Abstract

A new method of interpolation/approximation of univariate functions using exponential polynomials, both complete and reduced, generally using complex polynomials, was suggested. The solution is based on the Z-transformation of one variable function, predetermined by a discrete set of equally spaced samples. For the first time, the problem was solved for dynamic systems with proper frequencies of any multiplicity. The method of transition from time functions to full, and shortened operator models of selective radioelectronic devices was represented. In addition, the transfer ratio, reduced by Z-transform, corresponds exactly to the basic approximation in the modified method of the truncated operator equations. Based on some examples including IFA of ninth order (with three poles, each of which having multiplicity factor three) on exposure to complex FM/PM input signal, the usage possibility of precise as well as shortened exponential and operator polynomials aimed to design radioelectronic systems which are sensitive to phase variation during the transition process, was proved.

中文翻译：

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一维函数的 Z 变换指数逼近：理论与应用

摘要

提出了一种使用指数多项式（完整的和约简的，通常使用复多项式）对单变量函数进行插值/逼近的新方法。该解决方案基于一个变量函数的 Z 变换，由一组离散的等距样本预先确定。对于具有任意多重性的适当频率的动态系统，该问题第一次得到解决。介绍了从时间函数过渡到完整和缩短的选择性无线电电子设备操作员模型的方法。此外，通过 Z 变换减小的传递率与截断算子方程的修改方法中的基本近似完全一致。基于一些示例，包括九阶 IFA（具有三个极点，