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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.22 n.1 San José Jan./Jun. 2015

 

Wavelets infinitamente oscilantes y un eficiente algoritmo de implementación basado en la FFT

Infinitely oscillating wavelets and a efficient implementation algorithm based on the FFT

Marcela Fabio*+ Eduardo P. Serrano*

Resumen

En este trabajo presentamos el diseño de una wavelet ortogonal, infinitamente oscilante, localizada en el tiempo con decaimiento 1=jtjn y de banda limitada. Su aplicación conduce a la descomposición de señales en ondas de frecuencia instantánea bien definida. Presentamos además el algoritmo de implementación para el análisis y síntesis basado en la Transformada Rápida de Fourier con la misma complejidad que el algoritmo de Mallat.

Palabras clave: wavelet tipo pasa-banda; algoritmo de Mallat; FFT; análisis de multirresolución; frecuencia instantánea.

Abstract

In this work we present the design of an orthogonal wavelet, infinitely oscillating, located in time with decay 1=jtjn and limited-band. Its application leads to the signal decomposition in waves of instantaneous, well defined frequency. We also present the implementation algorithm for the
analysis and synthesis based on the Fast Fourier Transform (FFT) with the same complexity as Mallat’s algorithm.

Keywords: pass-band wavelet; Mallat’s algorithm; FFT; multiresolution analysis; instantaneous frequency.

Mathematics Subject Classification: 42C40, 44A05.



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Referencias

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[4] Li, L.C. (2010) “A new method of wavelet transform based on FFT for signal processing”, Second WRI Global Congres on Intelligent Systems, IEEE Computer Society: 203–206.         [ Links ]

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[7] Meyer, Y. (2001) Oscillating Pattern in Image Processing and Nonlinear Evolution Equations. American Mathematical Society, Providence RI.         [ Links ]

[8] Serrano, E.; Figliola, A. (2008) Littlewood-Paley spline wavelets: a simple and efficient tool for signal and image processing in industrial applications, Proceedings in Applied Mathematics and Mechanics (PAMM), Wiley InterScience, 7: 1040313–1040314.         [ Links ]

[9] Serrano, E.; Fabio, M. (2010) “Diseño de funciones elementales combinando la transformada wavelet y la transformada de Hilbert”, UMA 2010, Tandil, Argentina.         [ Links ]

[10] Serrano, E.; Fabio, M.; Aragón, A. (2011) “Caracterización de la frecuencia instantánea en señales tipo pasa-banda”, III MACI, Asociación Argentina de Matemática Aplicada, Computacional e Industrial. Bahía Blanca, Argentina.         [ Links ]

*Centro de Matemática Aplicada, Universidad de San Martín, Argentina. E-Mail: mfabio@unsam.edu.ar
Centro de Matemática Aplicada, Universidad de San Martín y Escuela Superior Técnica del Ejército “General Manuel N. Savio”, I.E.S.E., Argentina. E-Mail: eserrano@unsam.edu.ar

Received: 5/Mar/2012; Revised: 3/Sep/2014; Accepted: 17/Oct/2014

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