Linear Convolution

Matlab program to find Linear Convolution of given signals.

Linear Convolution: If x(n) is a sequence of N1 number of samples and h(n) with N2 number of samples, after convolution y(n) will have N=N1+N2-1 samples.

It can be used to find the response of a linear filter.

Zero padding is not necessary to find the response of a linear filter.

Matlab code

clc;

clear all; close all;

x=input('Enter the 1st Sequence x[n]='); h=input('Enter the 2nd Sequence h[n]=');

x1=input('Define the Initial Position of x[n] in Time(X) axis='); 

h1=input('Define the Initial Position of h[n] in Time(X) axis='); 

N1=length(x);

N2=length(h);

x2=x1+(N1-1); % End Position of x[n] in Time(X) axis 

h2=h1+(N2-1); % End Position of h[n] in Time(X) axis 

y1=x1+h1;

y2=x2+h2; y=conv(x,h);

disp('The Resultant Signal y[n]=');disp(y);

subplot(3,1,1);

stem(x1:x2,x);

title('(a) Input Signal x[n] ');

xlabel('Time-->'); ylabel('Amplitude');

subplot(3,1,2);

stem(h1:h2,h);

title('(b) Input Signal h[n]');

xlabel('Time-->'); ylabel('Amplitude');

subplot(3,1,3);

stem(y1:y2,y);

title('(c) Convolved Output Signal y[n]'); xlabel('Time-->');

ylabel('Amplitude');

Command window

Enter the 1st Sequence x[n] = [1 2 3 4]

Enter the 2nd Sequence h[n] = [1 1 1 1 1]

Define the Initial Position of x[n] in Time(X) axis = 2 

Define the Initial Position of h[n] in Time(X) axis = 0 T

he Resultant Signal y[n] = 1 3 6 10 10 9 7 4

Figure window