Question

The z-transform of –u(-n-1) is ___________

(a) \(\frac{1}{1-z}\)

(b) \(\frac{z}{1-z}\)

(c) \(\frac{1}{1-z^{-1}}\)

(d) \(\frac{z}{1-z^{-1}}\)

I got this question in an interview for job.

My question is taken from Properties of ROC in division Laplace Transform and System Design of Signals and Systems

Answer 1

Right option is (c) \(\frac{1}{1-z^{-1}}\)

Explanation: z [-u (-n-1)] = \(∑_{n=-1}^∞ [u(-n-1)] z^{-n}\)

= – [z + z^2 + z^3 + z^4…]

= \(\frac{z}{z-1}\)

= \(\frac{1}{1-z^{-1}}\).