Question

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

(a) X(-z)

(b) X(z^-1)

(c) X^-1(z)

(d) None of the mentioned

This question was posed to me in an interview for internship.

The origin of the question is Properties of Z Transform topic in chapter Z Transform and its Application – Analysis of the LTI Systems of Digital Signal Processing

Answer 1

Correct answer is (b) X(z^-1)

Best explanation: From the definition of z-transform, we have

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