EXPERIMENT - 13

AIM

To Demonstrate Linear and Circular Convolution and verify it's result analytically.

THEORY

In mathematics , convolution is a mathematical operation on two functions $f$ and $g$, producing a third function that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated. Convolution is similar to cross-correlation.

It has applications that include probability, statistics, computer vision, natural language processing, image and signal processing, engineering, and differential equations.

MATLAB COMMANDS USED

* plot(x,y,color,properties)
* conv(t);
* cconv(x);
* hold on;

MATLAB CODE

%Linear Convolution
x=[2,1,3,5];
y=[2,4,1];
lc=conv(x,y);

subplot(3,2,1);
stem(x,'filled');
title('Sequence x : [2,1,3,5]');
xlabel('n i.e. sample number');
ylabel('X(n)');

subplot(3,2,3);
stem(y,'filled');
title('Sequence y : [2,4,1]');
xlabel('n i.e. sample number');
ylabel('Y(n)');

subplot(3,2,5);
stem(lc,'filled');
xlabel('n i.e. sample number');
title({'Linear Convolution of Sequence
x and y',num2str(lc)});
ylabel('Convoluted Signal');

%Circular Convolution
x1=[1,4,6,7];
y1=[2,9,0,4];
cc=cconv(x,y,4);

subplot(3,2,2);
stem(x1,'filled');
title('Sequence x1 : [1,4,6,7]');
xlabel('n i.e. sample number');
ylabel('X1(n)');

subplot(3,2,4);
stem(y1,'filled');
title('Sequence y1 : [2,9,0,4]');
xlabel('n i.e. sample number');
ylabel('Y1(n)');

subplot(3,2,6);
stem(cc,'filled');
xlabel('n i.e. sample number');
title({'Circular Convolution of Sequence 
x1 and y1';num2str(cc)});
ylabel('Convoluted Signal');

print('convolutions','-dpng');

RESULT

Linear and Circular Convolution has been demonstrated and verified analytically.