Related papers: Multi-harmonic and special shape/pattern/template …
Astronomical data are typically irregular in time, e.g. the space (HIPPARCOS/TYCHO, KEPLER, GAIA, WISE etc.) and ground-based CCD (NSVS, ASAS, CRTS, SuperWASP etc.) and photographic (Harvard, Sonneberg, Odessa etc.) photometrical surveys.…
The software MAVKA is described, which was elaborated for statistically optimal determination of the characteristics of the extrema of 1000+ variable stars of different types, mainly eclipsing and pulsating. The approximations are…
We discuss different methods for phenomenological approximations of signals with (generally) irregularly spaced arguments. Such signals may be classified as periodic, multi-periodic, quasi-periodic (cyclic), burst-type and flicker-type (see…
We introduce the program MAVKA for determination of characteristics of extrema using observations in the adjacent data intervals, with intended applications to variable stars, but it may be used for signals of arbitrary nature. We have used…
In this review, we present some advanced algorithms and programs used in our scientific school with short description of types of astrophysical systems, which we study. However, we discuss mainly mathematical methods, which may be applied…
We address the problem of assessing the statistical significance of candidate periodicities found using the so-called `multi-harmonic' periodogram, which is being used for detection of non-sinusoidal signals, and is based on the…
We develop new elements of harmonic analysis on the complex sphere on the basis of which Bernstein's, Jackson's and Kolmogorov's inequalities are established. We apply these results to get order sharp estimates of $m$-term approximations.…
Advanced MAVKA software for the approximation of extrema observations is used to analyze the variability of the brightness of pulsating and eclipsing stars, but may be useful in analyzing signals of any nature. A new algorithm using a…
Clustering objects into synthetic groups is a natural activity of any science. Astrophysics is not an exception and is now facing a deluge of data. For galaxies, the one-century old Hubble classification and the Hubble tuning fork are still…
With their ability to handle an increased amount of information, multivariate and multichannel signals can be used to solve problems normally not solvable with signals obtained from a single source. One such problem is the decomposition…
We present a harmonic model for the data analysis of an all-sky cosmic microwave background survey, such as Planck, where the survey is obtained through ring-scans of the sky. In this model, resampling and pixelisation of the data are…
Calibration data are often obtained by observing several well-understood objects simultaneously with multiple instruments, such as satellites for measuring astronomical sources. Analyzing such data and obtaining proper concordance among the…
Ongoing and future surveys with repeat imaging in multiple bands are producing (or will produce) time-spaced measurements of brightness, resulting in the identification of large numbers of variable sources in the sky. A large fraction of…
The periodic standing wave method studies circular orbits of compact objects coupled to helically symmetric standing wave gravitational fields. From this solution an approximation is extracted for the strong field, slowly inspiralling…
Radio-astronomical observations are increasingly contaminated by interference, and suppression techniques become essential. A powerful candidate for interference mitigation is adaptive spatial filtering. We study the effect of spatial…
Current analysis of astronomical data are confronted with the daunting task of modeling the awkward features of astronomical data, among which heteroscedastic (point-dependent) errors, intrinsic scatter, non-ignorable data collection…
Light curves of astrophysical objects frequently contain strictly periodic signals. In those cases we can use that property to aid the detrending algorithm to fully disentangle an unknown periodic signal and an unknown baseline signal with…
Rational approximation schemes for reconstructing periodic signals from samples with poorly separated spectral content are described. These methods are automatic and adaptive, requiring no tuning or manual parameter selection. Collectively,…
We present and compare three generically applicable signal processing methods for periodic orbit quantization via harmonic inversion of semiclassical recurrence functions. In a first step of each method, a band-limited decimated periodic…
The data from Cosmic Microwave Background (CMB) experiments are becoming more complex with each new experiment. A consistent way of analysing these data sets is required so that direct comparison is possible between the various experimental…