Extraction of a deterministic component from ROSAT X-ray data using a wavelet transform and the principal component analysis

In the present work wavelet transform meth ads together with principal comp onent analysis and non-linear filtering are used to extract the determinist ic components in AGN X-ray 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 compo nents correspond to different frequencies. In the present case different co mponents correspond tc, different wavelet coefficient magnitudes, being equ ivalent to spectral densities. In addition to the ampligram a time scale sp ectrum is defined, being a forward wavelet transform of each ron (wavelet c oefficient magnitude) in the ampligram. The time scale spectrum of the ampl igram tells us more than the original wavelet spectrum does. The time scale spectrum reveals individual signal components and indicates the statistica l properties of each component: deterministic or stochastic. The ampligram and its time scale spectrum seems to be a useful tool to study processes re sulting in a mixture of stochastic and deterministic components. In the cas e of X-ray luminosity variations in the AGN it is expected that the describ ed data analysis technique will provide a conclusive proof of the existence of building blocks. The efficient decomposition of the luminosity variatio n data may be used to study the deterministic, quasi-periodic phenomena, li ke 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 dat a and in this way to extract real deterministic luminosity variations. As i t is shown by simulations in the final part of this work, the method is cap able to extract weak, of the order of few percent, deterministic variations embedded in a totally Poisson-like series of events. There may be also oth er applications of the method in astrophysics, for example to study X-ray p ulsars.