Discrete-Time Signal Processing (2nd Edition) (Prentice-Hall Signal Processing Series)

Electrical Engineering 431
Problem Set IV
Due: February 23, 2004
Reading : OSB: Chapter 7
4.1 Filter Design
Your boss wants you to design a digital fi lter according to the following speci fi cations.
(a) Design a Chebyshev fi lter using the bilinear transform that meets these speci fi cations. Use
Matlab to show the frequency response and the pole-zero plot.
(b) Use the Parks-McClellan algorithm to design a zero-phase FIR fi lter that meets these
speci fi cations.
(c) Compare the magnitude and phases of your two fi lters.
(d) What are the implications of the orders of the fi lters you found? In particular, which is
computationally more ef fi cient (in other words, which requires fewer computations per
output value)?
4.2 Bilinear Transforms
An integrator has the transfer function . We form a discrete-time fi lter “equivalent”
to the integrator by using the bilinear transform.
(a) What is the discrete-time transfer function and the corresponding unit-sample re-
sponse?