The mathematical background of the running example is the following: In Signal Processing, "the

Z-transform for discrete-time signals is the counterpart of the Laplace transform for continuoustime signals, and they each have a similar relationship to the corresponding Fourier transform.

Rosen, "Chirp

Z-transform based SPECAN approach for phase-preserving ScanSAR image generation," IEE Proc.

Generally, there are three common methods to derive the current expression at the loaded place: directly deducing by the volt-ampere characteristic [5], basing on the piecewise linear recursive convolution (PLRC) technique [6-8], using

Z-transform approach [9-12].

Beginning with deterministic signals and filters then moving to stochastic ones, he explores such topics as discrete time signals and systems, the

Z-transform, discrete filter design techniques, stochastic processes, and adaptive filters.

The design of these filters is based on the

z-transform.

Following the well-known approach developed by Stephenson and Mitalas (Stephenson and Mitalas 1971), based on the use of the

Z-transform (ZT) (Jury 1964), let us consider a thermal system, like a wall, in which u([tau]) is the input signal and y([tau]) is the correlated output signal.

The

z-transform is also covered, along with Hilbert transforms, for which a basic knowledge of complex variable theory is necessary.

The following analysis of the RiemannZeta function with a

z-transform shows the stability zones and requirements for the real and complex variables.

The

z-transform of e(n) signal can be expressed as:

Key words: Logarithmic mean, Identric mean,

Z-transform and convolution.

Chapter 3 is devoted to transform-domain representations of discrete-time signals, specifically the DTFT, DFT and

Z-Transform, together with their properties and applications.

The

z-transform has also been used in several works [6-8].