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UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Department of Electrical and Computer Engineering
ECE 410
Digital Signal Processing
Homework 9
Wednesday, October 22, 2008
Prof. Bresler, Prof. Jones
Due by October 29, 2008
Problem 1
(30 points)
(a) Given an ideal D/A with period
T
= 2 ms, and input sequence
y
[
n
] = cos(
nπ/
4) for all
n
,
(i) Determine a closed-form expression for the output
y
(
t
).
(ii) Sketch (by hand) the output for 0
≤
t
≤
20ms.
(iii) Determine a closed-form expression for the Fourier Transform of the output.
(iv) Sketch (by hand) the magnitude of the Fourier Transform of the output for 0
≤
Ω
≤
4000
π
(v) Identify on your sketch from (iv) the spurious component with the largest magnitude,
and determine a closed-form expression for its magnitude and frequency.
(b) Repeat (ii), (iv), and (v) in (a) above, when the ideal D/A is replaced by a zero-order hold.
(c) Repeat (i)-(v) in (a) above when the ideal D/A is replaced by a zero-order hold followed by
an analog compensator with frequency response

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