ECE4250
Fall 2008
Homework Set 1
Your solutions to these problems are due in the ECE425 handin box at 5:00 PM on
Monday, Sept. 8, 2008.
The handin box is located outside the south entrance to Phillips
Hall 219 (usual place) and we use the upper right hand box.
No late homework will be
accepted without an official university excuse.
Please work on these problems well in
advance of the due date as we fully expect you may have questions and/or need
suggestions.
Problem 1
ORDINARY LOWPASS SAMPLING
(a)
Consider an analog (continuoustime) signal that is bandlimited to ±17 kHz which is
sampled at 40 kHz.
(Assume a rectangularshaped spectrum.)
Plot the spectrum of the
sampled (discretetime) signal on the interval 100 kHz to +100 kHz.
Do not be concerned
with the actual amplitude scale of this spectrum.
(b)
If you had available ideal lowpass filters, give a range of cutoff frequencies for this
filter that could be used to recover the analog signal from its samples.
(c)
A practical (nonideal) analog lowpass filter that is very popular is the socalled
Butterworth filter.
[Later we shall see that this filter "characteristic" is very useful as a
"prototype" (model) for designing digital filters.]
For this problem, what you need to know
is that the magnitude of the Butterworth frequency response is given by:
A(f) =
{
f
c
2N
/
[ f
2N
+ f
c
2N
]
}
1/2
Here N is the "order" of the filter (number of poles), f
c
is the 3db cutoff frequency
(response drops to 1/√2 or “halfpower” frequency), and f is the variable frequency.
What
is the magnitude response of the Butterworth lowpass at f=0, f=1, and f=∞?
Using Matlab, calculate and plot A(f) for a normalized cutoff, f
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 Fall '05
 HEMAMI
 Lowpass filter, sampling rate, kHz, Phillips Hall

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