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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 P1(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. P1(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 ) z1 z1 y(n) Figure: P1(a) 1 π /3 2 π /3 π 2 π ϖ  F 1 (e j ϖ )  Figure: P1(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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