Signal separation with almost periodic components: a wavelets based method

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.