Time-frequency analysis of δ Scuti light curves using the wavelet transform.
δ Scuti stars are intermediate-mass stars (i.e. between 1.5 and 3 solar masses) pulsators located in the classical Cepheids instability strip, either in their pre- main sequence stage, or already in the main sequence or also moving from the main sequence to the giant branch. Their spectral types range from A to F. Before the era of space telescopes, these stars were thought to have a small number of pulsating frequencies, but with the data coming from space missions like CoRoT, Kepler, TESS, etc., it has been found that there are some δ Scuti stars with hundreds of pulsation frequencies. In the last years, some authors found an amplitude modulation in a few δ Scuti stars but a time-frequency analysis has not yet been performed up to date. In our work we have tried the continuous wavelet transform as well as a multi resolution analysis using wavelets as filters. Unlike the short time Fourier transform, that uses a fixed windows size, the wavelet transform uses short windows at high frequencies and long windows at low frequencies, making it like an adaptive analysis tool. The wavelet analysis relies on the use of a mother wavelet, i.e. a wave-like function of finite energy that can be scaled and shifted in a way that conserves the energy, so it can correlate with the variations o the signal, thus providing a measure of the instantaneous frequencies of the signal. The continuous wavelet transform is widely used in sound processing and pattern recognition applications, making it a suitable tool to use with light curves. We show this analysis applied to a sample of δ Sct stars and we try to give an explanation to the pulsating frequencies that show irregularities.