HW 2 (Due Thurs, Sept 7, start of class): Given a system with an impulse response function $h[t] = \frac{2}{(t+1)^2}$ use the convolution integral (in matlab) to calculate the response to the input $x[t] = 5cos(8t)$ for $t>0$. Plot results from $0<t<3$. Also, calculate the steady state response using phasor analysis, given that the frequency response function of the system is
$h[\omega] = 2 \frac{1}{2} e^{(-\omega^2 - 2(0.122434) - 2(1.57419))}$
Plot and compare it to the convolution solution.
Solution Hint
Using the convolution integral and the conv command in matlab:
t=0:.001:3; fs=1000; % timescale
h=?; % system impulse response
x=?; % input
yconv = conv(x,h,'full')/fs; % matlab convolution solution
figure(1), plot(t,yconv(1,1:3001), 'k-')
Using Phasor analysis:
w=8;
Yw=?
MagYw = ?
PhaYw = ?
yphas = ?
y[\omega] =?
y[t] =?
figure(2), plot(t, yconv(1:length(t)),'k-',t,yphas(1:length(t)),'k-')
Convolution: 1 pt
Phasor: 3 pt
