Q. Explain the Methods of Analysis for digital system?

Just as differential equations are used to represent systems with analog signals, difference equations are used for systems with discrete or digital data. Difference equations are also used to approximate differential equations, since the former are more easily programmed on a digital computer, and are generally easier to solve.

One of the mathematical tools devised for the analysis and design of discrete-data systems is the z-transform with z = e^Ts. The role of the z-transform for digital systems is similar to that of the Laplace transform for continuous-data systems. While the Laplace transform can be used to solve linear ordinary differential equations, for linear difference equations and linear systems with discrete or digital data, the z-transform becomes more appropriate to use. Since it is not a simple matter to perform an inverse Laplace transform on transcendental functions which involve terms like e-^kTs, the need arises to convert transcendental functions in s into algebraic ones in z. The development of z-transform methods of analysis are considered to be outside the scope of this book.

Various techniques and methods mentioned earlier, such as state-variable analysis, time-domain analysis, frequency-domain analysis, root-locus techniques, and Bode diagrams, are applied to the analysis of digital control systems. Details of these are obviously outside the scope of this introductory text.

Finally, no one can be an expert in all areas discussed in this chapter, or indeed in the preceding chapters. Therefore, it is always good advice to consult with those who are. The basics you have been exposed to will help you to select such consultants, either in or out of house,who will provide the knowledge to solve the problem confronting you.