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Annales Geophysicae An interactive open-access journal of the European Geosciences Union
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Volume 34, issue 4
Ann. Geophys., 34, 437-449, 2016
https://doi.org/10.5194/angeo-34-437-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Ann. Geophys., 34, 437-449, 2016
https://doi.org/10.5194/angeo-34-437-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Regular paper 19 Apr 2016

Regular paper | 19 Apr 2016

Effect of data gaps: comparison of different spectral analysis methods

Costel Munteanu1,2,3, Catalin Negrea1,4,5, Marius Echim1,6, and Kalevi Mursula2 Costel Munteanu et al.
  • 1Institute of Space Science, Magurele, Romania
  • 2Astronomy and Space Physics Research Unit, University of Oulu, Oulu, Finland
  • 3Department of Physics, University of Bucharest, Magurele, Romania
  • 4Cooperative Institute for Research in Environmental Sciences, Univ. of Colorado, Boulder, Colorado, USA
  • 5Space Weather Prediction Center, NOAA, Boulder, Colorado, USA
  • 6Belgian Institute of Space Aeronomy, Brussels, Belgium

Abstract. In this paper we investigate quantitatively the effect of data gaps for four methods of estimating the amplitude spectrum of a time series: fast Fourier transform (FFT), discrete Fourier transform (DFT), Z transform (ZTR) and the Lomb–Scargle algorithm (LST). We devise two tests: the single-large-gap test, which can probe the effect of a single data gap of varying size and the multiple-small-gaps test, used to study the effect of numerous small gaps of variable size distributed within the time series. The tests are applied on two data sets: a synthetic data set composed of a superposition of four sinusoidal modes, and one component of the magnetic field measured by the Venus Express (VEX) spacecraft in orbit around the planet Venus. For single data gaps, FFT and DFT give an amplitude monotonically decreasing with gap size. However, the shape of their amplitude spectrum remains unmodified even for a large data gap. On the other hand, ZTR and LST preserve the absolute level of amplitude but lead to greatly increased spectral noise for increasing gap size. For multiple small data gaps, DFT, ZTR and LST can, unlike FFT, find the correct amplitude of sinusoidal modes even for large data gap percentage. However, for in-situ data collected in a turbulent plasma environment, these three methods overestimate the high frequency part of the amplitude spectrum above a threshold depending on the maximum gap size, while FFT slightly underestimates it.

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We investigate the effect of data gaps for various methods of estimating the amplitude spectrum of a time series. We probe the effects of a single data gap of varying size and of numerous small gaps distributed within the time series. We use synthetic data sets and magnetic field measurements from the Venus Express spacecraft. For multiple gaps and turbulent magnetic data, we show that some advanced methods overestimate the high frequencies, while FFT slightly underestimates them.
We investigate the effect of data gaps for various methods of estimating the amplitude spectrum...
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