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MCE311
Homework # 4
Due on Wed Nov 30
th
, 2011
Question 1
(5.16): A function has the form
݂ሺݐሻ ൌ 3 sin 10ߨݐ 5 cos 40ߨݐ
and is sampled
at a rate of 30 samples per second. What false alias frequency(ies) would you expect in the
discrete data?
Solution:
݂ሺݐሻൌ3sinሺ2ߨ
5
ሻݐ5cosሺ2ߨ
20
ሻݐ
The function has frequencies of 5 and 20 Hz. The minimum sampling rate would then be 40 Hz
to avoid aliasing. Sampling at 30 Hz would not produce aliases for the 5 Hz signal but would for
the 20 Hz signal. The alias frequency can be evaluated using the folding diagram in Section 5.1.
f
a
=3020=10Hz
Or we can use the folding diagram:
f
N
= 30/2 = 15 Hz. f/f
N
= 20/15 = 1.3333. From the folding diagram, f
a
/f
N
= 0.666.
Thus f
a
= 0.666
15 = 10 Hz.
This is the difference between the sampling rate and the signal frequency.
Question 2 (5.17)
: A function has the form
݂ሺݐሻ ൌ 6 sin 20ߨݐ 5 cos 30ߨݐ
and is sampled
at a rate of 50 samples per second. What false alias frequency(ies) would you expect in the
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 Spring '11
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