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Astron. Astrophys. Suppl. Ser. 140, 125134
Extraction of a deterministic component from ROSAT Xray data
using a wavelet transform and the principal component analysis
L. Liszka
^{1}
^{}

M. Holmström
^{2}
Send offprint request: L. Liszka, email: ludwik@irf.se
1  Steward Observatory,
University of Arizona,
Tucson, AZ,
U.S.A.
2 
Swedish Institute of Space Physics,
S981 28 Kiruna, Sweden
Received April 23; accepted August 23, 1999
Abstract:
In the present work wavelet transform methods together with principal
component analysis and nonlinear filtering are used to extract the
deterministic components in AGN Xray variability from the photon event
history files. The photon history files are converted into so called
ampligrams using the Morlet wavelet transform. The ampligram may be
considered as an analogy to signal decomposition into Fourier components.
In that case different components correspond to different frequencies.
In the present case different components correspond to different wavelet
coefficient magnitudes, being equivalent to spectral densities. In addition
to the ampligram a time scale spectrum is defined, being a forward wavelet
transform of each row (wavelet coefficient magnitude) in the ampligram.
The time scale spectrum of the ampligram tells us more than the original
wavelet spectrum does. The time scale spectrum reveals individual signal
components and indicates the statistical properties of each component:
deterministic or stochastic.
The ampligram and its time scale spectrum seems to be a useful tool to
study processes resulting in a mixture of stochastic and deterministic
components. In the case of Xray luminosity variations in the AGN it is
expected that the described data analysis technique will provide a conclusive
proof of the existence of building blocks. The efficient decomposition of the
luminosity variation data may be used to study the deterministic,
quasiperiodic phenomena, like tones and chirps. The most important point of
the method is that it may be used to remove the influence of the Poisson
statistics in the photon data and in this way to extract real deterministic
luminosity variations. As it is shown by simulations in the final part of this
work, the method is capable to extract weak, of the order of few percent,
deterministic variations embedded in a totally Poissonlike series of events.
There may be also other applications of the method in astrophysics, for example
to study Xray pulsars.
Key words: methods: data analysis 
pulsars: individual 1E2259+586 
galaxies: individual NGC 4051; NGC 5548 
galaxies: Seyfert 
Xrays: galaxies
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