Shannon, TESPAR and approximation strategies

Abstract

This paper outlines the development and application of an alternative embodiment of Claude Shannon's celebrated sampling theorem qualified by Shannon in 1949 and tested more recently by the authors, via the classification of a wide variety of real-world band-limited waveforms. The work of Voelcker, Requicha et. al. is called upon and developed, to indicate key features of the basic coding concept, designated “Time-Encoded Signal Processing And Recognition” (TESPAR). TESPAR coding is based upon approximations to the locations of the 2TW Real and Complex Zeros, derived from an analysis of the band-limited waveforms under examination. Progressively informative numerical descriptors of the waveform may be obtained via a ranking of the 2TW samples (“Shannon Numbers”), derived from the analysis. TESPAR concepts are illustrated by reference to recent case-studies involving signal classifications across a spectrum from very-high frequency nano-second waveforms to very-low frequency wave-forms in the sub-Hz range. The key features of TESPAR in the speech processing arena are emphasized, illustrating: • • A capability to separate and classify many signals of interest that are indistinguishable in the frequency domain. • • An ability to code time-varying speech waveforms into optimum configurations for processing by Artificial Neural Networks. • • An ability to deploy, economically, massively parallel architectures for productive data fusion.