Year: 2025
Type: article
Abstract: In this paper, explicit exact representations of the Unit Step Function and Ramp Function are obtained. These important functions constitute fundamental concepts of operational calculus together with digital signal processing theory and are also involved in many other areas of applied sciences and engineering practices. In particular, according to a rigorous process from the viewpoint of Mathematical Analysis, the Unit Step Function and the Ramp Function are equivalently performed as bi-parametric single-valued functions with only one constraint imposed on each parameter. The novelty of this work, when compared with other investigations concerning accurate and/or approximate forms of Unit Step Function and/or Ramp Function, is that the proposed exact formulae are not exhibited in terms of miscellaneous special functions, e.g., Gamma Function, Biexponential Function, or any other special functions, such as Error Function, Complementary Error Function, Hyperbolic Function, or Orthogonal Polynomials. In this framework, one may deduce that these formulae may be much more practical, flexible, and useful in the computational procedures that are inserted into operational calculus and digital signal processing techniques as well as other engineering practices.
Source: Analytics
Author: John Constantine Venetis
Institution: National Technical University of Athens
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,207
OpenAlex ID: W4413683511