Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://revistas.ucr.ac.cr/index.php/matematica/oai
Time-frequency methods based on the Wavelet transform
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Keywords

time-frequency representations
wavelet transform
multiresolution analysis
wavelet packets
instantaneous frequency
representaciones tiempo-frecuencia
transformada wavelet
análisis de multirresolución
paquetes de wavelets
frecuencia instantánea

How to Cite

Serrano, E. P., Fabio, M., & Figliola, A. (2012). Time-frequency methods based on the Wavelet transform. Revista De Matemática: Teoría Y Aplicaciones, 19(2), 157–168. https://doi.org/10.15517/rmta.v19i2.1331

Abstract

The information contained in an analog signal is reveled by its numerical representation. The Fourier pair, in two complementary representations, expounds time and frequency structures. However, to detect and characterize those events which combine both structures in diverse and complex patterns, it is necessary to implement more refined methods joint with appropriate time-frequency representations.

Among various options, the wavelet transform provides an efficient tool time-scale. Their extensions lead to appropriate representations coexisting in the same analytical context. Make it possible implement flexible strategies, well adapted to the characteristics of the signal.

 

https://doi.org/10.15517/rmta.v19i2.1331
PDF (Español (España))

References

Cohen, L. (1995) Time-Frequency Analysis. Prentice Hall Signal Processing Series, New Jersey.

Jaffard, S.; Meyer, Y.; Ryan, R. (2003) Wavelets: Tools for Science and Tecnology. SIAM, Philadelphia.

Gröehenig, K. (2001) Foundations of Time-Frequency Analysis. Birkhäuser, Boston.

Huang N.E. et al. (1998) “The empirical mode decomposition and the Hilbert spectrum for non-stationary tyme series analysis”, Proc. R. Soc. A, Mathematical, Physical & Engineering Sciences 454(1971): 903–995.

Mallat, S. (2009) A Wavelet Tour of Signal Processing, The Sparse Way. Academic Press, San Diego.

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

Serrano, E.; Figliola A.; Fabio, M. (2009) “Diseño de Marcos de Paquetes de Wavelets”, XIII RPIC Reunión de Trabajo en Procesamiento de la Información y Control, 16–18 Sep 2009, Rosario, Argentina.

Serrano, E.; Aragón, A. (2009) “Métodos numéricos basados en onditas para el cálculo de la Transformada de Hilbert”, XIII RPIC Reunión de Trabajo en Procesamiento de la Información y Control, 16–18 Sep 2009, Rosario, Argentina.

Walnut, D.F. (2003) An Introduction to Wavelet Analysis. Birkhäuser, Boston.

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