statical signal processing.pdf

# C how does the detector change when the value of m is

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(c) How does the detector change when the value of m is not known? 5.52 Noise generated by a system having zeros complicates the calculations for the colored noise detection problem. To illustrate these difficulties, assume the observation noise is produced as the output of a filter governed by the difference equation N ( ) = aN ( - 1 )+ w ( )+ bw ( - 1 ) , a 6 = - b , where w ( ) is white, Gaussian noise. Assume an observation duration sufficiently long to capture the colored effects. (a) Find the covariance matrix of this noise process. (b) Calculate the Cholesky factorization of the covariance matrix. (c) Find the unit-sample response of the optimal detector’s whitening filter. If it weren’t for the finite observation interval, would it indeed have an infinite-duration unit-sample response as claimed on Page 181? Describe the edge-effects of your filter, contrasting them with the case when b = 0. 5.53 It is frequently claimed that the relation between noise bandwidth and reciprocal duration of the ob- servation interval play a key role in determining whether DFT values are approximately uncorrelated. While the statements sound plausible, their veracity should be checked. Let the covariance function of the observation noise be K N ( ) = a | | .

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• Fall '08
• Papamichalis,P

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