Spectral Logic and Its Applications for the Design of Digital Devices

CHAPTER 11

EXAMPLES OF APPLICATIONS AND GENERALIZATIONS OF SPECTRAL METHODS ON LOGIC FUNCTIONS

In preceding chapters, we discussed some particular applications of spectral logics in switching theory (including extensions to multiple-valued functions), circuit synthesis with emphasis to the optimization problems, design of devices with self-error-correction, and testing of digital systems. Main tools were several transforms on finite Abelian groups, primarily the groups were and and related operators.

Spectral techniques, however, are a more general theory and have interesting and important applications in many other areas, including, for instance, signal and image processing, communications, pattern recognition, system identification and design, as well as in solving certain problems in applied mathematics. These applications are mostly based on the fact that the Walsh transform is the Fourier transform on dyadic groups (6), which has simple implementations both in hardware and in software by binary digital circuits, since the basis functions take values 1 and − 1.

In order to illustrate the power of spectral methods in various areas of computing and engineering, this chapter presents a few examples of applications of transforms that are considered in this book, as well as discusses ...