Q3) Using the graphical method of Section 4.10-1, draw a rough sketch of the amplitude and phase response of an LT
system described by the transfer function
$s^2 - 2s + 50$
$H(s) = \frac{s^2 - 2s + 50}{s^2 + 2s + 50} = \frac{(s - 1 - j7)(s - 1 + j7)}{(s + 1 - j7)(s + 1 + j7)}$
What kind of filter is this?
Q4) The pole-zero plot of a second-order system $H(s)$ is shown in Figure below. The dc response
of this system is minus 2, $H(j0) = -2$.
a) Letting $H(s) = k \frac{s^2 + b_1s + b_2}{s^2 + a_1s + a_2}$, determine the constants $k$, $b_1$, $b_2$, $a_1$, $a_2$.
b) Using the graphical method of Sec. 4.10-1, hand-sketch the magnitude response $|H(j\omega)|$
over $-10 \le \omega \le 10$.
c) Using the graphical method of Sec. 4.10-1, hand-sketch the phase response $\angle H(j\omega)$ over -
$10 \le \omega \le 10$.
d) What is the output $y(t)$ in response to input $x(t) = -3 \cos(3t \pi/3) - \sin(4t - \pi/8)$
