630F09_hw6 - ENEE 630 Fall 2009 Homework#6 Problem 1 The...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ENEE 630 Fall 2009 Homework #6 Problem 1 The tap-input vector of a transversal filter is defined by u ( n ) = α ( n ) s ( ω ) + v ( n ) where s ( ω ) = [1 ,e- jω ,...,e- jω ( M- 1) ] T v ( n ) = [ v ( n ) ,v ( n- 1) ,...,v ( n- M + 1)] T i.e. u ( n- k ) = α ( n ) · e- jkω + v ( n- k ) for k = 0 ,...,M- 1. For the tap-input vector at a given time n , α ( n ) is a complex random variable with zero mean and variance σ 2 α = E [ | α ( n ) | 2 ], and α ( n ) is uncorrelated with the w.s.s. process v ( n ). (a) Determine the correlation matrix of the tap-input vector u (n). (b) Suppose that the desired response d(n) is uncorrelated with u (n). What is the value of the tap-weight vector of the corresponding Wiener filter? (c) Suppose that the variance σ 2 α is zero, and the desired response is defined by d ( n ) = v ( n- k ) where 0 ≤ k ≤ M- 1. What is the new value of the tap-weight vector of the Wiener filter? (d) Determine the tap-weight vector of the Wiener filter for a desired response defined by d ( n ) = α ( n ) e- jwτ where τ is a prescribed delay....
View Full Document

{[ snackBarMessage ]}

Page1 / 4

630F09_hw6 - ENEE 630 Fall 2009 Homework#6 Problem 1 The...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online