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Unformatted text preview: EE 378 Handout #13 Statistical Signal Processing Wednesday, May 16, 2007 Homework Set #6 Due: Wednesday, May 23, 2007. Announcement: You can hand in the HW either after class or deposit it, before 5pm, in the Homework in box in the 378 drawer of the class file cabinet on the second floor of the Packard Building. 1. The following graph (Fig. 1) represents the dependencies between 6 random variables. As discussed in class, an edge between random variables means that the joint pmf can be written as a factor of products involving pairs X i and X j for the random variables X i and X j that are connected in the graph. Figure 1: Problem 1 X1 X2 X3 X4 X5 X6 Using the graph, state whether or not the statements given below necessarily hold true. (a) X 1 and X 6 are conditionally independent given X 2 and X 5 . (b) X 1 and X 6 are conditionally independent given X 3 and X 4 . (c) X 2 and X 3 are independent. (d) X 2 and X 3 are conditionally independent given X 4 . 1 2. Let X ( n + 1) = aX ( n ) + bW ( n ) Z ( n ) = cX ( n ) Y ( n ) = Z ( n ) + V ( n ) , where { V ( n ) } and { W ( n ) } are zeromean, unitvariance white noise processes, inde pendent of each other, and a = 0 . 5, b = 0 . 2, and c = 0 . 2. (a) Draw a block diagram of the model. (b) Find the causal Wiener filter for estimating Z ( n ) based on Y ( k ), < k n ....
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This note was uploaded on 03/03/2011 for the course EE 378 taught by Professor Weissman,i during the Spring '07 term at Stanford.
 Spring '07
 Weissman,I
 Signal Processing

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