Z transform is used to convert discrete time Domain into a complex frequency domain where, discrete time domain represents an order of complex or real Numbers. It is generalize form of Fourier Transform, which we get when we generalize Fourier transform and get z transform. The reason behind this is that Fourier transform is not sufficient to converge on all sequence and when we do this thing then we get the power of complex variable theory that we deal with noncontiguous time systems and signals.

This transform is used in many applications of mathematics and signal processing. The lists of applications of z transform are:-

-Uses to analysis of digital filters.

-Used to simulate the continuous systems.

-Analyze the linear discrete system.

-Used to finding frequency response.

-Analysis of discrete signal.

-Helps in system design and analysis and also checks the systems stability.

-For automatic controls in telecommunication.

-Enhance the electrical and mechanical energy to provide dynamic nature of the system.

If we see the main applications of z transform than we find that it is analysis tool that analyze the whole discrete time signals and systems and their related issues. If we talk the application areas of

This transform wherever it is used, they are:-

-Digital signal processing.

-Population science.

-Control theory.

-Digital signal processing.

Z-transforms represent the system according to their location of poles and zeros of the system during transfer function that happens only in complex plane. It is closely related to Laplace Transform. Main functionality of this transform is to provide access to transient behavior (transient behavior means changeable) that monitors all states stability of a system or all behavior either static or dynamic. This transform is a generalize form of Fourier transform from a discrete time signals and Laplace transform is also a generalize form of Fourier transform but from continuous time signals.