How to Explain The Empirical Success of Generalized Trigonometric Functions in Processing Discontinuous Signals

Authors

Pedro Barragan Olague, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

10-2015

Comments

Technical Report: UTEP-CS-15-77

To appear in Mathematical Structures and Modeling, 2016, Vol. 37, pp. 25-29.

Abstract

Trigonometric functions form the basis of Fourier analysis - one of the main signal processing tools. However, while they are very efficient in describing smooth signals, they do not work well for signals that contain discontinuities - such as signals describing phase transitions, earthquakes, etc. It turns out that empirically, one of the most efficient ways of describing and processing such signals is to use a certain generalization of trigonometric functions. In this paper, we provide a theoretical explanation of why this particular generalization is the most empirically efficient one.