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**Unformatted text preview: **UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Department of Electrical and Computer Engineering ECE 410 Digital Signal Processing Homework 7 Wednesday, October 8, 2008 Prof. Bresler, Prof. Jones Due by October 15, 2008 Problem 1 . Given that X ( z ) = 3 . 5- 7 . 5 z- 1- 19 z- 2 1- 3 z- 1- 10 z- 2 + 24 z- 3 . (a) (10 points) Find and sketch all possible ROC’s for X ( z ). Determine whether the system is left-sided/right-sided/2-sided in each case. When the system is left-sided or right-sided, is it causal or noncausal? (b) (5 points) For each ROC, state whether the system is BIBO stable. Give reasoning for full credit. (c) (5 points) Find the Inverse Z-transform x [ n ] for each ROC. Problem 2 . A sequence x [ n ] = 4(2)- n u [- n ]- 9(- 3)- n u [ n- 1] is the input to an LSI system with the transfer function H ( z ). It produces a two-sided output sequence with z-transform of the form: Y ( z ) = 2 ( z + 1 / 3)( z- 1) ....

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