The $$\boldsymbol{z}$$-Transform Analysis of Discrete Time Signals and Systems

Abstract

The z-transformz-transform is the discrete counterpart of Laplace transform. The Laplace transform converts integro-differential equations into algebraic equations. In the same way, the z-transform converts difference equations of discrete time systems to algebraic equations which simplifies the discrete time system analysis. There are many connections between Laplace and z-transforms except for some minor differences. DTFT represents discrete time signals in terms of complex sinusoids. When this sort of representation is generalized and represented in terms of the complex exponential, it is termed as z-transform. This sort of representation has a broader characterization of the system with signals. Further, the DTFT is applicable only for stable systems whereas z-transform can be applied even to unstable systems which means that z-transform can be used to a larger class of systems and signals. It is to be noted that many of the properties in DTFT, Laplace transform and z-transform are common except that the Laplace transform deals with continuous time signals and systems.