MEEN 260
Introduction to Engineering Experimentation
Homework 12: Digital Filters
Solutions
Assigned:
Thursday, 17 Apr. 2008
Due:
Thursday, 24 Apr. 2008, 9:00 am
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
y= sin(5*t)+0.5*sin(10*tpi/4)+0.6*sin(16*tpi/3)+0.25*sin(25*tpi/6);
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 b), using Matlab command
given in the lecture notes with cut off frequency 2 Hz.
d)
Plot the filtered signal and compare with original signal given in the figure. What conclusion
can you make from the comparison?
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View Full DocumentSolution:
a)
The maximum sampling period which will not result in aliasing is twice the maximum
frequency of the components of the combined summation of signals.
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 Fall '08
 LANGARI
 Signal Processing, 1 K, Lowpass filter, 25 rad, 20 sec, 50 rads

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