Searching data for periodic signals.pdf

Searching data for periodic signals Andrzej Kr´olak1,2 1Max-Planck-Institute for Gravitational Physics, Albert-Einstein-Institute, Schlaatzweg 1, 14473 Postsdam, Germany. 2 ´ 8 Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, 00-950 War- 9 saw, Poland 9 1 r Abstract. We present two statistical tests for periodicities in the time series. We a M apply the two tests to the data taken from Glasgow prototype interferometer in March 1996. We find that the data contain several very narrow spectral features. We inves- 6 tigate whether these features can be confused with gravitational wave signals from 1 pulsars. 1 v 1 Introduction 5 5 0 The work presented here was motivated by an analysis of Gareth Jones [1] 3 of the data taken from Glasgow prototype in 1996. His visual inspection of 0 the periodogram of the data revealed presence of 3 very narrow (1 bin wide) 8 significant spectral features. 9 / c q 2 Statistical tests for periodicities in the data - r using the discrete Fourier transform g : v A standard method to search the time series for periodic signals is to perform i X the Fourier transform (FT) of the series and examine the modulus of FT for r significant values. Let xn be a real-valued discrete time random process given at