Signal separation with almost periodic components: a wavelets based method
O.A. Rossoa, A. Figliolaa, S. Blancoa, and P.M. Jacovkisa,b
a Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón II, Ciudad Universitaria, 1428 Buenos Aires, Argentina, e-mail: rosso@ic.fcen.uba.ar, rosso@ba.net.
b Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, 1428 Buenos Aires, Argentina.
]]> Recibido el 28 de mayo de 2003.
Abstract
Natural time series usually show either a combination of periodic phenomena with stochastic components or chaotic behavior. In many cases, when nonlinear characteristics are computed, they will essentially indicate the most remarkable effects and the results will underestimate or overestimate the real complexity of the system. For that reason signal separation of the frequency bands representing well known phenomena, like periodic or almost periodic behaviors, allows comprehension of the hidden nonlinear or stochastic phenomena involved. In this work a signal separation method based on trigonometric wavelet packets is described. The method has been applied, as an example, to a time series of daily mean discharges of the Atuel river in Argentina, that presents strong annual and semiannual oscillations due to meteorological effects. The correlation dimension and the maximum Lyapunov exponent of the residual time series were obtained taking away its known almost periodic components.
Keywords: Time-frequency signal analysis; wavelet analysis; signal separation; meteorological time series.
Resumen
Las series de tiempo representan una combinación de fenómenos periódicos y componentes estocásticas o comportamiento caótico. En muchos casos, cuando se computan cuantificadores no lineales para dichas series temporales, es de desear que éstos resalten las características más notables de las mismas y que sus resultados no subvaloren o sobrestimen la complejidad real del sistema. Por esa razón, la separación de bandas de frecuencia que representan fenómenos bien conocidos, tales como el caso de comportamientos periódicos o cuasi-periódicos, permite la comprensión de fenómenos no-lineales y/o fenómenos estocásticos ocultos involucrados en la ge/-neración de dichas series temporales. En este trabajo un método de separación de señales basado en paquetes wavelet trigonométricos es descrito. El método ha sido aplicado, como un ejemplo, a una serie temporal de descargas media diarias del río de Atuel en Argentina. Esta serie temporal presenta una fuerte oscilación anual y semestral debido a efectos meteorológicos. La dimensión de la correlación y el máximo exponente de Lyapunov correspondientes a la serie de tiempo residual fueron obtenidos luego de eliminar las componentes cuasi-periódicas conocidas.
Descriptores: Análisis de señales en tiempo-frecuencia; análisis de wavelets; separación de señales; series temporales meteorológicas.
]]>PACS: 05.45.Tp; 02.70.Hm; 92.40.Fb
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Acknowledgments
This work was partially supported by the Consejo Nacional de Investigaciones Científicas y Tecnicas (CONICET, Argentina) and by university of Buenos Aires grand I50. The authors wish to thank Dr. Rosa Compagnucci for useful comments and for providing the Atuel River records used in this work. The continuous support and stimulation of Prof. Dr. G.D. Pacal are gratefully acknowledged.
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