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Brazilian Journal of Physics

, Volume 47, Issue 2, pp 167–181 | Cite as

On the Effects of Gaps and Uses of Approximation Functions on the Time-Scale Signal Analysis: A Case Study Based on Space Geophysical Events

  • Luciano A. Magrini
  • Margarete O. Domingues
  • Odim Mendes
General and Applied Physics
  • 111 Downloads

Abstract

The presence of gaps is quite common in signals related to space science phenomena. Usually, this presence prevents the direct use of standard time-scale analysis because this analysis needs equally spaced data; it is affected by the time series borders (boundaries), and gaps can cause an increase of internal borders. Numerical approximations can be used to estimate the records whose entries are gaps. However, their use has limitations. In many practical cases, these approximations cannot faithfully reproduce the original signal behaviour. Alternatively, in this work, we compare an adapted wavelet technique (gaped wavelet transform), based on the continuous wavelet transform with Morlet wavelet analysing function, with two other standard approximation methods, namely, spline and Hermite cubic polynomials. This wavelet method does not require an approximation of the data on the gap positions, but it adapts the analysing wavelet function to deal with the gaps. To perform our comparisons, we use 120 magnetic field time series from a well-known space geophysical phenomena and we select and classify their gaps. Then, we analyse the influence of these methods in two time-scale tools. As conclusions, we observe that when the gaps are small (very few points sequentially missing), all the methods work well. However, with large gaps, the adapted wavelet method presents a better performance in the time-scale representation. Nevertheless, the cubic Hermite polynomial approximation is also an option when a reconstruction of the data is also needed, with the price of having a worse time-scale representation than the adapted wavelet method.

Keywords

Signals with gaps Adaptive wavelet Numeric approximations Data treatment Space Geophysics 

Notes

Acknowledgements

Authors acknowledge the support and grants received from CAPES, CNPq (grants: 306038/2015−3, and 312246/2013−7), FAPESP (grant 2015/25624−2), and FINEP. We also thank NASA for the data set — OmniWeb service (http://omniweb.gsfc.nasa.gov) —, and Prof. Peter Frick for the original version of the code used on this work and scientific discussions during his visits to INPE.

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Copyright information

© Sociedade Brasileira de Física 2017

Authors and Affiliations

  • Luciano A. Magrini
    • 1
  • Margarete O. Domingues
    • 2
  • Odim Mendes
    • 3
  1. 1.National Institute for Space Research (INPE), Associated Laboratory of Computation and Applied Mathematics (LAC), Graduation Program of Applied Computation (CAP)Instituto Federal de Educação, Ciência e Tecnologia de Sao Paulo.São José dos CamposBrazil
  2. 2.National Institute for Space Research (INPE)Associated Laboratory of Computation and Applied Mathematics (LAC)São José dos CamposBrazil
  3. 3.National Institute for Space Research (INPE)Space Geophysics Division (DGE)São José dos CamposBrazil

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