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Unformatted text preview: EE 378 Handout #3 Statistical Signal Processing Wednesday, April 25, 2007 Homework Set #3 Due: Wednesday, May 2, 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. For a stationary zero-mean process, X n with power spectral density S xx ( e jω ) and k th- order correlation matrix R k , show that λ max λ min ≤ S max S min where S max and S min are the largest and smallest values of S xx ( e jω ) and λ max and λ min are the largest and smallest eigenvalues of the k th-order correlation matrix, R k 2. The power spectral density S xx ( e jω ) of every real-valued WSS process is real, even, and nonnegative. In this problem you will show that, conversely, if S xx ( e jω ) is a real, even, nonnegative function with R π- π S xx ( e jω ) dw < ∞ , then S xx ( e jω ) is the psd for some WSS random process. Let us consider the case that 1 π Z π- π S xx ( e jω ) dw = 1 . Define the random process X ( n ) = cos(Ω n + Θ) , where Ω is a random variable on (- π,π ] with a pdf, 1 π S xx ( e jω ) and Θ ∼ U[0 , 2 π ] are independent.independent....
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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
- Signal Processing