Time-frequency analysis of HD 174936 and HD 174966 using the synchrosqueezed wavelet transform

Abstract

δ Scuti stars are intermediate-mass pulsators located in the classical Cepheid instability strip with spectral types ranging from A to F. In the last years, some authors found an amplitude and frequency modulation in some of these stars. In our work we have chosen the continuous wavelet transform as the more appropriate tool to perform a time-frequency analysis of the light curves of HD 174936 and HD 174966. We have chosen this tool because, unlike the short time Fourier transform, that uses a fixed windows size, the continuous wavelet transform uses short windows at high frequencies and long windows at low frequencies, making it like an adaptive analysis tool. In order to improve the resolution of the frequencies obtained by the continuous wavelet transform, we have also used the synchrosqueeze algorithm to “focus” the result. Then, we are capable to obtain a measure of the instantaneous frequencies of the signal in a wide range of frequencies. To check our results, we have compared them with the synchrosqueezed continuous wavelet transform of a synthetic signal generated with the frequencies previously obtained by a classical approach. Our results show that some frequencies are stable, at least within the observation run time, although some others show some kind of variation. This is the first time that such variations in the oscillation frequencies of HD 174936 and HD 174966 are reported.