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We define y[n] = nx[n] – (n-1)x[n]. Now, z[n] = z[n-1] + y[n], is z[n] stable?

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in Signals and Systems by (1.2m points)
We define y[n] = nx[n] – (n-1)x[n]. Now, z[n] = z[n-1] + y[n], is z[n] stable?

(a) Yes

(b) No

The question was posed to me during an internship interview.

My question comes from Discrete Time Signals topic in division Signals and Systems Basics of Signals and Systems

1 Answer

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by (42.1k points)
Correct option is (a) Yes

The explanation: As we take the sum of y[n], terms cancel out and deem z[n] to be BIBO stable.

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