Question

The z-transform of x[n]= {1,0,-1,0,1,-1} (1st 1 as the reference variable) is __________

(a) 1+2z^-2 -4 z^-4 + 5z^-5

(b) 1-z^-2 + z^-4 – z^-5

(c) 1-2z^2 + 4z^4 – 5z^5

(d) 1-z^2 + z^4 – z^5

This question was posed to me during a job interview.

This is a very interesting question from Properties of Z-Transforms in section Z-Transform and Digital Filtering of Signals and Systems

Answer 1

Correct choice is (b) 1-z^-2 + z^-4 – z^-5

Easiest explanation: Performing z-transform on x (n-n0), we get z^-n0 X (z)

Now, x[n] = δ[n] – δ[n-2] + δ[n-4] – δ[n-5]

So, X (z) = 1-z^-2 + z^-4 – z^-5, z≠0.