In lab6 you found convolution htxt using three methods analy

In lab#6 you found convolution (h(t)*x(t)) using three methods (analytically, graphically (area using rectangular approximation or quad), and MATLAB in-built function). h(t) = sin(pi t) (u(t) - u(t - 1)) x(t) = 1.5(u(t) - u(t -1)) You found that the shape of the plot of h(t)*x(t) agrees in all the three methods bill the magnitude does not, why so? Explain how those three methods calculate convolution.

Solution

%linear convolution.

% to write a program to do linear convolution for continus and discrete

% time signals and plot the graphs.

%linear convolution for continuous LTI system.

close all;

clear all;

clc;

t=0:0.01:5;

x=exp(t);

y=exp(t.^2);

z=conv(x,y);

subplot(3,1,1);

plot(t,x);

xlabel(\'time\');

ylabel(\'amplitude\');

title(\'time signal-1\');

subplot(3,1,2);

plot(t,y);

xlabel(\'time\');

ylabel(\'amplitude\');

title(\'time signal-2\');

subplot(\'3,1,3\');

plot(z);

xlabel(\'time\');

ylabel(\'amplitude\');

title(\'convoluted signal\');

example-2:

close all;

clear all;

clc;

x=[1 2 3];

y=[6 7 8];

z=conv(x,y);

subplot(3,1,1);

stem(x);

xlabel(\'time\');

ylabel(\'amplitude\');

title(\'time signal-1\');

subplot(3,1,2);

stem(y);

xlabel(\'time\');

ylabel(\'amplitude\');

title(\'time signal-2\');

subplot(3,1,3);

stem(z);

xlabel(\'time\');

ylabel(\'amplitude\');

title(\'convoluted signal\')