Why we do the Z-Transform of a discrete time signal in the study of digital signal Processing……??
Digital Signal Processing is highly complex and integrated. Although it is possible to study the operating characteristics of a linear discrete system by using either basic difference equations or the equivalent convolution-summation representation, you want to reach a meaningful understanding of the signal. Since DSP are of orders higher than one, a transformation method is used to simplify the analysis and synthesis of systems whose dynamics are governed by linear difference or differential equations. The z-transform is a rule by which a sequence of numbers is converted into a function of the complex variable z. Because of the z-transform’s basic structure, it possesses properties that will enable you to solve linear difference equations using simple algebraic manipulations. Through the process of taking a z-transfor, we transform (change, map, etc) a sequence of numbers into a function of the complex variable z. The analysis of the digital signal can then be expressed in these terms
