Question

The z-transform of x[n]= {2,4,5,7,0,1} (5 as the reference variable) is ___________

(a) 2z^2 + 4z + 5 +7z + z^3, z≠∞

(b) 2z^-2 + 4z^-1 + 5 + 7z + z^3, z≠∞

(c) 2z^-2 + 4z^-1 + 5 + 7z + z^3, 0<|z|<∞

(d) 2z^2 + 4z + 5 + 7z^-1 + z^3, 0<|z|<∞

I had been asked this question in an interview for job.

I want to ask this question from Properties of Z-Transforms in section Z-Transform and Digital Filtering of Signals and Systems

Answer 1

Correct choice is (d) 2z^2 + 4z + 5 + 7z^-1 + z^3, 0<|z|<∞

For explanation I would say: Performing z-transform on x (n+n0), we get z^n0 X (z)

Now, x[n] = 2δ[n+2] + 4δ[n+1] + 5δ[n] + 7δ[n-1] + δ[n-3]

So, X (z) = 2z^2 + 4z + 5 + 7z^-1 + z^3, 0<|z|<∞.