Analysis methods for multi-spacecraft data

Large amounts of data, like one or more time series from some spacecraft carried instruments, have to be reduced and presented in understandable quantities. As physical theories and models often are formulated in terms of frequency rather than time, it is often useful to transform the data from the time domain into the frequency domain. The transformation to frequency domain and application of statistics on the result is known as spectral analysis. The literature on spectral analysis is voluminous. In most cases, it is written by experts in signal processing, which means that there are many texts available outlining the fundamental mathematics and elaborating the fine points. However, this is not the only background needed for a space physicist who is put to the task of actually analysing spacecraft plasma data. Simple questions on normalisation, physical interpretation, and how to actually use the methods in practical situations are sometimes forgotten in spectral analysis texts. This chapter aims at conveying some information of that sort, offering a complement to the textbooks rather than a substitute for them. The discussion is illustrated with idealised examples as well as real satellite data. In order not to expand the chapter into a book in itself, we concentrate on the application of basic Fourier and wavelet methods, not treating interesting topics in time series analysis like stationarity tests, filtering, correlation functions, and nonlinear analysis methods. Higher order methods like bispectral analysis are also neglected. Fundamentals of such items are covered by many of the references to this chapter, and methods particularly suited for multipoint measurements are of course found throughout this book. Other introductions with multi-spacecraft applications in mind can be found in the paper by Glassmeier and Motschmann [1995] and in other papers in the same publication. The disposition of the chapter is as follows. First, we introduce the basic concepts in Section1.2, where we also discuss time-frequency methods for the analysis of nonstationary signals. The practical implementation of classical Fourier techniques is treated in Section1.3, while the implementation of Morlet wavelet analysis is discussed in Section 1.4. In Section1.5, we turn to the simultaneous analysis of two or more signals by the cross spectrum technique, particularly relevant for the analysis of multipoint measurements. Finally, we touch upon the use of parametric spectral methods in Section 1.6.