PROGRAM WWZ: WAVELET ANALYSIS OF ASTRONOMICAL SIGNALS WITH IRREGULARLY SPACED ARGUMENTS

Abstract

ABSTRACT. A program WWZ is introduced, which real-izes the wavelet analysis using an improved modification of the algorithm of the Morlet wavelet for a general case of ir-regularly spaced data, which is typical for the databases available in virtual observatories. Contrary to the well-known analogs, working with regularly spaced (equidistant in time) arguments, we have implemented an improved algorithm presented by Andronov, (1998KFNT...14..490A, 1999sss..conf...57A), which significantly increases the sig-nal-to-noise ratio. The program has been used to study semi-regular pulsating variable stars (U Del et al.), but can be used for the analysis of signals of any nature. Key words: variable stars, and cyclic os-cillations, long-period pulsating variables, data analysis, wavelet analysis, U Del. One of the main directions of modern astrophysics is the study of variable stars. Specificity of astronomical observation is that in many cases the times at which the observation are obtained, are irregularly spaced. This is characteristic to collections of photographic negatives Sky Patrol, available in a variety of observatories, as well as to more modern CCD sky surveys. Such observa-tions are sometimes available through the Internet and included in national and international projects Observatory. In Ukraine there are programs VIRGO ( Virtual X-ray and gamma-ray observatory) and UkrVO ( Ukrainian Virtual Observatory (Vavilova et al. 2012)). Wavelet analysis is a method of investigating changes in the period of signals that are not strong periodic, but it is has sense to introduce “instantaneous” values of the “period” or “cycle length”. In astronomy, such signals are called quasi-periodic oscillations (QPO) and are com-mon to many types of variable stars - low-mass X-ray binaries, cataclysmic and symbiotic systems, semi-regular pulsating stars etc. Mathematical foundations of the theory of wavelets are presented e.g. in the monographs by Daubechies (1992) and Vitjazev (2001) and reviews (e.g. Astafieva 1996). For the time series analysis, often is used the Morlet wavelet, which is based on a combination of the Fourier transform with the weight function being proportional to the Gaussian function. This conversion is included in the popular software, e.g. MatLab, SciLab. This algorithm allows to analyze only the signals, which are equally spaced in time, i.e. t