Chapter 9 - Discrete-Time Signals and Systems

Abstract

The theory of discrete- and continuous-time signals and systems is similar, but there are significant differences. As functions of an integer variable, discrete-time signals are naturally discrete or obtained from analog signals by sampling. Periodicity coincides for both types of signals, but integer periods in discrete-time periodic signals impose new restrictions. Energy, power, and symmetry of continuous-time signals are conceptually the same as for discrete-time signals. Basic signals just like those for continuous-time signals are defined without mathematical complications. Extending linearity and time invariance to discrete-time systems, a convolution sum represent them. Significant differences with continuous-time systems is that the solution of difference equations can be recursively obtained, and that the convolution sum provides a class of non-recursive systems not present in the analog domain. Causality and BIBO stability are conceptually the same for both types of systems. Basic theory of two-dimensional signals and systems are introduced. The theory of one-dimensional signals and systems are easily extended to two dimensions, however, many of the one-dimensional properties are not valid in two dimensions. Simulations using MATLAB clarify the theoretical concepts.