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# Solutions Manual for Adaptive Filter Theory 5th Edition by Haykin IBSN 9780132671453

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Solutions Manual for Adaptive Filter Theory 5th Edition by Haykin IBSN 9780132671453 Full download: http://downloadlink.org/p/solutions-manual-for-adaptive-filter-theory-5th-edition-by-haykin-ibsn-9780132671453/  Chapter 2   Problem 2.1   a)   Let w k = x +  j y  p(− k) = a +  j  b  We may then write f = w k     p ∗   ( − k  )   =(x +  j y)(a −    j  b )   =(ax +  by) +  j(ay −    bx )  Letting where f = u +  j v   u = ax +  by v = ay −    bx Hence,     ∂ u ∂ u   = a =  b   ∂ x ∂ y  ∂ v ∂ v  = a   ∂ y ∂ x   = −  b    From these results we can immediately see that ∂ u ∂ v  =   ∂ x ∂ y  ∂ v ∂ u   ∂ x = −   ∂ y In other words, the product term w k     p ∗   (− k) satisfies the Cauchy-Riemann equations, and so this term is analytic.  b)   Let Let f = w k     p ∗   ( − k  )   =(x −    j y)(a +  j  b )   =(ax +  by) +  j(bx −   ay )   with f = u +  j v   u = ax +  by v =  bx −  ay  Hence,   ∂ u ∂ u   = a   ∂ x ∂ y  ∂ v ∂ v  =  b   ∂ x ∂ y  =  b   = − a   From these results we immediately see that ∂ u ∂ v  =   ∂ x ∂ y  ∂ v ∂ u   ∂ x = −   ∂ y In other words, the product term w ∗    p(− k) does not satisfy the Cauchy-Riemann equations, and so this term is not analytic.    d   Problem 2.2   a)   From the Wiener-Hopf equation, we have w 0 = R  − 1    p (1) We are given that 1   0 . 5   R = 0.5 1  0 . 5   p = 0.25 Hence the inverse of R is 1 0.5  − 1 R  − 1 =   =  0.5 1 1 1 −0.5   − 1 0 . 75   −0.5 1   Using Equation (1), we therefore get 1   1   − 0 . 5   0 . 5  w 0 =  0.75  −0.5 1 0.25   1   0 . 375   =  0.75 0  0 . 5   = 0   b)   The minimum mean-square error is J min   = σ 2 −  p H   w 0   = σ 2   −   0 . 5   0 . 25   = σ 2 − 0.25 0 . 5   0
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