
xlabel('t')
ylabel('y')
grid on
gtext('1841014009')
subplot(4,1,2)
plot(t,y1)
title('for y1')
xlabel('t')
ylabel('y1')
grid on
gtext('1841014009')
 
subplot(4,1,3)
plot(t,y2)
title('for y2')
xlabel('t')
ylabel('y2')
grid on
gtext('1841014009')
  
subplot(4,1,4)
plot(t,y3)
title('for y3')
xlabel('t')
ylabel('y3')
grid on
gtext('1841014009')
 
if round(y)==round(y3)
    disp('system is linear');
    text(-2,-0.5, ('System Is Linear'));
    
else disp('system is non linear');
    text(-2,-0.5, ('System Is Non-Linear'));
end
% FOR STABILITY TEST
clc
clear all
close all
t=0:0.01:10
l=length(t)
for i=1:l
    if t(i)>=0
        x(i)=1;
        
    else x(i)=0;
    end
end
 
y=exp(-2*t).*x
c=0
for i=1:l-1
    if (y(i)>y(i+1))
        c=c+1;
    end
end
 
subplot(2,1,1)
plot(t,x)
title('for x')
xlabel('t')
ylabel('x')
grid on
gtext('1841014009')
subplot(2,1,2)
plot(t,y)
title('for y')
xlabel('t')
ylabel('y')
grid on
gtext('1841014009')
if(c~=0)
    disp('system is stable');
    text(2,0.5, ('System Is Stable'));
else 
    disp('system is unstable');
    text(2,0.5, ('System Is Untable'));
end