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Matematicheskie Zametki, 2008, Volume 84, Issue 5, Pages 732–740
DOI: https://doi.org/10.4213/mzm4002 (Mi mzm4002) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Meyer Wavelets with Least Uncertainty Constant

E. A. Lebedevaa, V. Yu. Protasovb

a Kursk State University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (538 kB) Citations (9)
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DOI: https://doi.org/10.4213/mzm4002
Abstract: In the present paper, we construct a system of Meyer wavelets with least possible uncertainty constant. The uncertainty constant minimization problem is reduced to a convex variational problem whose solution satisfies a second-order nonlinear differential equation. Solving this equation numerically, we obtain the desired system of wavelets.
Keywords: Meyer wavelet, uncertainty constant, variational problem, second-order nonlinear differential equation, Sobolev space, Fourier transform.
Received: 28.08.2007
English version:
Mathematical Notes, 2008, Volume 84, Issue 5, Pages 680–687
DOI: https://doi.org/10.1134/S0001434608110096
Bibliographic databases:
UDC: 517.518.36+517.972.9
Language: Russian
Citation: E. A. Lebedeva, V. Yu. Protasov, “Meyer Wavelets with Least Uncertainty Constant”, Mat. Zametki, 84:5 (2008), 732–740; Math. Notes, 84:5 (2008), 680–687
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    1. E. A. Kiselev, L. A. Minin, I. Ya. Novikov, S. N. Ushakov, “Localization of the window functions of dual and tight Gabor frames generated by the Gaussian function”, Sb. Math., 215:3 (2024), 364–382  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Alkan S., Aydin M.N., Coban R., “A Numerical Approach to Solve the Model of An Electromechanical System”, Math. Meth. Appl. Sci., 42:16, SI (2019), 5266–5273  crossref  mathscinet  isi
    3. Iglewska-Nowak I., “Uncertainty Product of the Spherical Gauss-Weierstrass Wavelet”, Int. J. Wavelets Multiresolut. Inf. Process., 16:4 (2018), 1850030  crossref  mathscinet  zmath  isi  scopus
    4. Lebedeva E.A., Prestin J., “Periodic Wavelet Frames and Time Frequency Localization”, Appl. Comput. Harmon. Anal., 37:2 (2014), 347–359  crossref  mathscinet  zmath  isi  scopus
    5. Power Systems Signal Processing For Smart Grids, 2013, 383  crossref
    6. Fufeng Miao, Xisheng Tang, Zhiping Qi, IEEE PES Innovative Smart Grid Technologies, 2012, 1  crossref
    7. Abdollahi A., Cheshmavar J., Taghavi M., “Wavelets generated by the Rudin-Shapiro polynomials”, Cent. Eur. J. Math., 9:2 (2011), 441–448  crossref  mathscinet  zmath  isi  elib  scopus
    8. E. A. Lebedeva, “On the uncertainty principle for Meyer wavelets”, J. Math. Sci. (N. Y.), 182:5 (2012), 656–662  mathnet  crossref
    9. Frunt J., Kling W.L., Ribeiro P.F., “Wavelet Decomposition for Power Balancing Analysis”, IEEE Trans. Power Deliv., 26:3 (2011), 1608–1614  crossref  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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