Question

The Z-Transform X(z) of a discrete time signal x(n) is defined as ____________

(a) \(\sum_{n=-\infty}^{\infty}x(n)z^n\)

(b) \(\sum_{n=-\infty}^{\infty}x(n)z^{-n}\)

(c) \(\sum_{n=0}^{\infty}x(n)z^n\)

(d) None of the mentioned

The question was posed to me in an online quiz.

This interesting question is from Z Transform topic in section Z Transform and its Application – Analysis of the LTI Systems of Digital Signal Processing

Answer 1

Right option is (b) \(\sum_{n=-\infty}^{\infty}x(n)z^{-n}\)

To elaborate: The z-transform of a real discrete time sequence x(n) is defined as a power of ‘z’ which is equal to X(z)=\(\sum_{n=-{\infty}}^{\infty} x(n)z^{-n}\), where ‘z’ is a complex variable.