Abstract
In this paper, we define a new class of almost orthogonal polynomials which can be used successfully for modelling of electronic systems which generate orthonormal basis. Especially, for the classical weight function, they can be considered like a generalization of the classical orthogonal polynomials (Legendre, Laguerre, Hermite, ...). They are very suitable for analysis and synthesis of imperfect technical systems which are projected to generate orthogonal polynomials, but in the reality generate almost orthogonal polynomials.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
MacInnes, C.S.: The Reconstruction of Discontinuous Piecewise Polynomial Signals. IEEE Transactions on Signal Processing 53(7), 2603–2607 (2005)
Karam, L.J., McClellan, J.H.: Complex Chebyshev Approximation for FIR Filter Design. IEEE Transactions on Circuits-II: Analog and Digital Signal Processing 42(3), 207–216 (1995)
Nie, X., Raghuramireddy, D., Unbehauen, R.: Orthonormal Expansion of Stable Rational Transfer Functions. Electronics Letters 27(16), 1492–1494 (1991)
Tseng, C.C.: Digital Differentiator Design Using Fractional Delay Filter and Limit Computation. IEEE Transactions on Circuits and Systems-4, Regular Papers 52(10), 2248–2259 (2005)
Benyi, A., Torres, R.H.: Almost Orthogonality and a Class of Bounded Bilinear Pseudodifferential Operators. Mathematical Research Letters 11, 1–11 (2004)
Ben-Yaacov, I., Wagner, F.O.: On Almost Orthogonality in Simple Theories. J. Symbolic Logic 69(2), 398–408 (2004)
Cotlar, M.: A Combinatorial Inequality and Its Applications to L 2-Spaces. Rev. Mat. Cuyana 1, 41–55 (1955)
Szegő, G.: Orthogonal Polynomials, 4th edn., vol. 23. Amer. Math. Soc. Colloq. Publ. (1975)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Danković, B., Rajković, P., Marinković, S. (2009). On a Class of Almost Orthogonal Polynomials. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-00464-3_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00463-6
Online ISBN: 978-3-642-00464-3
eBook Packages: Computer ScienceComputer Science (R0)