Orthogonal Polynomials – Development and Design

XVII International Conference on Systems, Automatic Control and Measurements, SAUM 2024 (pp. 104-111)

АУТОР(И) / AUTHOR(S): Nikola Danković , Saša S. Nikolić , Dragan Antić , Miodrag Spasić , Petar Đekić

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DOI:  10.46793/SAUM24.104D

САЖЕТАК / ABSTRACT:

This paper gives some previously obtain results and contributions achieved in last fifteenth years on the topic of theory of orthogonal polynomials, i.e., orthogonal filters. This theory is based on new definitions and specific generalizations of orthogonal functions and polynomials, derived directly in complex domain. The main subject of this paper will be the possibility of some new applications of orthogonal polynomials in identification, modelling, signal processing and control of dynamical systems. Accordingly, the paper is divided into six sections. All chapters begin with a short mathematical background. In this paper we give some main results for classical, almost, improved almost, quasi-, generalized, and digital orthogonal polynomials.

КЉУЧНЕ РЕЧИ / KEYWORDS:

orthogonal polynomials, almost orthogonal polynomials, quasi-orthogonal polynomials, discrete orthogonal polynomials, generalized orthogonal polynomials, Legendre type polynomials

ПРОЈЕКАТ / ACKNOWLEDGEMENT:

This work was supported by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia [grant number 451-03-66/2024-03/200102].

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