Question

The z-transform of u[n] is _________

(a) \(\frac{1}{1-z^{-1}}\), |Z|>1

(b) \(\frac{1}{1-z^{-1}}\), |Z|<1

(c) \(\frac{z}{1-z^{-1}}\), |Z|<1

(d) \(\frac{z}{1-z^{-1}}\), |Z|>1

I had been asked this question during a job interview.

Enquiry is from Properties of Z-Transforms in section Z-Transform and Digital Filtering of Signals and Systems

Answer 1

The correct answer is (a) \(\frac{1}{1-z^{-1}}\), |Z|>1

The best I can explain: Performing z-transform on u[n], we get,

X (z) = \(∑_{n=0}^∞ x[n]z^{-n}\)

= \(\frac{1}{1-z^{-1}}\), |Z|>1.