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 f lter according to the following speci f cations.
(a) Design a Chebyshev f lter using the bilinear transform that meets these speci f 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 f lter that meets these
speci f cations.
(c) Compare the magnitude and phases of your two f lters.
(d) What are the implications of the orders of the f lters you found? In particular, which is
computationally more ef f 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 f 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?
(b)