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Digtal Signal Processing And Modeling www.themegallery.com The Design of FIR Least Squares Inverse Filters Chapter 4.4.5 Application 2006. 09. 21 / KIM JEONG JOONG / 20067168

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statistical D.S.P GOALS Given or The design of an inverse filter is important applications Signal is to be transmitted across a nonideal channel Channel is linear and has a system Funtion G(z) The chance of making errors at output of the receiver channel equalization filter The goal is to find an equalizer H(z)

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statistical D.S.P Inverse System In Most applications, the inverse system Not practical solution If G(z) is minimum phase, Inverse filter is causal and stable Or Inverse filter is not both causal and stable Constraining h(n) to be FIR requires We find the best approximation to the inverse filter

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statistical D.S.P Optimum inverse filter Where Shanks method Optimum least squares inverse filter ; k = 0,1,2, …., N-1

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statistical D.S.P Least squares solution

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statistical D.S.P Define the coefficients(1) Given e(n) = 0, ( n >= 0 )

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statistical D.S.P Define the coefficients(2) Given

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statistical D.S.P FIR least squares inverse filter special case FIR least squares inverse filter

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