# hw18 - Determine Var Y 2 n and E Y 2 2 n(iii(2 pts...

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ENEE 324 ASSIGNMENT 18 Due Thu 11/12 Let X 1 ,X 2 ,... be pairwise uncorrelated random variables with mean μ and variance σ 2 , i.e., Cov( X i ,X j ) = ( σ 2 , i = j ; 0 , i 6 = j . The sequence { X n , n 1 } is the input to a time-varying causal ﬁlter which produces an output at every even-valued time instant 2 n . The value of that output is the average of the most recent n inputs: Y 2 n = X 2 n + X 2 n - 1 + ··· + X n +1 n (i) (2 pts.) Determine E [ Y 2 n ]. (ii) (3 pts.)
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Unformatted text preview: Determine Var[ Y 2 n ] and E [ Y 2 2 n ]. (iii) (2 pts.) Determine Cov( X 1 ,Y 2 n ) for every n ≥ 1. (iv) (2 pts.) Determine Cov( X 2 ,Y 2 n ) for every n ≥ 1. (v) (5 pts.) Determine Cov( X 2 n ,Y 2( n + m ) ) for every n ≥ 1 and m ≥ 0. (vi) (6 pts.) Determine Cov( Y 2 n ,Y 2( n + m ) ) for every n ≥ 1 and m ≥ 0....
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## This note was uploaded on 03/21/2010 for the course ENEE 324 taught by Professor Ephrimedes during the Fall '05 term at Maryland.

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