An Explicit Form of Signum Function

John Venetis ()
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John Venetis: Section of Mechanics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens, 15773 Athens, Greece

Mathematics, 2024, vol. 12, issue 20, 1-10

Abstract: In this paper, the author derives an analytical exact form of signum function, which evidently constitutes a fundamental concept of Communication Systems and Control Theory along with digital control systems and is also involved in many other fields of applied mathematics and engineering practices. In particular, this significant function is performed in a simple manner as a finite combination of purely algebraic representations. The novelty of this work when compared to other analytical expressions of this nonlinear function is that the proposed explicit representation is not performed in terms of miscellaneous special functions, such as Bessel functions, error function, and beta function, and also is neither the limit of a function nor the limit of a sequence of functions with a point-wise or uniform convergence.

Keywords: signum function; analytical expression; tangent function; irrational quantity; integer part of real variable (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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