Hello, I am trying to solve this problem but I am very stuck. Can anybody please

Question

Hello, I am trying to solve this problem but I am very stuck. Can anybody please show me STEP BY STEP how to solve this type of problems so that I can approach them in a future?

Thanks so much in advance!

Given: 2s 16s2+2s+1 in time domain equals 1 15 e 16 sin t hot) e 16 COS 15 8 15 16 16 where 2 0.25, 2 0.1,2 0.5 Consider a causal input z(t) COS (t) cos(21 tu(t) cos (22t)w(t). a Plot corresponding output y (t) along with its magnitude and phase b) Comment on how the output u in this step compare with output in step 3 Hint: Fourier transform of cos(Sot)u(t) cannot be obtained from Laplace transform, since the ROC does not include j2 axis. To find Fourier transform of cos(Sot)u(t), use modulation property: FIcos(S2ot)u(t)] 0.5 U(2 20) U(2 S20), where U (2) Flu(t)] Fourier transform of unit-step which can be obtained from the table.

Explanation / Answer

clc;
close all;
clear all;

f = -(1/2*pi):0.1:(1/2*pi);
t = 1./f;
cons = sqrt(15)/16;
omega0 = 0.25;
omega1 = 0.1;
omega2 = 0.5;
ht = 0.125*( exp(-t/16).*cos(t*cons) - (1/sqrt(15))*exp(-t/16).*sin(t*cons)); %h(t)
xt = (t>0).*( cos(omega0*t) + cos(omega1*t) + cos(omega2*t)); %u(t) is implemented as t>0
yt = conv(xt,ht);

t1 = -(2*pi):4*pi/length(yt):(2*pi)-(4*pi/length(yt));
figure
plot(t1,yt);

Yjw = fft(yt);
omega = -1:2/length(Yjw):1-(1/length(Yjw));
length(omega)
figure
plot(omega,abs(Yjw));
figure
plot(omega,angle(Yjw));

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