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MEEN 364
Homework Set 3
Fall 2004
September 16, 2004
Homework Set 3– Due September 23, 2004 @ 5:00 PM
Note: Clearly label all the plots. Credit will not be given for unlabeled plots.
1.
A 10Hz continuoustime sinusoidal signal corrupted by highfrequency noise,
)
160
cos(
)
140
sin(
3
)
20
sin(
)
(
t
t
t
t
x
a
π
+
+
=
is sampled at 200 Hz.
a)
Plot the discrete Fourier transform (DFT)’s magnitude of the sampled discrete
time signal
x
[n] with respect to frequency (Hint: Use the MATLAB function,
‘fft’) when the continuoustime signal is sampled for
(1) 1 s,
(2) 10 s,
(3) 100 s.
Comment on the differences you observe in your plots.
(Hint: Visit the website
http://www.bores.com/courses/intro/basics/1_resol.htm
and read the frequency resolution).
b)
For three cases of part (a), downsample the signal (Hint: Use the MATLAB
function ‘dyaddown’ or ‘downsample’) to a sampling frequency of 100 Hz
without passing the signal through a lowpass filter.
Plot the magnitude of the resulting DFT with respect to frequency. What do you
observe? Is there aliasing? If yes, explain in detail how to obtain the aliased
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