Chapter 9 - Discrete-time Signals and Systems

Abstract

Although the theory of discrete- and continuous-time signals and systems are similar there are significant differences. Letting the discrete-time signals be functions of an integer variable unifies the treatment of signals obtained from analog signals by sampling and those that are naturally discrete. The discrete frequency is circular, and depends on the sampling period used whenever the discrete-time signal results from sampling. Conceptually, periodicity coincides for both types of signals, but discrete-time periodic signals must have integer periods which imposes restrictions not present in continuous-time periodic signals. Energy, power, and symmetry of continuous-time signals are conceptually the same for discrete-time signals. One can define basic signals just like those for continuous-time signals, but without their mathematical complications. Extending the concept of linear time-invariance to discrete-time systems, we obtain a convolution sum to represent them. A significant difference over 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 without counterpart in the analog domain. Causality and BIBO stability are conceptually the same for both types of systems. Simulations using MATLAB clarify the theoretical concepts.