Other
Scientific paper
Feb 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999sss..conf...57a&link_type=abstract
Self-Similar Systems, Dubna, Russia, 29 July - August 1998 eds. V.B.Priezzhev and V.P.Spiridonov, Joint Inst. Nucl. Res., 1999,
Other
Data Reduction: Wavelet Analysis, Periodogram Analysis, Stars: Semi-Regular: Mode Switching, Stars: Rv Tau-Type, Multiperiodic, Stars: Individual: Df Cyg, Stars: Individual: Af Cyg
Scientific paper
The wavelet analysis is extended to the irregularly spaced signal based on the additional weights used in the least squares approximation. For the best fit frequency obtained by maximizing the wavelet Z-transform in the notation of Foster (1996), the variance of the smoothed data and the corresponding amplitude are computed. The optimal wavelet smoothing algorithm is developed. Precise analytic expressions for these parameters as well as for the weighted wavelet transform are derived and illustrated on numerical examples of the harmonic, multi-frequency signals, autoregressive models, real data and the ''running parabola'' (RP, Andronov, 1997) fits. The response functions corresponding to different basic and weight functions are compared. The values of the power index of the test functions obtained by using the wavelet, ''scalegram'' (RP) and periodogram analysis are obtained. For the first-order autoregressive model, the corrected shape of the autocorrelation function is presented. Results obtained by using the least-squares extension of the Morlet wavelet with other wavelets are compared. They are applied to the stars of different types - cataclysmic, semi-regular, symbiotic - as well as to the numerical models.
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