SS Lab Class No 6

%{
SS_lab_06
Rahat Sir
Date: 23-10-2019
%}
% Convolution_4
% x(t) = (t-1) (u(t-1)-u(t-3)
tx = 1:.01:3;
x = tx - 1;
% h(t) = u(t+1) - 2u(t-2)
th1 = -1:.01:2;
th2 = 2:.01:10;

th = [th1 th2];

h = [ones(size(th1)) -1.*ones(size(th2))];
% convolution integral
y = conv(x,h);

%% Convolution_5
% interconnection of system
% Cascade system

%first System
th1 = 0:.01:3;
th2 = 0:.01:3;
th22 = 3:.01:6;

h1 = th1 .* exp(-3*th1);

tx = 0:.01:3;

x = ones(size(tx));
w = conv(x,h1).* .01; % 0 to 6
tw = linspace(min(tx)+min(th1),max(tx)+max(th1), length(w));
h2 =[th2.*cos(pi * th2) zeros(size(th22))];

y = conv(w,h2).*.01;
ty = linspace(min(th2)+min(tw),max(th2)+max(tw), length(y));
figure
plot(ty,y);

% Second System
h2 = th2.* cos(pi * th2);
w2 = conv(h1,h2).* .01;
tw = linspace(min(th2)+min(th1),max(th2)+max(th1), length(w2));
x2 = [x zeros(size(th22))];
tx2 = [tx th22];
y2 = conv(x2,w2).*.01;
ty2 = linspace(min(tx2)+min(tw),max(tx2)+max(tw),length(y2));
figure
plot(ty2,y2);