Time domain characteristics of rational systems with scale-invariant frequency response

G. Maskarinec, B. Onaral
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引用次数: 8

Abstract

The class of rational systems characterized by a magnitude response which is scale invariant for a specific scale change, or equivalently γ-homogeneous rational systems, are useful in modeling power-law processes. Such systems can be constructed by cascading frequency-scaled replicas of a prototype rational function which satisfies certain conditions. In this communication, we study the time domain characteristics of such systems. We show that, in the case of degree-1 or degree-2 prototypes, the magnitudes of the partial fraction expansion coefficients constitute a geometric sequence. Furthermore, in the degree-2 case, the angles of the partial fraction expansion coefficients are equal. Using these properties, we demonstrate that the impulse response of a e, γ-homogeneous rational system is essentially a linear combination of dilations of a prototype waveform and therefore exhibits a wavelet-like decomposition.
具有标度不变频率响应的有理系统的时域特性
一类有理系统,其特征是对特定的尺度变化具有尺度不变的幅度响应,或者等效的γ-齐次有理系统,在幂律过程的建模中很有用。这种系统可以通过满足一定条件的原型有理函数的级联频率缩放副本来构建。在本文中,我们研究了这类系统的时域特性。我们证明,在1次或2次原型的情况下,部分分式展开系数的大小构成一个几何序列。此外,在二阶情况下,部分分式展开系数的角度相等。利用这些性质,我们证明了e, γ-齐次有理系统的脉冲响应本质上是原型波形膨胀的线性组合,因此表现出小波样分解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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