Analytical Representations of Heaviside and Ramp Function

In this paper, explicit exact forms of Heaviside Step Function and Ramp Function are presented. These significant functions constitute fundamental concepts of operational calculus and digital signal processing theory and are also involved in many other areas of applied sciences and engineering. In particular, Heaviside and Ramp Function are performed as bi-parametric single - valued functions with only one restriction imposed on each parameter. The novelty of this work when compared to other investigations concerning exact forms of Unit Step Function and/or Ramp Function, is that the proposed analytical 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, Orthogonal polynomials etc. Hence, these formulae may be much more practical, flexible and useful in the computational procedures which are inserted into operational calculus and digital signal processing techniques as well as other engineering practices.