Question

If X(z) is the z-transform of the signal x(n) then what is the z-transform of a^nx(n)?

(a) X(az)

(b) X(az^-1)

(c) X(a^-1z)

(d) None of the mentioned

The question was asked during an online exam.

Origin of the question is Properties of Z Transform topic in portion Z Transform and its Application – Analysis of the LTI Systems of Digital Signal Processing

Answer 1

Correct option is (c) X(a^-1z)

Explanation: We know that from the definition of z-transform

Z{a^nx(n)}=\(\sum_{n=-\infty}^{\infty}a^n x(n) z^{-n}=\sum_{n=-\infty}^{\infty}x(n)(a^{-1}z)^{-n}=X(a^{-1}z)\).