University of Illinois
Spring 2011
ECE 361:
Problem Set 2
Matched and Unmatched Filtering, and Signal Design
Due:
Thursday February 3 at 9:30 a.m.
Reading:
Lecture Notes: Lectures 25
Throughout this Problem Set, assume that the bits being transmitted are equally likely to be 0 or 1.
1.
[Matched Filtering]
A communication system uses signals
s
0
(
t
) and
s
1
(
t
) to communicate over a white Gaussian noise
channel with twosided power spectral density
N
0
/
2. The receiver is an optimum receiver (matched
filter) for the signal set, and the maximumlikelihood decision rule is used.
For the three sets of signals given below, compute the signal energies
E
0
and
E
1
, the value of
h
s
0
, s
1
i
,
and the error probability achieved by the optimum receiver.
Note: You are
not
asked for the impulse response of the matched filter, or the sampling time
T
0
, or the
values of ˆ
s
0
(
T
0
) and ˆ
s
1
(
T
0
), or the variance of the noise at the receiver filter output, and you should
not need any of these to find the answers to the question asked.
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 Spring '09
 Signal Processing, Additive white Gaussian noise, Estimation theory, spectrum, error probability

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