Q1
Consider the system displayed in the figure below (left plot) where LP is an ideal low-pass
filter with cutoff frequency $\omega_c = 5\pi$. The Fourier Transform (FT) of the input signal, $X(j\omega)$, is
displayed in the same figure (right plot).
1.5
$X(j\omega)$
$z(t)$
1
$x(t)$
LP
$y(t)$
0.5
$-\pi$
$\pi$
$\omega$
$\cos(5\pi t)$
Sketch the FT of the $z(t)$ (shown in the figure) and the FT of the output $y(t)$.
ANSWER:
Q2
Write in matrix form the state-space equations for the following block diagram:
$y(t)$
$w(t)$
5
3
Find the Laplace transfer function of this system using the state-space model approach.
ANSWER:
