problem set9

problem set9 - 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 9 Due: December 6, 2007 Problem 9.1 Calculate the Kullback-Leibler divergence between the following pairs of densities. (a) Jointly Gaussian random vectors having the same mean vectors but dissimilar covariance matrices. (b) Two univariate statistically independent Laplacian random variables having the same variance but different means. Problem 9.2 Let’s explore how well Stein’s Lemma predicts optimal detector performance probabilities. Consider the two-model detection problem wherein L statistically inde- pendent, identically distributed Gaussian random variables are observed. Under M 0 , the mean is zero and the variance one; under M 1 , the mean is one and the variance one. (a) Find an expression for the false-alarm probability P F when the miss probability is constrained to be less than α . (b) Find the Kullback-Leibler distance corresponding to the false-alarm probability’s
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problem set9 - ELEC 531: STATISTICAL SIGNAL PROCESSING...

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