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 What is the ROC of the system function H(z) if the discrete time LTI system is BIBO stable?
  • a)
    Entire z-plane, except at z=0
  • b)
    Entire z-plane, except at z=∞
  • c)
    Contain unit circle
  • d)
    None of the mentioned
Correct answer is option 'C'. Can you explain this answer?
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What is the ROC of the system function H(z) if the discrete time LTI s...
 
Explanation: A discrete time LTI is BIBO stable, if and only if its impulse response h(n) is absolutely summable. That is,
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What is the ROC of the system function H(z) if the discrete time LTI s...
Answer: a) Entire z-plane, except at z=0.

Explanation:
BIBO stability means that the system is bounded-input bounded-output stable, which implies that any bounded input to the system results in a bounded output. Therefore, the ROC of the system function must include the unit circle in the z-plane, since the output of a stable system cannot grow unbounded as the input oscillates around the unit circle.

Additionally, since the system is LTI (linear and time-invariant), the ROC must be symmetric about the origin. Therefore, if the ROC includes the unit circle, it must also include the entire z-plane except for possibly z=0. However, if the system has a finite impulse response (FIR), then the ROC must include z=0 as well.
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What is the ROC of the system function H(z) if the discrete time LTI system is BIBO stable?a)Entire z-plane, except at z=0b)Entire z-plane, except at z=∞c)Contain unit circled)None of the mentionedCorrect answer is option 'C'. Can you explain this answer?
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