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Orthonormality in Interpolation Schemes for Reconstructing Signals

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Applications of Mathematics and Informatics in Military Science

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 71))

Abstract

Given only a few of initial Fourier coefficients for a continuous-time periodic signal, we construct efficient rational approximants to the whole signal everywhere on his domain of definition. The convergence of these approximants depends on the orthonormality of the chosen generating polynomial system {V m+1(eit) :m=0,1,…} into L 2[−π,π]. The form of each V m+1(x) is characterized by recurrence relations dues to the connection between Schur and Szegö theories.

Mathematics Subject Classification (2010): 41A20, 41A21, 42A16, 42C05, 65B99, 65D05, 65T40

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Authors and Affiliations

  1. Department of Military Science, Hellenic Army Academy, 166 73, Vari Attikis, Greece

    Nicholas J. Daras

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Correspondence to Nicholas J. Daras .

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  1. , Department of Military Science, Hellenic Military Academy, Vari Attikis, 166 73, Greece

    Nicholas J. Daras

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Daras, N.J. (2012). Orthonormality in Interpolation Schemes for Reconstructing Signals. In: Daras, N. (eds) Applications of Mathematics and Informatics in Military Science. Springer Optimization and Its Applications, vol 71. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4109-0_5

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