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The Design of FIR Least Squares Inverse Filters

The Design of FIR Least Squares Inverse Filters. Chapter 4.4.5 Application 2006. 09. 21 / KIM JEONG JOONG / 20067168. GOALS. Given or The design of an inverse filter is important applications

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The Design of FIR Least Squares Inverse Filters

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  1. The Design of FIR Least Squares Inverse Filters Chapter 4.4.5 Application 2006. 09. 21 / KIM JEONG JOONG / 20067168 www.themegallery.com

  2. 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)

  3. 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

  4. Optimum inverse filter • Where Shanks’ method Optimum least squares inverse filter ; k = 0,1,2,…., N-1

  5. Least squares solution

  6. Define the coefficients(1) • Given • e(n) = 0, ( n >= 0 )

  7. Define the coefficients(2) • Given

  8. FIR least squares inverse filter special case • FIR least squares inverse filter

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