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ELEC 531: STATISTICAL SIGNAL PROCESSING
Department of Electrical and Computer Engineering
Rice University
Fall 2007
Problem Set 8
Due: November 20, 2007
Problem 8.1
The performance for the optimal detector in equal signal energy, white
Gaussian noise problems depends only on the distance between the signals, i.e. only
on the norm
k
s
1

s
0
k
. Let’s conﬁrm this result experimentally. Deﬁne the signal
under one hypothesis to be a unitamplitude sinusoid having one cycle within the 50
sample observation interval. Observations of this signal are contaminated by additive
white Gaussian noise having variance equal to 1.5. The hypotheses are equally likely.
(a) Let the second hypothesis be a cosine of the same frequency. Calculate and
estimate (in simulation) the detector’s falsealarm probability.
(b) Now let the signals correspond to squarewaves constructed from the sinusoids
used in the previous part. Normalize them so that they have the same energy as
the sinusoids. Calculate and estimate the detector’s falsealarm probability.
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 Fall '07
 Lexa
 Signal Processing

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