{"title":"Time domain characteristics of rational systems with scale-invariant frequency response","authors":"G. Maskarinec, B. Onaral","doi":"10.1109/81.502209","DOIUrl":null,"url":null,"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.","PeriodicalId":104733,"journal":{"name":"IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications","volume":"66 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1996-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/81.502209","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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.