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If a system do not have a bounded output for bounded input, then the system is said to be __________

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If a system do not have a bounded output for bounded input, then the system is said to be __________

(a) Causal

(b) Non-causal

(c) Stable

(d) Non-stable

This question was addressed to me in an interview for internship.

Question is taken from Discrete Time Systems topic in chapter Discrete Time Signals and Systems of Digital Signal Processing

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The correct option is (d) Non-stable

Easiest explanation: An arbitrary relaxed system is said to be BIBO stable if it has a bounded output for every value in the bounded input. So, the system given in the question is a Non-stable system.

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