EE 451

Homework Assignment 6
Due Oct. 8, 1999

1.
Consider the continuous-time system with the transfer function

\begin{displaymath}H(s) = \frac{\Omega_0^2}{s^2 + \sqrt{2} \Omega_0 s + \Omega_0^2 }\end{displaymath}

with $\Omega_0 = 2 \pi (250)$.
(a)
Is this a low-pass, high-pass, or band-pass filter?
(b)
Use the method of impulse invariance to transform this filter into a discrete-time filter. Use a sampling frequency of 2 kHz. Plot the poles and zeros of the discrete-time filter using MATLAB's zplane function.
(c)
Plot the frequency response of the discrete-time filter (magnitude and phase). Does this look like the type of filter you specified in Part (a)?
2.
Repeat Problem 1 for the system with the transfer function

\begin{displaymath}H(s) = \frac{s^2}{s^2 + \sqrt{2} \Omega_0 s + \Omega_0^2 }\end{displaymath}

3.
Problem 4.18
4.
Problem 4.20
5.
Probelm 4.24
6.
Problem 4.36
7.
Problem 4.44. Note that the input to the system should be rc(t), not x[n].


Bill Rison
1999-10-01