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Orthogonal rational functions: A transformation analysis
KTH, Superseded Departments, Signals, Sensors and Systems.ORCID iD: 0000-0002-1927-1690
2003 (English)In: SIAM Review, ISSN 0036-1445, E-ISSN 1095-7200, Vol. 45, no 4, 689-705 p.Article in journal (Refereed) Published
Abstract [en]

Finite impulse response (FIR) models are among the most basic tools in control theory and signal processing and are routinely used in almost all fields of application. The connections to orthogonal polynomials are well known. However, infinite impulse response (IIR) models often provide much more compact descriptions and in many cases give improved performance. The objective of this paper is to present a simple framework for the derivation and analysis of orthogonal IIR transfer functions, which are directly related to orthogonal rational functions. Orthogonality simplifies approximation analysis and leads to improved numerical properties. The basic idea is to use a fractional transformation to map the problem to a new domain, where an FIR description is most appropriate. This FIR representation is then mapped back to the original domain to give an orthogonal IIR representation. It is then straightforward to extend many results for FIR. models to IIR model structures with arbitrary stable poles; i.e., properties of orthogonal polynomials are easily generalized to orthogonal rational functions. Much of the theory to be presented is classical, e.g., Laguerre and Kautz functions, and we will make use of well-known results in orthogonal filter theory. However, our main contribution is to present a uniform and transparent theory which also covers more novel results that have mainly been presented in the signals, systems, and control literature in the last decade.

Place, publisher, year, edition, pages
2003. Vol. 45, no 4, 689-705 p.
Keyword [en]
orthogonal rational functions, transfer functions, orthogonal matrices, Laguerre functions, state space theory, all-pass transfer functions, generalized orthonormal basis, system-identification, laguerre, models
National Category
Control Engineering
URN: urn:nbn:se:kth:diva-23008DOI: 10.1137/s0036144500376637ISI: 000187039200002OAI: diva2:341706
QC 20100525 QC 20120104Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2013-09-05Bibliographically approved

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