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Unformatted text preview: Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.432 Stochastic Processes, Detection and Estimation Problem Set 10 Spring 2004 Issued: Thursday, April 29, 2004 Due: Thursday, May 6, 2004 Final Exam: Our final will take place on May 19, 2004, from 9:00am to 12:00 noon . You are allowed to bring three 8 1 × 11 sheets of notes (both sides). 2 Reading: For this problem set: Chapter 7 Next: Section 4.8, Addenda to Chapters 6 and 7 Problem 10.1 Let y ( t ) = x ( t ) + v ( t ) where x ( t ) and v ( t ) are uncorrelated, zeromean processes, with 3 S xx ( s ) = 1 − s 2 5 S vv ( s ) = 9 − s 2 (a) Find the noncausal Wiener filter extimating x ( t ) based on y ( t ). Also find the corresponding meansquare estimation error. (b) Find the causal and causally invertible whitening filter for y ( t ). You will find that whitening y ( t ) requires differentiation. (c) Find the causal Wiener filter for estimating x ( t ). You should find that the overall filter doesn’t involve any differentiation. Also, find the associated mean square estimation error. Problem 10.2 Consider the system depicted in Fig. 21 (on the next page), where w ( t ) and v ( t ) are independent, zeromean noise processes with E [ w ( t ) w ( β )] = λ ( t − β ) 1 . E [ v ( t ) v ( β )] = λ ( t − β ) 5 1 1 −−−−−−− s+2 1 −−−−−−− s+1 x ( t ) w ( t ) z ( t ) ⊕ y ( t ) v ( t ) Figure 21 (a) Determine the noncausal Wiener filter for estimation x...
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This note was uploaded on 01/11/2012 for the course EE 6.432 taught by Professor Prof.gregorywornell during the Spring '04 term at MIT.
 Spring '04
 Prof.GregoryWornell
 Electrical Engineering

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