{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}