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PS9 10

# PS9 10 - University of Minnesota Dept of Electrical and...

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University of Minnesota Dept. of Electrical and Computer Engineering EE 8581 DETECTION AND ESTIMATION THEORY Spring 2010 Problem Set 9 Assigned: May 3, 2010 Due: May 10, 2010 Readings : Read Levy Chapter 13. Problem 1 Let a(t) and n(t) be independent, zero mean stochastic processes with power spectra S a (s) and S n (s) respectively, where 𝑆𝑆 𝑎𝑎 ( 𝑠𝑠 ) = 1 1 − 𝑠𝑠 2 and 𝑆𝑆 𝑛𝑛 ( 𝑠𝑠 ) = 1 1 4 𝑠𝑠 2 . Suppose that we observe r(t)= a(t) +n(t) . 1. Find the causal and causally invertible whitening filter for r(t) . Does the filter require differentiation of r(t) ? 2. Find the optimal realizable filter for estimating a(t) from r(s) , - < 𝑠𝑠 ≤ 𝑡𝑡 . Problem 2 Let y(t) be the solution of the differential equation 𝑑𝑑𝑑𝑑 ( 𝑡𝑡 ) 𝑑𝑑𝑡𝑡 + 𝛼𝛼
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