Question

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

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

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

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

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

This question was posed to me in semester exam.

The doubt is from The Z-Transform in portion Z-Transform and Digital Filtering of Signals and Systems

Answer 1

Right answer is (a) \(\frac{1}{1-z}\)

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

Z[x(n)] = X(Z) = \(∑_{n=-∞}^∞ x(n) z^{-n} = ∑_{n=-∞}^∞ u(-n) z^{-n} = ∑_{n=-∞}^0 (1) z^{-n}\)

=\(∑_{n=0}^∞ z^n = \frac{1}{1-z}\).