Purpose

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.

Design/methodology/approach

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.

Findings

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.

Practical implications

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.

Originality/value

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.

中文翻译：

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单变量时域多项式的变换以提取时间弧

目的

本文旨在提出一种特殊变换，该变换适用于任意阶数的单变量多项式，从而生成建议的偏移消除多项式。这种基于变换的方法用于时间弧函数的分析和综合，时间弧函数是同时具有两个或多个值的时域多项式函数。使用提出的变换，还可以在测量中提取时间弧的淹没值。

设计/方法/方法

该方法涉及两步数学过程，其中生成拟议的多项式的加权修正导数的变换，然后与线性或斜坡函数相乘。该转换根据所考虑变量的类型在时域或空间域中进行拉伸，从而导致对诸如时间导数和相对速度之类的参数进行修改。

发现

在此修改的时域中对各种参数进行了详细分析，并给出了结果。另外，使用所提出的方法，还可以在测量中提取任何时间弧函数的淹没值，从而揭示时间弧。

实际影响

还针对具有运算放大器的基于时间的产生电弧的平方根电路提出了一个典型的实施研究结果，该电路用于提取函数的淹没值。

创意/价值

所提出的基于变换的方法在提取浸没在常规实验测量中的时间弧函数的值方面具有主要应用，从而提供了一种新的方法来解开此类特殊函数。