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A NONHARMONIC FOURIER SERIES AND DYADIC SUBDIVISION SCHEMES

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영남수학회 (Youngnam Mathematical Society)|2010.01|East Asian Mathematical Journal|제26권 제1호|pp. 105-113

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참고문헌

키워드

Fourier coefficientwavelet analysisnonharmonic Fourier series
주제분류수학

초록

In the spectral analysis, Fourier coefficients are very important to give informations for the original signal f on a finite domain, because they recover f. Also Fourier analysis has extension to wavelet analysis for the whole space R. Various kinds of reconstruction theorems are main subject to analyze signal function f in the field of wavelet analysis. In this paper, we will present a new reconstruction theorem of functions in L1(R) using a nonharmonic Fourier series. When we construct this series, we have used dyadic subdivision schemes.

Abstract

In the spectral analysis, Fourier coefficients are very important to give informations for the original signal f on a finite domain, because they recover f. Also Fourier analysis has extension to wavelet analysis for the whole space R. Various kinds of reconstruction theorems are main subject to analyze signal function f in the field of wavelet analysis. In this paper, we will present a new reconstruction theorem of functions in L1(R) using a nonharmonic Fourier series. When we construct this series, we have used dyadic subdivision schemes.

참고문헌 (8)

  1. C. K. Chui, "An introduction to wavelets" (1992), Academic Press
  2. Daubechies, I., "Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Ap-plied Mathematics, Vol. 61" (1992), Society for Industrial and Applied Mathematics
  3. Gerald B. Folland, "Real Analysis: Modern Techniques and Their Applications", pp.245~246 (1984), John Wiley & Sons
  4. Tom H. Koornwinder, "WAVELETS: An Elementary Treatment of Theory and Ap-plications, Series in Approximations and Decompositions-Vol.1" (1995), World Scientic
  5. S. Lang, "Analysis I, 6th printing", pp.231~234 (1978), Addition-Wesley Publishing Company
  6. Jae S. Lim, "Two Dimensional Signal and Image Processing" (1990), Prentice Hall
  7. Alan V. Oppenheim, "Signals & Systems" (1997), Prentice-Hall International, INC.
  8. Jungsoo Rhee, "Gibbs Phenomenon and certain nonharmonic Fourier series", Preprint

관련 논문AI추천

NEW LOOK AT THE CONSTRUCTIONS OF MULTIWAVELET FRAMES김래영, 김홍오, 임재근대한수학회 · 대한수학회보2010 · 제47권 제3호A NOTE ON THE PARAMETRIZATION OF MULTIWAVELETS OF CL TYPEI-P Kim, S. Y. Hwang장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2015 · 제18권 제1호Characterization of orthonormal high-order balanced multiwavelets in terms of moments권순걸대한수학회 · 대한수학회보2009 · 제46권 제1호A weighted Fourier series with signed good kernels임경수, Sony Chan대한수학회 · 대한수학회보2017 · 제54권 제3호Gibbs phenomenon and certain nonharmonic Fourier series이정수대한수학회 · 대한수학회논문집2011 · 제26권 제1호Riesz and Tight Wavelet Frame Sets in Locally Compact Abelian GroupsArvind Kumar Sinha, Radhakrushna Sahoo경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2021 · 제61권 제2호

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