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