Laguerre and Kautz Models

Abstract

The decomposition of signals and systems into appropriate basis components is a central problem in many fields of engineering and science. It would be an overwhelming task to give a general survey on modeling using general orthonormal basis functions. Since the impulse response of a stable finite dimensional linear system can be represented by a sum of exponentials (times polynomials), it seems reasonable to use basis functions of the same type. This leads to what we here will refer to as Kautz functions, which are the Laplace transforms of a class of orthogonalized exponentials. The well-known Laguerre functions are a special case of Kautz functions. In particular, we will discuss the following topics: Optimal basis functions given certain a priori information about the system; Properties and construction of orthonormal basis functions for approximation of dynamical systems; Use of orthonormal basis functions in system identification.