630F09_hw2 - ENEE 630 F’09 Homework #2 Due: Friday...

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Unformatted text preview: ENEE 630 F’09 Homework #2 Due: Friday October 2, 2009 at 6:00 PM Problem 1 Consider the structure shown in Fig P-1(a), where W is the 3 × 3 DFT matrix. This is a three channel synthesis bank with three filters F ( z ), F 1 ( z ), F 2 ( z ). (For example F ( z ) = Y ( z ) /Y ( z ) with y 1 ( n ) and y 2 ( n ) set to zero.) a) Let R ( z ) = 1 + z- 1 , R 1 ( z ) = 1- z- 2 , R 2 ( z ) = 2 + 3 z- 1 . Find expressions for the three synthesis filters F ( z ), F 1 ( z ), F 2 ( z ). b) The magnitude response of F 1 ( z ) is sketched in Fig. P-1(b). Plot the responses | F ( e jω ) | and | F 2 ( e jω ) | . Does the relation between F ( z ), F 1 ( z ), and F 2 ( z ) depend on choices of R k ( z )? y (n) y 1 (n) y 2 (n) W R (z 3 ) R 1 (z 3 ) R 2 (z 3 ) z-1 z-1 y(n) Figure: P-1(a) 1 π /3 2 π /3 π 2 π ϖ | F 1 (e j ϖ ) | Figure: P-1(b) 1 Problem 2 For a uniform DFT analysis bank, we know that the filters are related by H k ( z ) = H ( zW k ), 0 ≤ k ≤ M- 1, with W = e- j 2 π/M . Let M = 5 and define two new transfer...
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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.

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630F09_hw2 - ENEE 630 F’09 Homework #2 Due: Friday...

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