630_rec_7_sol - ENEE630 ADSP 1 RECITATION 7 w solution...

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ENEE630 ADSP RECITATION 7 w/ solution October 29/30, 2009 1. Determine if each of the following are valid autocorrelation matrices of WSS processes. R a = 4 1 1 - 1 4 1 - 1 - 1 4 , R b = 2 1 1 1 2 0 1 0 2 , R c = 2 j 0 j 0 2 j 0 - j 0 2 j , R d = 1 0 2 0 1 0 2 0 1 . Solution: Recall that the properties of an autocorrelation matrix for a WSS process is that (1) R is Toeplitz; (2) R H = R ; (3) R is non-negative definite. R a is NOT Hermitian; R b is NOT Toeplitz; R c is NOT Hermitian; R d is NOT non-negative definite ( λ = 1 , - 1 , 3). 2. Consider the random process y ( n ) = x ( n ) + v ( n ), where x ( n ) = Ae j ( ωn + φ ) and v ( n ) is zero mean white Gaussian noise with a variance σ 2 v . We also assume the noise and the complex sinusoid are independent. Under the following conditions, determine if y ( n ) is WSS. Justify your answers. (a)
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This note was uploaded on 10/31/2010 for the course EE 630 taught by Professor Wu during the Spring '10 term at Aarhus Universitet, Aarhus.

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630_rec_7_sol - ENEE630 ADSP 1 RECITATION 7 w solution...

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