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This paper aims to present a special transformation that is applied to univariable polynomials of an arbitrary order, resulting in the generation of the proposed offset eliminated polynomial. This transform-based approach is used in the analysis and synthesis of temporal arc functions, which are time domain polynomial functions possessing two or more values simultaneously. Using the proposed transform, the submerged values of temporal arcs can also be extracted in measurements.

The methodology involves a two-step mathematical procedure in which the proposed transform of the weighted modified derivative of the polynomial is generated, followed by multiplication with a linear or ramp function. The transform introduces a stretching in the temporal or spatial domain depending on the type of variable under consideration, resulting in modifications for parameters such as time derivative and relative velocity.

Detailed analysis of various parameters in this modified time domain is performed and results are presented. Additionally, using the proposed methodology, the submerged value of any temporal arc function can also be extracted in measurements, thereby unraveling the temporal arc.

A typical implementation study with results is also presented for an operational amplifier-based temporal arc-producing square rooting circuit for the extraction of the submerged value of the function.

The proposed transform-based approach has major applications in extracting the values of temporal arc functions that are submerged in conventional experimental measurements, thereby providing a novel method in unraveling that class of special functions.