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2011 | 9 | 2 | 441-448

Tytuł artykułu

Wavelets generated by the Rudin-Shapiro polynomials

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Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
In this paper, we consider the well-known Rudin-Shapiro polynomials as a class of constant multiples of low-pass filters to construct a sequence of compactly supported wavelets.

Wydawca

Czasopismo

Rocznik

Tom

9

Numer

2

Strony

441-448

Opis fizyczny

Daty

wydano
2011-04-01
online
2011-02-18

Bibliografia

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  • [2] Billhart J., Lomont J.S., Morton P., Cyclotomic properties of the Rudin-Shapiro polynomials, J. Reine Angew. Math., 1976, 288, 37–65
  • [3] Butzer P.L., Fischer A., Rückforth K., Scaling functions and wavelets with vanishing moments, Comput. Math. Appl., 1994, 27(3), 33–39 http://dx.doi.org/10.1016/0898-1221(94)90044-2
  • [4] Byrnes J.S., Quadrature mirror filter, low crest factor arrays, functions achieving optimal uncertainty principle bounds, and complete orthonormal sequences - a unified approach, Appl. Comput. Harmon. Anal., 1994, 1(3), 261–266 http://dx.doi.org/10.1006/acha.1994.1013
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  • [6] Chui C.K., An Introduction to Wavelets, Wavelet Anal. Appl., 1, Academic Press, Boston, 1992
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  • [8] la Cour-Harbo A., On the Rudin-Shapiro transform, Appl. Comput. Harmon. Anal., 2008, 24(3), 310–328 http://dx.doi.org/10.1016/j.acha.2007.05.003
  • [9] Daubechies I., Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math., 1988, 41(7), 909–996 http://dx.doi.org/10.1002/cpa.3160410705
  • [10] Daubechies I., Ten Lectures on Wavelets, CBMS-NSF Regional Conf. Ser. in Appl. Math., 61, SIAM, Philadelphia, 1992
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  • [12] Haar A., Zur Theorie der orthogonalen Funktionensysteme, Math. Ann., 1910, 69(3), 331–371 http://dx.doi.org/10.1007/BF01456326
  • [13] Hernández E., Weiss G., A First Course on Wavelets, Stud. Adv. Math., CRC Press, Boca Raton, 1996
  • [14] Hong D., Wang J., Gardner R., Real Analysis with an Introduction to Wavelets and Applications, Elsevier Academic Press, Burlington-San Diego-London, 2005
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  • [16] Lebedeva E.A., Protasov V.Yu., Meyer wavelets with least uncertainty constant, Math. Notes, 2008, 84(5–6), 680–687 http://dx.doi.org/10.1134/S0001434608110096
  • [17] Li D.F., Peng S.L., Chen H.L., Local properties of periodic cardinal interpolatory wavelets, Acta Math. Sinica (Chinese Ser.), 2001, 44(5), 947–960
  • [18] Mallat S.G., Multiresolution approximations and wavelet orthonormal bases of L 2(ℝ), Trans. Amer. Math. Soc., 1989, 315(1), 69–87
  • [19] Meyer Y., Wavelets and Operators, Cambridge Stud. Adv. Math., 37, Cambridge University Press, Cambridge, 1992
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Bibliografia

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bwmeta1.element.doi-10_2478_s11533-010-0094-4
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