A transform of univariable time domain polynomial for extraction of temporal arcs

What is it about?

In this paper, a special transformation is applied to univariable polynomials of an arbitrary order wherein the constant term is eliminated, resulting in the generation of the proposed Offset Eliminated Polynomial (OEP). The OEP and the proposed transform can be considered to be effecting a stretching to the temporal or spatial domain depending on the type of variable under consideration, resulting in modifications for various parameters like time derivative and relative velocity which are analysed. In addition, the paper also analyses the concept of Temporal Arcs, which are time domain polynomial functions possessing two or more values at the same time instant. Using the OEP based proposed transform, the submerged value of the temporal arcs can also be extracted out in measurements, resulting in the unraveling of that class of special functions.

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