# 5-27 - EE 341 Discrete-Time Linear Systems Week 9 Spring...

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EE 341 Discrete-Time Linear Systems – Week 9 Spring 2011 7 2. Left-sided signals have ROC of form min zr  , i.e., it converges INSIDE circle min  (EGG YOLK). Examine for left-sided [] x n 0 () [] n n n X zx n z  As n  , need (1 ) 0 n z  or 0 z This happens for values of z inside rather than outside the poles. What about convergence at 0 z ? If [] x n is left-sided but not strictly anticausal ([] 0 xn for 0 0 nn  but 0 []0 ) e.g. [] [ 1 ] u n  , then 1 1 10 n n X zz z      does not converge at 0 z so don’t include 0 z in the ROC.

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EE 341 Discrete-Time Linear Systems – Week 9 Spring 2011 8 3. 2-sided signals have ROC of the form 12 (BAGEL OR DONUT) rz r  4. Finite Duration [] x n has ROC of entire z-plane except possibly 0 z or z   1 [1 ] 0 nz z  ] z    FACT: A ROC must contain the unit circle for BIBO stability – this holds for causal, anticausal, and two-sided signals.
EE 341 Discrete-Time Linear Systems – Week 9

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5-27 - EE 341 Discrete-Time Linear Systems Week 9 Spring...

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