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


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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