Linear Convolution matlab code

AIM:

To verify Linear Convolution.

EQUIPMENTS:

Operating System         – Windows XP

Constructor                  - Simulator

Software                      - CCStudio 3 & MATLAB 7.5

THEORY:

Convolution is a formal mathematical operation, just as multiplication, addition, and integration. Addition takes two numbers and produces a third number, while convolution takes two signals and produces a third signal. Convolution is used in the mathematics of many fields, such as probability and statistics. In linear systems, convolution is used to describe the relationship between three signals of interest: the input signal, the impulse response, and the output signal.

In this equation, x1(k), x2(n-k) and y(n) represent the input to and output from the system at time n. Here we could see that one of the input is shifted in time by a value every time it is multiplied with the other input signal. Linear Convolution is quite often used as a method of implementing filters of various types.

% MATLAB program for linear convolution

%linear convolution program

clc;

clear all;

close all;

disp('linear convolution program');

x=input('enter i/p x(n):');

m=length(x);

h=input('enter i/p  h(n):');

n=length(h);

x=[x,zeros(1,n)];

subplot(2,2,1), stem(x);

title('i/p sequencce x(n)is:');

xlabel('---->n');

ylabel('---->x(n)');grid;

h=[h,zeros(1,m)];

subplot(2,2,2), stem(h);

title('i/p sequencce h(n)is:');

xlabel('---->n');

ylabel('---->h(n)');grid;

disp('convolution of x(n) & h(n) is y(n):');

y=zeros(1,m+n-1);

for i=1:m+n-1

    y(i)=0;

    for j=1:m+n-1

        if(j<i+1)

        y(i)=y(i)+x(j)*h(i-j+1);

        end

    end

end

y

subplot(2,2,[3,4]),stem(y);

title('convolution of x(n) & h(n) is :');

xlabel('---->n');

ylabel('---->y(n)');grid;

Result: