EL 611 HW 7

# EL 611 HW 7 - EL611 3 Homework 6 1 A discrete-time causal...

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EL611 3 Homework 6 1) A discrete-time causal LTI system has the system function ! ! = 1 + 0 . 2 ! ! ! ( 1 9 ! ! ! ) ( 1 + 0 . 81 ! ! ! ) a) Is the system stable? b) Find expressions for a minimum-phase system ! ! ( ! ) and an all-pass system ! !" ( ! ) such that ! ! = ! ! ! ! !" ( ! ) 2) For each of the following system functions, state whether or not it is a minimum-phase system. Justify your answer. ! ! ! = 1 2 ! ! ! ( 1 + ! ! ! ! ! ) 1 ! ! ! ! ! ( 1 + ! ! ! ! ! ) ! ! ! = 1 + ! ! ! ! ! ( 1 ! ! ! ! ! ) 1 ! ! ! ! ! ( 1 + ! ! ! ! ! ) ! ! ! = 1 ! ! ! ! ! 1 ! ! ! ! ! ( 1 + ! ! ! ! ! ) ! ! ! = ! ! ! ( 1 ! ! ! ! ! ) 1 ! ! ! ! ! ( 1 + ! ! ! ! ! ) 3) For each of the following system functions, specify a minimum phase system function such that the magnitude of the frequency response of the two systems is the same.

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