ABSTRACT
Analog systems are designed and analyzed with the use of Laplace transforms. On the other hand, discrete-time systems are analyzed by using a similar technique, called the z-Transform. The basic lines of reasoning are the same for both cases: After determining the impulse response of the system, the response of any other input signal can be extracted by simple mathematical operations. The behavior and the stability of the system can be predicted from the zeros and poles of the transfer function. There are three methods for calculating the inverse transform of a function, X(z): power series expansion; expansion partial fraction; complex integration. z-Transform gives a significant amount of possibilities in system analysis for: effective computation of the response of a discrete Linear Time-Invariant (LTI) system; analysis of the stability of an LTI system; and characterization of an LTI in relation to its behavior in the frequency domain.
