Signal Processing Using Maple V

Abstract

It is common practice to use frequency domain techniques to determine the characteristics of signals and systems. Signals are often characterized by their frequency spectrum and a great deal of insight into the behavior of a linear time-invariant (LTI) system can be gained by examining its frequency response. As a result of the dramatic increase in the speed and decrease in the cost of digital hardware, discrete-time signal processing techniques based on the discrete Fourier transform (DFT) have become more and more prevalent. This paper describes a number of special commands that exploit both the symbolic and numeric computational capabilities of MapleV to provide a signal processing environment that is both flexible and easy to use. Using these commands, the results of processing continuous-time signals with continuous-time systems described by their s-plane transfer functions or discrete-time systems described by their z-plane transfer functions are easily determined. Important concepts such as aliasing and causality can be explored. Although designed for a class in systems engineering, the procedures should be of use to practicing professionals as well. First, some of the special commands will be described followed by an example of showing the response of both continuous-time and discrete-time systems to a pulse input. Listings of the command procedures are given in the appendix. Additional commands are under development and listings are available from the author.