Z-Transform

We need first review some related concepts:

• Laplace transform: It transforms a function of a real variable \(t\) (often time) to a function of a complex variable \(s\) (complex frequency).
• Fourier transform:
• Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation.

Unilateral Z-transform

\[X(z)=Z\{x[n]\}=\sum_{n=0}^\infty x[n]z^{-n}\]

Unfortunately, there is no off-the-shelf python library for Z-tranform computation.

(A possible alternative is the Chirp z-Transform algorithm)

Further discussion is remain to be continued.