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Unformatted text preview: (Ω) = 2 α α 2 + Ω 2 , Ω ∈ R . Determine the transfer function of the: (a) optimal Wiener ﬁlter H opt ( s ), (b) optimal causal Wiener ﬁlter H cau ( s ). Determine the corresponding minimum mean-squared error associated with these ﬁlters. 1 Problem # 4.0 Let ² [ n ] and v [ n ] be two zero mean, independent white noise processes. In this problem we will look at a more general estimation problem where the observa-tions are given by: u [ n ] = ∞ X k ==-∞ h [ k ] ² [ n-k ] + v [ n ] , where h [ n ] represents a distortion operator. The desired signal d [ n ] is of the form: d [ n ] = ∞ X k =-∞ p [ n ] ² [ n-k ] . Determine the optimal Wiener smoother K ( z ) that estimates d [ n ] from the observations u [ n ] in terms of P ( z ) and H ( z ). Determine the corresponding MMSE. 2...
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- Fall '11
- Signal Processing, Estimation theory, power spectral density, Wiener process, adaptive filtering