Question

9. MATLAB Problem: Use Matlab to find the convolution y(t) of f(t)2tu(t) and h(t) ut1u(t-1). You should submit a printout of the matlab code as an m-file with comments (using %) explaining the role of each line. You should also submit a plot ofy(t) for-l sts 4. You may find Computer Example C2.4 on page 137 useful EXAMPLE FROM BOOK IS BELOW. System Response to External Input: The Zero-Sta 2.4 QComputer Example C2.4 Find c(t) = f(t) * g(t) for the signals in Fig. 2.9. t1=-10:01:0,t1=t1'; gl=-2*exp(2*t1); t2=0:.01:10:t2-t2'; g2=2"exp(+2); f=[zeros(size(g 1));ones(size(g2)); c=0.01"conv(f,g); t--20:.01:5;t-t'; plot(t,c(1:length(t))) O

Answer 1

t1--1: .01 :-.01; t2-0:.01:4; tl-tl % from-1 % t2 from 0 to 4 t1 to -0.01 t= [t1;t2]; % merge t1 and t2 ut-[zeros (size (t1)) ; ones (size (t2 ) ) ] ; %(ut-1 for t>-0 and ut-0 for t<0 %unit step function ht [ 12 13 %calculation of ht using ut and t values while i<length (t) ht (i)Fut (i+l)-ut (i-l) end 19 20 21 - yt= . 01 conv (ut , ht); %convolution plot (t, yt (1: length (t)) ) ; %plot!

0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002 1 -0.5 0 0.5.5 2 2.53 3.5 4

matlab code:

t1=-1:.01:-.01; % t1 from -1 to -0.01
t2=0:.01:4; % t2 from 0 to 4
t1=t1';
t2=t2';
t=[t1;t2]; % merge t1 and t2

ut=[zeros(size(t1));ones(size(t2))]; %unit step function
%(ut=1 for t>=0 and ut=0 for t<0
ft=2*t'*ut; %ft value
ht=[];

%calculation of ht using ut and t values
i=2;
while i<length(t)
ht(i)=ut(i+1)-ut(i-1)
i=i+1;
end

yt=.01*conv(ut,ht); %convolution
plot(t,yt(1:length(t))); %plot