Spectral Kurtosis statistics of transient signals

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Abstract

We obtain analytical approximations for the expectation and variance of the Spectral Kurtosis estimator in the case of Gaussian and coherent transient time domain signals mixed with a quasi-stationary Gaussian background, which are suitable for practical estimations of their signal-to-noise ratio and duty-cycle relative to the instrumental integration time. We validate these analytical approximations by means of numerical simulations and demonstrate that such estimates are affected by statistical uncertainties that, for a suitable choice of the integration time, may not exceed a few per cent. Based on these analytical results, we suggest a multiscale Spectral Kurtosis spectrometer design optimized for real-time detection of transient signals, automatic discrimination based on their statistical signature, and measurement of their properties.

Original languageEnglish (US)
Pages (from-to)2530-2540
Number of pages11
JournalMonthly Notices of the Royal Astronomical Society
Volume458
Issue number3
DOIs
StatePublished - Mar 8 2016

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science

Keywords

  • Instrumentation: Spectrographs
  • Methods: Statistical

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