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Is y[n] = n*sin(n*pi/4)u[-n] a stable system?

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in Signals and Systems by (1.2m points)
Is y[n] = n*sin(n*pi/4)u[-n] a stable system?

(a) Yes

(b) No

(c) Marginally stable

(d) None of the mentioned

I got this question during an interview for a job.

My question is from Properties of LTI Systems topic in portion Time-Domain Analysis of CT Systems of Signals and Systems

1 Answer

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by (42.1k points)
The correct choice is (b) No

Easy explanation: The ‘n’ term in the y[n] will dominate as it reaches to negative infinity, and hence could reach infinite values. Eventhough + infinity would not be a problem, still the resultant system would be unstable.

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