A COMPREHENSIVE REVIEW OF ORTHOGONAL POLYNOMIALS AND FUNCTIONS WITH APPLICATION IN FILTER DESIGN

Le résumé fourni par la source

This paper presents some of the results and contributions to the theory of orthogonal polynomials, orthogonal functions and corresponding filters, achieved in the last fifteen years. This theory is based on new definitions and specific generalisations of orthogonal functions and polynomials derived directly in the complex domain. The main objective of this paper is to enable some new applications of orthogonal polynomials in the identification, modelling, signal processing and control of dynamical systems. Accordingly, the paper is divided into seven sections. All central chapters, which describe specific classes of orthogonal polynomials and functions, begin with a brief mathematical background and proposed forms for filter design. In this paper, we give some main results for classical, almost, improved almost, quasi-, generalised and their applications in filter design.

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