Application of statistical techniques to the analysis of solar coronal oscillations

In this work, the application of two different techniques to the analysis of coronal time series is investigated. The first technique, called empirical mode decomposition, was developed by Huang and coworkers and can be used to decompose a signal in its characteristic timescales, allowing, among other applications, efficient filtration of the signal. The second technique, called complex empirical orthogonal function (CEOF) analysis, is an extension of the well-known principal component analysis, to which the Hilbert transform has been added. The CEOF analysis allows identification of the dominant spatial and temporal structures in a multivariate data set and is thus ideally suited to the study of propagating and standing features that can be associated with waves or oscillations. Here we apply both methods to time series obtained from a coronal loop and obtain detailed two-dimensional information about a propagating and a standing wave with periods around 5 and 10 minutes, respectively.