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The system defined by h[n] = 2^n u[n-2] is _______________

(a) Stable and causal

(b) Causal but not stable

(c) Stable but not causal

(d) Unstable and non-causal

This question was posed to me in an international level competition.

The question is from Characterization and Nature of Systems topic in portion Laplace Transform and System Design of Signals and Systems

1 Answer

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by (42.1k points)
The correct answer is (b) Causal but not stable

To explain I would say: Given that, h[n] = 2^n u [n-2]

For causal system, h[n] = 0 for n<0.

Hence, the given system is stable.

Since, \(∑_{n=2}^∞ 2^n = ∞\)

So, given system is not stable.

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