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Given the z-transform pair 3^nn^2 u[n] ↔ X (z). The time signal corresponding to {X(z)}^2 is...

Given the z-transform pair 3^nn^2 u[n] ↔ X (z). The time signal corresponding to {X(z)}^2 is ___________

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asked Sep 30, 2022 in Signals and Systems by Lucy (1.2m points)

Given the z-transform pair 3^nn^2 u[n] ↔ X (z). The time signal corresponding to {X(z)}^2 is ___________

(a) {x[n]}^2

(b) x[n]*x[n]

(c) x[n]*x[-n]

(d) x[-n]*x[-n]

I got this question in a national level competition.

My question is based upon Inverse Z-Transform topic in section Z-Transform and Digital Filtering of Signals and Systems

signals and systems
z-transform and digital filtering
inverse z-transform

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1 Answer

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answered Oct 8, 2022 by leeyal (42.1k points)

The correct choice is (b) x[n]*x[n]

The best explanation: Y (z) = X (z) H (z)

Y (z) = X (z) X (z) ↔ y[n]

Or, y [n] = x[n]*x[n]

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