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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.