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Self-Similar Rational Models for Power-Law Processes
Journal article

Self-Similar Rational Models for Power-Law Processes

Gregory J. Maskarinec and Banu Onaral
IFAC Proceedings Volumes, v 27(1)
Mar 1994

Abstract

In this extended abstract, we provide a brief summary of our approach to rational modeling of power-law processes. Many natural phenomena are characterized by spectral attenuation following a power-law form. We recognize such power-law behavior as a manifestation of the scale-invariant properties of the underlying physical or physiological processes. To construct rational models which capture this property, we have introduced the concept of self-similar rational systems and formalized the notion of scale-invariance for a specific scale change by defining the γ-homogeneity principle [18, 19]. Self-similar rational systems consist of a cascade of frequency scaled replicas of a prototype rational function F(s). γ-homogeneous rational systems, which constitute a special class of self-similar rational systems, are characterized by a frequency response which is scale-invariant for a specific scale change. In this presentation, we focus on the construction of γ-homogeneous rational system functions. We also list the γ-homogeneous properties of the frequency response, the time response and the residue distributions for the particular case of degree-1 and degree-2 F(s). Proofs and technical details which have appeared in our earlier publications are not included.

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