Comparisons between two wavelet functions in extracting coherent structures from solar wind time series

Abstract

Nowadays, wavelet analysis of turbulent flows have become increasingly popular. However, the study of geometric characteristics from wavelet functions is still poorly explored. In this work we compare the performance of two wavelet functions in extracting the coherent structures from solar wind velocity time series. The data series are from years 1996 to 2002 (except 1998 and 1999). The wavelet algorithm decomposes the annual time-series in two components: the coherent part and non-coherent one, using the daubechies-4 and haar wavelet function. The threshold assumed is based on a percentage of maximum variance found in each dyadic scale. After the extracting procedure, we applied the power spectral density on the original time series and coherent time series to obtain spectral indices. The results from spectral indices show higher values for the coherent part obtained by daubechies-4 than those obtained by the haar wavelet function. Using the kurtosis statistical parameter, on coherent and non-coherent time series, it was possible to conjecture that the differences found between two wavelet functions may be associated with their geometric forms.

Global geomagnetic responses to the IMF <i>B</i><sub>z</sub> fluctuations during the September/October 2003 high-speed stream intervals

“…First, we use the WT to remove the long-term trend from the time series, and second, we use the WT to perform the cross-wavelet spectrum (XWS) analysis between two time series. For more details of the first approach, see Bolzan et al (2009). For the second approach the following must be valid: if X(t) and Y (t) are time series and if W X (a, b), W Y (a, b) are their WT, the XWS analysis (Torrence and Compo, 1998;Bolzan and Vieira, 2006) is given by…”

“…Indeed, different wavelet functions cause different behavior on the white noise and red noise present in different time series. Bolzan et al (2009), using two kinds of wavelet function in order to extract the CSs, have shown that each wavelet has a different performance due to its mathematical shape. Thus it is possible to assess how different wavelet functions when applied to the same observation data, and taking into account the noise, may lead to different results.…”

Influence of a new discrete‐time LQR‐based motion cueing on driving simulator

“…Multi-sensory interaction in dynamic driving simulator. Equation (27) calculates the total sensed roll jerk at cabin (vehicle) level. This level signifies the vehicle dynamics model that moves in the visual environment during the simulator drive experiments.…”

“…The wavelet transform is used as a mathematical instrument in order to analyze any non-stationary time series, showing the temporal variability of the PSD [27].…”

Multifractal analysis of interplanetary magnetic field obtained during CME events

“…However, considering a common physical process, its statistical characteristics related to the pattern of variability should not vary significantly. Moreover, we consider the present analysis a complementary one of those events with which we had earlier work (Bolzan et al, 2005a(Bolzan et al, , 2009bSahai et al, 2005).…”