Additional constraints to ensure three vanishing moments for orthonormal wavelet filter banks and transient detection

Authors

  • Julio Cezar Uzinski Department of Electrical Engineering - FEIS, Universidade Estadual Paulista - UNESP
  • Henrique Mohallem Paiva Mectron - Organização Odebrecht
  • Francisco Villarreal Department of Mathematics - FEIS, UNESP - Universidade Estadual Paulista
  • Marco Aparecido Queiroz Duarte Department of Mathematics - UEMS, Universidade Estadual de Mato Grosso do Sul
  • Roberto Kawakami Harrop Galvão Department of Electronic Engineering - ITA

DOI:

https://doi.org/10.5540/tema.2015.016.01.0017

Abstract

This article presents an improvement to the formulation of Sherlock and Monro for the wavelet parameterization for the obtainment of the restrictions which ensure three vanishing moments. In order to test the formulation presented, a transient signal detection is presented.

References

I. Daubechies, "Ten Lectures on Wavelets''. Philadelphia, PA: SIAM, 1992.

T. Froese, S. Hadjiloucas, R.K.H. Galvão, V.M. Becerra, C.J. Coelho, Comparison of extrasystolic ECG signal classifiers using discrete wavelet transforms, Pattern Recognit. Lett., vol. 27, pp. 393-407, Apr. 2006.

R.K.H. Galvão, G.E. José, H.A.D. Filho, M.C.U. Araujo, E.C. Silva, H.M. Paiva, T.C.B. Saldanha, E.S.O.N. Souza, Optimal wavelet filter construction using X and Y data, Chemometrics and Intelligent Laboratory Systems, Volume 70, pp. 1-10, Jan. 2004

S. Mallat, "A Wavelet Tour of Signal Processing''. San Diego, EUA: Academic Press, 1998.

H.M. Paiva, M.N. Martins, R.K.H. Galvao, J. Paiva, On the space of orthonormal wavelets: additional constraints to ensure two vanishing moments, Signal Processing Letters, IEEE , vol.16, no.2, pp.101-104, Feb. 2009.

J. P. L. M. Paiva, C.A. Kelencz, H.M. Paiva, R.K.H. Galvão, M. Magini, Adaptive wavelet EMG compression based on local optimization of filter banks, Physiological Measurement, vol. 29, pp. 843-856, 2008.

B.G. Sherlock, D.M. Monro, On the space of orthonormal wavelets, Signal Processing, IEEE Transactions on, vol.46, no.6, pp.1716-1720, Jun 1998.

J. C. Uzinski, H. M. Paiva, F. Villarreal, M.A.Q. Duarte, R.K.H. Galvão, Additional constraints to ensure three vanishing moments for orthonormal wavelet filter banks, Congresso de matemática aplicada e computacional - Centro-Oeste, Cuiabá - MT, Jul 2013.

P.P. Vaidyanathan, "Multirate Systems and Filter Banks''. Englewood Cliffs, NJ: Prentice-Hall, 1993.

H. Zou, A.H. Tewfik, Parametrization of compactly supported orthonormal wavelets, Signal Processing, IEEE Transactions on , vol.41, no.3, pp.1428-1431, Mar 1993.

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Published

2015-05-29

How to Cite

Uzinski, J. C., Paiva, H. M., Villarreal, F., Duarte, M. A. Q., & Galvão, R. K. H. (2015). Additional constraints to ensure three vanishing moments for orthonormal wavelet filter banks and transient detection. Trends in Computational and Applied Mathematics, 16(1), 17–29. https://doi.org/10.5540/tema.2015.016.01.0017

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Original Article