Dataset pre-processing Considerations

If you examine the introduction and methodology sections of this paper http://articles.adsabs.harvard.edu/full/2001MNRAS.325.1383H you'll find application of windowed fourier techniques made publicly available via a formulation, and that has also been "tested in anger" upon Miras and multiperiodic semiregular stars as defined and applied by John Howarth of the BAA. This practical use of such (his first interest was in trying to untangle the horribly messy lightcurve of the multiperiodic semiregular variable W Cygni) by John H. over the years, in tandem with an industry application he had of the method, meant he had experience of the algorithms in terms of practical data manipulation. Comments on windowing and on filtering are included for instance, but John was the mathematician, not I, so I can not speak authoritatively on such matters. Outliers and occasional long gaps were in fact not a problem in practice, as long as the gaps were not many in number (one or two) and flanked by long runs of data, the analysis tended to pick up where it left off (although there could be a jump between phase "zeropoint" before and after a large gap). Evidently messy data inbetween time was sparse, and could be identified and removed and/or flagged if preferred by comparing phase over time against the raw magnitude over time lightcurve. The basic windowing technique in this form is quite simple, although not a programmer Iwas able to convert this algorithm into a form of MS Basic many years ago, despite the fact that the latter was heavily trigonometric functionally challenged. It should be fairly amenable to inclusing in VSTAR. You will no doubt recognise a lot of the formulae from your earlier VSTARwork. In the above noted paper up to section 3, all prior to section 3, is purely John Howarth's work, outlining his procedure. He did the maths at that time, I'd do the practical application. However he'd also chip in on the conclusions and any discussion sections especially when mathematical interpretation of results was essential. Phase over time derived in this way plots the same, but with inverted Yaxis, as O-C, except it gives a more objectively appraisable plot, and a tighter and smoother plot. This is for a quite simple reason, O-C tracks the migration of a special, unique, somewhat subjectively measured, point upon a lightcurve, ie the time of maximum (or minimum, or whatever other predefined point is being used). Fourier deconvolution of a lightcurve tracks the migration and evolution of the _whole_ lightcurve. At core John tended to take a representative period (usually the main period derived via DFT) as a test period, and track the phase and amplitude evolution of the lightcurve (from the JD and magnitude data) relative to the midpoint of the data (this is from memory). The test period does not even have to be accurate, but the less accurate it is the more useless the results, and the more accurate it is the more direct conclusions about the real star can be made and given. Remember, as a cardinal rule, that for both O-C and fourier element evolution over time, _slope_ from the horizontal in any direction, merely means that the period at that time was different, the steepness of the slope correlates to the size of the difference, and the direction with it was a smaller or longer period. IT DOESNOT mean the period was changing continually. An arc, sometimes parabolic, but certainly well defined, is what results when there is an actual rate of change of period away from the input test period. A horizontal line, albeit often with some scatter and waggle for MIras (usually to not too large an amount), represents a static period close indeed to the test period. John