Multi-scale signal transform and application of solar time series through phase analysis

Synchronization can be considered as a fundamental property for dynamical system in scientific fields, which is used to describe the asynchronous behaviour in time-frequency domain. The statistical analysis of solar time series can obtain some useful information to characterise and predict the long-term variability of the Sun. In this paper, two analysis approaches, including wavelet coherence transform and cross-correlation analysis, are combined to analyze the statistical connection of polar faculae between low latitudes and high latitudes for the time period from 1951 to 1998. Analysis results indicated that the combination technique is an appropriate choice for studying the asynchronous behavior between the two time series, because the classical analysis techniques can easily get some incorrect results.