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ecen444-fall09-hw9

# ecen444-fall09-hw9 - ECEN 444 Digital Signal Processing...

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ECEN 444: Digital Signal Processing, Fall‘09 Homework #9 Homework Assignment #9 Due date – Dec. 07, 2009 (Mon), 12:40PM in class. Problem 1. Filter Implementation (20 points) Consider a causal rational LTI system with the following system function: H ( z ) = 1 - 2 z - 1 1 - (1 + j ) z - 1 1 - (1 - j ) z - 1 1 - 0 . 5 z - 1 1 - (1+ j ) 2 z - 1 1 - (1 - j ) 2 z - 1 Implement the above filter in the following forms, using only real coefficients. Draw the block diagram for your implementation. (a) Direct Form I structure. (b) Direct Form II structure. (c) Transposed Direct Form II structure. (d) Cascaded form structure, where two systems H 1 ( z ) and H 2 ( z ) are connected in series. H 1 ( z ) is a first order rational LTI system, and H 2 ( z ) is a second order rational LTI system. (e) Parallel form structure, where three systems H 0 ( z ) , H 1 ( z ) and H 2 ( z ) are connected in parallel. H 0 ( z ) is a zero order system (i.e., a constant multiplier), H 1 ( z ) is a first order rational LTI system, and H 2 ( z ) is a second order rational LTI system.

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ecen444-fall09-hw9 - ECEN 444 Digital Signal Processing...

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