Jury E.I. Theory and Application of the z-Transform Method

Krieger Publishing, 1973. — 329 p.During the early fifties, considerable interest and activity arose among engineers and systems theorists in the relatively new area of discrete system theory. This activity and aroused interest were mainly motivated by I he advancement made in digital computer technology and its widespread application in system analysis and design. Several methods of analysis of discrete systems were proposed and applied. Among them were the transform techniques and operators' methods. One transform method, which found wide application in the analysis, is the z-transform method. It represents the counterpart of the Laplace transform as applied to continuous system theory. In this text the z-transform method is extensively developed and applied to many areas of discrete system theory.
The subject matter is mainly addressed to engineers and systems theorists; however, some of the material developed would also be of interest to applied mathematicians. Whenever it is found necessary, most of the theorems and lemmas are proved on a somewhat rigorous mathematical basis. However, to limit the text and to place more emphasis on the applications, the rigor is sometimes sacrificed. Consequently, certain theorems are touched on briefly without proofs. Convergence problems are not vigorously pursued, but are left to the reader for further study. In most of the unproven material the pertinent references are cited so that the reader can easily find the rigorous derivations of the theory.
z-Transform Definition and Theorems.
z-Transform Method of Solution of Linear Difference Equations.
Stability Consideration for Linear Discrete Systems.
Convolution z-Transform.
Convolution z-Transform Applied to Nonlinear Discrete Systems.
Periodic Modes of Oscillation in Nonlinear Discrete Systems.
z-Transform Method in Approximation Techniques.
Applications to Various Areas of System Theory.
z-Transform Pairs.
Pairs of Modified z-Transforms.
Total Square Integrals.
Closed Forms of the Function Σn^rxⁿ.