Question

Find the Z-transform of x(n) = u(-n).

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

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

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

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

This question was addressed to me during an online interview.

The doubt is from Properties of Z-Transforms in division Z-Transform and Digital Filtering of Signals and Systems

Answer 1

Correct choice is (c) \(\frac{1}{1-z}\)

Best explanation: Given x(n) = u(-n)

Time reversal property of Z-transform states that

If x(n) ↔ X(z), then x(-n) ↔ X(\(\frac{1}{z}\))

Z[u(-n)] = \(\left(\frac{1}{z-1}\right)_{z=(1/z)} = \frac{1/z}{(1/z)-1} = \frac{1}{1-z}\).