convolution of signals

Convolution for both signals and sequence:

Convolution is defined as mathematical way of combining two signals in order to form third the signal. It plays a significant role because it relates the input signal and impulse response of the system to the output of the system. Which is used to provide relationship of LTI system.

Some important properties of convolution are:

Let us consider two signals x₁(t) and x₂(t) for these the convolution is

x₁(t)* x₂(t) = ) )  = ) )

Commutative property:

The commutative property of convolution is

x₁(t)*x₂(t) = x₂(t) *x₁(t)

Distributive property:

The Distributive property of convolution is

x₁(t)*[ x₂(t)+ x₃(t)]= [x₁(t)* x₂(t)]+[ x₁(t)* x₃(t)]

Associative property:

The Associative property of convolution is

x₁(t)*[ x₂(t)*x₃(t)]= [x₁(t)* x₂(t)]* x₃(t)

Convolution performs the following operations are:

• Folding
• Multiplication
• Addition
• Shifting

clc;

close all;

   clear all;

%program for convolution of two sequences

x=input(‘enter input sequence: ‘);

h=input(‘enter impulse response: ‘);

y=conv(x,h);

subplot(3,1,1);

stem(x);

xlabel(‘n’);

ylabel(‘x(n)’);

title(‘input sequence’)

subplot(3,1,2);

stem(h);

xlabel(‘n’);

ylabel(‘h(n)’);

title(‘impulse response sequence’)

subplot(3,1,3);

stem(y);

xlabel(‘n’);

ylabel(‘y(n)’);

title(‘linear convolution’)

disp(‘linear convolution y=’);

disp(y)

%program for signal convolution

t=0:0.1:10;

x1=sin(2*pi*t);

h1=cos(2*pi*t);

y1=conv(x1,h1);

figure;

subplot(3,1,1);

plot(x1);

xlabel(‘t’);

ylabel(‘x(t)’);

title(‘input signal’)

subplot(3,1,2);

plot(h1);

xlabel(‘t’);

ylabel(‘h(t)’);

title(‘impulse response’)

subplot(3,1,3);

plot(y1);

xlabel(‘n’);

ylabel(‘y(n)’);

title(‘linear convolution’);