Question

The inverse Z-transform of  z/(z+1)^2 is ______________

(a) (-1)^n+1

(b) (-1)^n-1 n

(c) (-1)^n-1

(d) (-1)^n+1 n

I had been asked this question in a job interview.

I would like to ask this question from Inverse Z-Transform in portion Z-Transform and Digital Filtering of Signals and Systems

Answer 1

Correct choice is (b) (-1)^n-1 n

To explain: U (z) = \(\frac{z}{z^2+2z+1}\)

 = \(z^{-1} – \frac{2+z^{-1}}{z^2+2z+1}\)

= \(z^{-1} – 2z^{-2} + \frac{2z^{-2}+3z^{-1}}{z^2+2z+1}\)

= \(z^{-1} – 2z^{-2} + 3z^{-3} – \frac{4z^{-2}+3z^{-3}}{z^2+2z+1}\)

So, U (z) = \(∑_{n=0}^∞ (-1)^{n-1} nz^{-n}\)

Hence, un = (-1)^n-1 n.