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630_rec_8 - x n in terms of a 1 and a 2 3 Assume v n is a...

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ENEE630 ADSP RECITATION 8 November 5/6, 2009 1. [Rec.7 P2(a) continued] Determine the PSD of the WSS process y ( n ) = Ae j ( ω 0 n + φ ) + v ( n ), where v ( n ) is zero mean white Gaussian noise with a variance σ 2 v , and φ is uniformly distributed over the interval [0 , 2 π ]. 2. Let a real-valued AR(2) process be described by v ( n ) = x ( n ) + a 1 x ( n - 1) + a 2 x ( n - 2) where v ( n ) is a white noise of zero-mean and variance σ 2 , and v ( n ) and past values x ( n ) are uncorrelated. (a) Determine and solve the Yule-Walker Equations for the AR process. (b) Find the variance of the process
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Unformatted text preview: x ( n ) in terms of a 1 and a 2 . 3. Assume v ( n ) is a white Gaussian random process with zero mean and variance 1. The two ﬁlters in Fig. R8.2 are G ( z ) = 1 1-. 4 z-1 and H ( z ) = 2 1-. 5 z-1 . v ( n )-G ( z )-H ( z )-u ( n ) Figure R8.3: (a) Is u ( n ) an AR process? If so, ﬁnd the parameters. (b) Find the autocorrelation coeﬃcients r u (0), r u (1), and r u (2) of the process u ( n ). 1...
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