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MEEN 260
Introduction to Engineering Experimentation
Homework 12: Digital Filters
Assigned:
Thursday, 23 Apr. 2008
Due:
Thursday, 30 Apr. 2008, 5:00 pm
Learning Objectives:
After completing this homework assignment, you should be able to:
1)
Design and apply digital filters
2)
Identify different digital filter types (recursive, nonrecursive, etc.)
Homework Problems:
Problem 1)
Digital Filters Design
The following analog signal contains four frequencies, 5, 10, 16, and 25 rad/s and the signal for
0 <
t
< 20 sec is shown below
()
( )
sin 5
0.5sin 10
0.6sin 16
0.25sin 25
43
6
ut
t
t
t
t
π
ππ
⎛⎞
=+
−
+
+
+
−
⎜⎟
⎝⎠
a)
Find the maximum sampling period (minimum sampling frequency) that will not
result in
aliasing of the given signal.
b)
Calculate the Nyquist frequency, f
nyquist
for T
s
= 0.05s
and plot the sampled version of the
signal of
u(t)
.
c)
Design a 3
rd
order Butterworth filter for the digitized signal from c), using Matlab command
given in the lecture notes with cut off frequency 2 Hz.
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 Fall '08
 LANGARI

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