The document describes experiments performed on linear time-invariant (LTI) systems. It generates ramp, exponential, and step input signals, and observes the system responses when convolved with each other and the unit step using built-in convolution functions as well as a manual convolution method. The purpose is to characterize LTI systems based on their impulse responses.

1. %lab-3%
clc
clear all
close all
% Practical: Exp-3 Title: Response of Linear Time
Invariant(LTI) System
% Name: Omkar Rane
% Batch: 1 Block: 1
% Roll No: SETB118
% Seat No: S177086
%a) To observe responses of LTI system whose impulse
response is known.
%b) To characterize the system based on observations of
responses.
%______________________________________________________%
clear all;
close all;
clc
%ramp signal%
t=-5:0.1:5;
l=length(t);
for i=1 : l
if(t(i)<0)
ramp_sig(i)=0;
else
ramp_sig(i)=t(i);
end
end
subplot(621);
plot(t,ramp_sig);
axis([-5 5 -0.5 1.5]);
title('Ramp signal');
%_________________________________________________________%

2. %Exponential Signal%
t=-5:0.01:5;
l=length(t);
a=3;
for i=1 : l
if(t(i)<0)
exp_sig(i)=0;
else
exp_sig(i)=exp(-a*t(i));
end
end
subplot(6,2,2);
plot(t,exp_sig);
axis([-5 5 -0.5 1.5]);
title('exponential signal');
%________________________________________________________%
%step Signal%
t=-5:0.01:5;
l=length(t);
for i=1 : l
if(t(i)<0)
unit_step(i)=0;
else
unit_step(i)=1;
end
end
subplot(623);
stairs(t,unit_step);
axis([-5 5 -0.5 1.9]);
title('unit step ');

3. %___________________________________________________%
%Convolution of signal with built In function %
y1=conv(unit_step,unit_step);
subplot(624);
plot(y1);
title('step and step');
y2=conv(exp_sig,unit_step);
subplot(625);
plot(y2);
title('exp and step');
y3=conv(unit_step,ramp_sig);
subplot(626);
plot(y3);
title('step and ramp');
Output:

4. %Convolution without use of built in function%
clc
clear all
close all
x=input('Enter x:');
h=input('Enter h :');
m=length(x);
n=length(h);
X=[x,zeros(1,n)];
H=[h,zeros(1,m)];
for i=1:n+m-1
y(i)=0;
for j=1:m
if(i-j+1>0)
y(i)=y(i)+X(j)*H(i-j+1); % convoultion formula
else
end
end
end
subplot(211);
stem(y);
xlabel('n');
ylabel('y[n]');
title('Convolution without inbuilt function');
z=conv(x,h);
subplot(212);
stem(z);

5. Output:

6. Convolution Using Simulink:

9. Output: