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If all the poles of H(z) are outside the unit circle, then the system is said to be _____________

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If all the poles of H(z) are outside the unit circle, then the system is said to be _____________

(a) Only causal

(b) Only BIBO stable

(c) BIBO stable and causal

(d) None of the mentioned

I have been asked this question by my college director while I was bunking the class.

The question is from Analysis of LTI System in Z Domain topic in division Z Transform and its Application – Analysis of the LTI Systems of Digital Signal Processing

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Correct answer is (d) None of the mentioned

Best explanation: If all the poles of H(z) are outside an unit circle, it means that the system is neither causal nor BIBO stable.

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