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For an LTI discrete system to be stable, the square sum of the impulse response should be

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in Signals and Systems by (1.2m points)
For an LTI discrete system to be stable, the square sum of the impulse response should be

(a) Integral multiple of 2pi

(b) Infinity

(c) Finite

(d) Zero

This question was posed to me in a national level competition.

Query is from Properties of LTI Systems in division Time-Domain Analysis of CT Systems of Signals and Systems

1 Answer

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by (42.1k points)
Correct answer is (c) Finite

The best explanation: If the square sum is infinite, the system is an unstable system. If it is zero, it means h(t) = 0 for all t. However, this cannot be possible. Thus, it has to be finite.

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