630F09_hw3

# 630F09_hw3 - ENEE 630 Fall’2009 Homework #3 Problem 1 In...

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

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

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

Unformatted text preview: ENEE 630 Fall’2009 Homework #3 Problem 1 In a two-channel QMF bank, if the filters are related as H 1 ( z ) = H (- z ) ,F ( z ) = H ( z ) ,F 1 ( z ) =- H 1 ( z ) and if H ( z ) is chosen to have real coefficients and linear phase, then the distortion function is given by T ( e jw ) = 1 2 e- jwN ( | H ( e jw ) | 2- (- 1) N | H ( e j ( π- w )) | 2 ) (1) If filter order N is even, this implies T ( e j π 2 ) = 0, so in order to avoid strong attenuation on ω = π 2 , the filter order N for this filter bank structure has to be odd for many applications. Now consider a modified QMF bank shown in Figure P-1 where the filters could be FIR or IIR. Express ˆ X ( z ) in terms of X(z). With H 1 ( z ) = H (- z ), show that the choice F ( z ) = H ( z ) and F 1 ( z ) = H 1 ( z ) cancels aliasing. With this choice write down the distortion T(z) in terms of H ( z ).-1 z-1 z x[n] H(z) H(z) 1 F(z) F(z) 1 x[n] ^ 2 2 2 2 Figure : P-1 a) Now let H ( z ) be a real coefficient linear phase FIR lowpass filter of order N. Simplify) be a real coefficient linear phase FIR lowpass filter of order N....
View Full Document

## This note was uploaded on 10/31/2010 for the course EE 630 taught by Professor Wu during the Spring '10 term at Aarhus Universitet, Aarhus.

### Page1 / 3

630F09_hw3 - ENEE 630 Fall’2009 Homework #3 Problem 1 In...

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

View Full Document
Ask a homework question - tutors are online