Z Transform
• Introduction to the z-transform
• The Z-Transform
• The z-Transform
• The Transforms and Applications Handbook
• The Z-Transform
• The Z-transform converts a discrete time-domain signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation.
• It is like a discrete equivalent of the Laplace transform.
• The switching of spaces to transform calculus problems into algebraic operations on transforms is called operational calculus. The Laplace and z transforms are the most important methods for this purpose.
• One-sided z-transform

$X(z) = \Sigma_{n=0}^{\infty} x(n) z^{-n}$

• Two-sided z-transform

$X(z) = \Sigma_{n=-\infty}^{\infty} x(n) z^{-n}$

• Give a sequence, the set of values of z for which the z-transform converges, i.e., $|X(z)|< \infty$, is called the region of convergence.   $|X(z)| \leq \Sigma_{n=-\infty}^{-1} |x(n)r^{-n}| + \Sigma_{n=0}^{\infty}|\frac{x(n)}{r^n}|$
$|X(z)| \leq \Sigma_{n=1}^{\infty} |x(-n)r^{n}| + \Sigma_{n=0}^{\infty}|\frac{x(n)}{r^n}|$
page revision: 48, last edited: 21 Mar 2016 01:52