On Z-transform and Its Applications

In this thesis we study Z-transform (the two-sided Z-transform), the one-sided Z-transform and the two-dimensional Z-transform with their properties, their inverses and some examples on them. We also present the relation between Z-transform and Laplace transform and between Z-transform and Fourier transform. Some applications of Z-transform including solutions of some kinds of linear difference equations, analysis of linear shift-invariant systems, implementation of FIR and IIR filters and design of IIR filters from analog filters are discussed. Chirp Z-transform algorithm is also presented with two applications: enhancement in poles and high resolution and narrow band frequency analysis