Time series analysis of sunspot oscillations using the wavelet transform

By decomposing a time series into time-frequency space, one is able to determine both the dominant mode of variability and how those modes vary in time. We take advantage of this property of the wavelet analysis in order to examine the temporal variation of the period of the umbral oscillations using ground-based observations of the solar atmosphere. We use this real-life signal in order to test the capabilities of different wavelets and to see the problems that arise in analyzing such a signal. We use the continuous wavelet transform in order to perform the analysis and the "a` trous" algorithm as a detrending tool.