Question

Find the Z-transform of the causal sequence x(n) = {1,0,-2,3,5,4}. (1 as the reference variable)

(a) 1 – 2z^-2 + 3z^-3 + 5z^-4 + 4z^-5

(b) 1 – 2z^2 + 3z^3 + 5z^4 + 4z^5

(c) z^-1 – 2z^2 + 3z^3 + 5z^4 + 4z^5

(d) z – 2z^3 + 3z^4 + 5z^5 + 4z^6

This question was addressed to me by my college professor while I was bunking the class.

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

Answer 1

The correct option is (a) 1 – 2z^-2 + 3z^-3 + 5z^-4 + 4z^-5

Explanation: Given sequence values are :

x(0)=1, x(1)=0, x(2)=-2, x(3)=3, x(4)=5, x(5)=4.

We know that

\(X(Z) = \sum\limits_{n=-∞}^{∞} x(n) z^{-n}\)

X(Z) = x(0) + x(1) z^-1 + x(2) z^-2 + x(3) z^-3 + x(4) z^-4 + x(5) z^-5

X(Z) = 1 – 2z^-2 + 3z^-3 + 5z^-4 + 4z^-5.