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Extraction of a Deterministic Component from ROSAT X-ray Data
Using a Wavelet Transform and the Principal Component Analysis:

Analysis of random pulses and simulated data.

Ludwik Liszka

Steward Observatory

University of Arizona

Tucson, AZ

USA

### Abstract

The main purpose of this part of the study is to
calibrate the method of separation of deterministic
variations of an event series from its Poisson
part. The method is used for search for deterministic
structures in computer-generated random number
sequences and also in the output of, what is believed,
unpredictable physical processes, like noise-diode
generated pulses or the radioactive beta-decay.
It has been found that a beta-decay generated event
series contains less deterministic structures than the
other tested. Four typical deterministic components
are then added to the beta-decay event series and the
ampligram and time scale spectrum (analysis tools
deless events to the total series, reflects clearly in the
ampligram and in the time scale spectrum. The second
part of the paper deals with simulation of photon flux
consisting of a random or deterministic sequence
of Poisson-like, decaying, elementary building
blocks. Again, a clear difference is found between
time scale spectra of photon series consisting of randomly
distributed building blocks and those consisting
of quasi-regular repetition of building blocks. Finally,
a technique is presented to remove the deterministic
or Poisson-like part of the event series. This
can be used to improve the beta-decay series, decreasing
the amplitude of the deterministic component by
a factor of ten, or to obtain wavelet spectra of pure
deterministic variations of the photon flux.

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