Question

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

(a) \(\frac{1}{2}\)(x[n+2]-x[n-2])

(b) (x[n+2]-x[n-2])

(c) \(\frac{1}{2}\)(x[n-2]-x[n+2])

(d) (x[n-2]-x[n+2])

I got this question in semester exam.

The above asked question is from Inverse Z-Transform in section Z-Transform and Digital Filtering of Signals and Systems

Answer 1

Correct answer is (a) \(\frac{1}{2}\)(x[n+2]-x[n-2])

The explanation: Y (z) = \(\frac{z^2-z^{-2}}{2}\) X (z) ↔ y[n]

= \(\frac{1}{2}\)(x[n+2]-x[n-2]).