Article
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An Explicit Form of Ramp Function
Version 1
: Received: 20 November 2023 / Approved: 20 November 2023 / Online: 20 November 2023 (15:26:18 CET)
A peer-reviewed article of this Preprint also exists.
Venetis, J.C. An Explicit Form of Ramp Function. AppliedMath 2024, 4, 442-451. Venetis, J.C. An Explicit Form of Ramp Function. AppliedMath 2024, 4, 442-451.
Abstract
In this paper, an analytical form of Rump Function is presented. This seminal function
constitutes a fundamental concept of digital signal processing theory and is also involved in many
other areas of applied mathematics.
In particular, Rump Function is performed in a simple manner as the limit of a sequence of real
functions letting ? tend to infinity. This limit is zero for strictly negative values of the real variable ?
whereas it coincides with the independent variable ? for strictly positive values of the variable ?.
The novelty of this work compared to other research studies concerning analytical expressions of
the Ramp Function, is that the proposed formula is not exhibited in terms of miscellaneous special
functions, e.g. Gamma Function, Biexponential Function or any other special functions such as
Error Function, Hyperbolic Function, Orthogonal polynomials etc.
Hence, this formula may be much more practical, flexible and useful in the computational
procedures which are inserted into digital signal processing techniques and other engineering
practices.
Keywords
Ramp Function; analytical expression; absolute value
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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