Question

What is the z-transform of the following finite duration signal?

(a) 2 + 4z + 5z^2 + 7z^3 + z^4

(b) 2 + 4z + 5z^2 + 7z^3 + z^5

(c) 2 + 4z^-1 + 5z^-2 + 7z^-3 + z^-5

(d) 2z^2 + 4z + 5 +7z^-1 + z^-3

I had been asked this question in semester exam.

My doubt stems from Z Transform in portion Z Transform and its Application – Analysis of the LTI Systems of Digital Signal Processing

Answer 1

Right option is (d) 2z^2 + 4z + 5 +7z^-1 + z^-3

To explain: We know that, for a given signal x(n) the z-transform is defined as X(z)=\(\sum_{n=-\infty}^{\infty} x(n)z^{-n}\)

Substitute the values of n from -2 to 3 and the corresponding signal values in the above formula

We get, X(z) = 2z^2 + 4z + 5 + 7z^-1 + z^-3.