{sc Combine} is an add-on to {sc SigSpec} and {sc Cinderella}. A {sc SigSpec} result file or a file generated by {sc Cinderella} contains the significant sinusoidal signal components in a time series. In this file, {sc Combine} checks one frequency a
fter the other for being a linear combination of previously examined frequencies. If this attempt fails, the corresponding frequency is considered ``genuine. Only genuine frequencies are used to form linear combinations subsequently. A purely heuristic model is employed to assign a reliability to each linear combination and to justify whether to consider a frequency genuine or a linear combination.
{sc Cinderella} is a software solution for the quantitative comparison of time series in the frequency domain. It assigns probabilities to coincident peaks in the DFT amplidude spectra of the datasets under consideration. Two different modes are avai
lable. In conditional mode, {sc Cinderella} examines target and comparison datasets on the assumption that the latter contain artifacts only, returning the conditional probability of a target signal, although there is a coincident signal in the comparison data within the frequency resolution. In composed mode, the probability of coincident signal components in both target and comparison data is evaluated. {sc Cinderella} permits to examine multiple target and comparison datasets at once.
{sc SigSpec} computes the spectral significance levels for the DFT amplitude spectrum of a time series at arbitrarily given sampling. It is based on the analytical solution for the Probability Density Function (PDF) of an amplitude level, including d
ependencies on frequency and phase and referring to white noise. Using a time series dataset as input, an iterative procedure including step-by-step prewhitening of the most significant signal components and MultiSine least-squares fitting is provided to determine a whole set of signal components, which makes the program a powerful tool for multi-frequency analysis. Instead of the step-by-step prewhitening of the most significant peaks, the program is also able to take into account several steps of the prewhitening sequence simultaneously and check for the combination associated to a minimum residual scatter. This option is designed to overcome the aliasing problem caused by periodic time gaps in the dataset. {sc SigSpec} can detect non-sinusoidal periodicities in a dataset by simultaneously taking into account a fundamental frequency plus a set of harmonics. Time-resolved spectral significance analysis using a set of intervals of the time series is supported to investigate the development of eigenfrequencies over the observation time. Furthermore, an extension is available to perform the {sc SigSpec} analysis for multiple time series input files at once. In this MultiFile mode, time series may be tagged as target and comparison data. Based on this selection, {sc SigSpec} is capable of determining differential significance spectra for the target datasets with respect to coincidences in the comparison spectra. A built-in simulator to generate and superpose a variety of sinusoids and trends as well as different types of noise completes the software package at the present stage of development.
The exact period determination of a multi-periodic variable star based on its luminosity time series data is believed a task requiring skill and experience. Thus the majority of available time series analysis techniques require human intervention to
some extent. The present work is dedicated to establish an automated method of period (or frequency) determination from the time series database of variable stars. Relying on the SigSpec method (Reegen 2007), the technique established here employs a statistically unbiased treatment of frequency-domain noise and avoids spurious (i. e. noise induced) and alias peaks to the highest possible extent. Several add-ons were incorporated to tailor SigSpec to our requirements. We present tests on 386 stars taken from ASAS2 project database. From the output file produced by SigSpec, the frequency with maximum spectral significance is chosen as the genuine frequency. Out of 386 variable stars available in the ASAS2 database, our results contain 243 periods recovered exactly and also 88 half periods, 42 different periods etc. SigSpec has the potential to be effectively used for fully automated period detection from variable stars time series database. The exact detection of periods helps us to identify the type of variability and classify the variable stars, which provides a crucial information on the physical processes effective in stellar atmospheres.
