problem set8

# problem set8 - ELEC 531 STATISTICAL SIGNAL PROCESSING...

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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 unit-amplitude 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 false-alarm probability. (b) Now let the signals correspond to square-waves 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 false-alarm probability.

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