任意阶算子的有理逼近——奇异标度方程

Rational approximation of arbitrary order operators-Strange scaling equations

摘要:

用连分式展开法和标度拓展理论得到两类新型非正则标度方程——奇异标度方程.探究奇异标度方程的有理函数序列在运算有效性、运算性能、运算振荡周期方面与以往分抗迭代方程的不同之处和优势之处.由复平面内的零极点分布证明了奇异标度方程是物理可实现的，并且总结了逼近性能，此方程为分抗逼近电路的实现与设计提出了一种新模型和新思路.由零极点与阶频特征的局域化特征，找出了任何物理可实现的非正则标度方程运算振荡现象产生的原因.

Abstract:

Two new types of irregular scaling equations-strange scaling equations are obtained by the continuous expansion method and scale expansion theory. This paper explores the differences and advantages of the rational function sequences of strange scaling equations in terms of computational effectiveness, computational performance, and operational oscillation period. It is proved by the zeropole distribution in the complex plane that the strange scale equations are physically achievable, and the approximation performance is summarized. These equations propose a new model and a new idea for the realization and design of the fractance approximation circuits. From the localized features of the zeropole and the frequency characteristics, the reason for the operational oscillation of any physically achievable irregular scaling equation is found.