Comparison between Windowed FFT and Hilbert-Huang Transform for Analyzing Time Series with.pdfVIP

Comparison between Windowed FFT and Hilbert-Huang Transform for Analyzing Time Series with.pdf

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Comparison between Windowed FFT and Hilbert-Huang Transform for Analyzing Time Series with

a r X i v : a s t r o - p h / 0 6 0 9 0 1 2 v 1 1 S e p 2 0 0 6 Comparison between Windowed FFT and Hilbert-Huang Transform for Analyzing Time Series with Poissonian Fluctuations: A Case Study Dong Han1 and Shuang-Nan Zhang2, 3 ABSTRACT Hilbert-Huang Transform (HHT) is a novel data analysis technique for non- linear and non-stationary data. We present a time-frequency analysis of both simulated light curves and an X-ray burst from the X-ray burster 4U 1702-429 with both the HHT and the Windowed Fast Fourier Transform (WFFT) meth- ods. Our results show that the HHT method has failed in all cases for light curves with Poissonian fluctuations which are typical for all photon counting in- struments used in astronomy, whereas the WFFT method can sensitively detect the periodic signals in the presence of Poissonian fluctuations; the only draw- back of the WFFT method is that it cannot detect sharp frequency variations accurately. Subject headings: —methods: data analysis—stars: oscillations (including pulsations)— X-rays: bursts 1. INTRODUCTION In X-ray binaries, matter flows onto the neutron star or black hole through an accretion disk and X-rays are emitted by the accretion flow from inner regions that host the strongest gravitational fields in the Universe. The space time characteristics of the X-ray emitting regions lead to the conclusion that the dynamical time scale for the accretion process of X-ray emitting is millisecond. That means, the millisecond X-ray variability is caused by 1Department of Engineering Physics Center for Astrophysics, Tsinghua University, Beijing 100084; handong@mail.tsinghua.edu.cn 2Department of Physics Center for Astrophysics, Tsinghua University, Beijing 100084; zhangsn@mail.tsinghua.edu.cn 3Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049 – 2 – orbital motion, neutron-star spin, disk- and neutron-star oscillations. So the millisecond X- ray variabilities are imp

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