A Study on Some Discrete Transforms of Engineering Sciences

Abstract

Transform methods has their great importance in the field of applied sciences, especially in engineering sciences. To most of us Laplace transform is well known and we are acquainted to solve differential equations with this important tool. But it deals with the continuous variable/analog signals. In this computer world we need the tools to deal with discrete variable/digital signals. Unfortunately we have a little knowledge about them i.e. we are not familiar with discrete transforms. The main objective of this thesis was to be familiarized with some discrete transforms. For the purpose Ztransform, which is the most conversant one of the family of discrete transforms is taken. Also discrete counterpart of the Fourier transform, DFT and its calculation technique Fast Fourier Transform (FFT) is considered. Some detail of those transforms has been addressed. Fortunately we have devised a lemma for Z-transform, along with its proof has been presented. Finally a brief introduction to the newest transform, the Wavelet transform is introduced.