Generalization of the cross-wavelet function

We introduce the method of multiple cross-wavelet algorithm, hereafter also as Einstein's cross functions, for the time-frequency study of solar activity records or any astronomical and geophysical time series in general. The main purpose of this algorithm is to allow the simultaneous examination of the time-frequency information contents in n > 2 time series available. Previous cross-wavelet algorithm only permit the study of two time series at a time and was not extended to the generalized n > 2 problems until now. Furthermore, our new work lifted the restriction from the original formulation that are valid only for stationary processes. We applied our new algorithm to several of the solar activity proxies available in order to demonstrate the broad and powerful utility of this technique. We have used solar activity proxy records that are obtained under different geophysical archives and time periods which are, in turn, suitable for studying both the statistical and physical properties for solar variations valid on timescales of multi-century, millennium to several millennia. We focus on documenting the methodology in this paper rather than any elaborate interpretation of the results.