Question

The z-transform of {3,0,0,0,0,6,1,-4} (1 as the reference variable) is ___________

(a) 3z^5 + 6 + z^-1 – 4z^-2, 0≤|z|<∞

(b) 3z^5 + 6 + z^-1 – 4z^-2, 0<|z|<∞

(c) 3z^5 + 6 + z – 4z^-2 0<|z|<∞

(d) 3z^5 + 6 + z^-1 – 4z^-2, 0≤|z|<∞

This question was addressed to me during an interview for a job.

The origin of the question is Properties of Z-Transforms topic in chapter Z-Transform and Digital Filtering of Signals and Systems

Answer 1

The correct choice is (b) 3z^5 + 6 + z^-1 – 4z^-2, 0<|z|<∞

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

Now, x[n] = 3δ[n+5] + 6δ[n] + δ[n-1] – 4δ[n-2]

So, X (z) = 3z^5 + 6 + z^-1 – 4z^-2, 0<|z|<∞.