An introduction to multiple-window analysis of array data

Summary form only given. The basic theory and some recent developments in the theory of multiple-window methods for array data are reviewed. Applied to small samples or nonstationary data, this method has numerous advantages over conventional techniques. It is a small sample theory, essentially an inverse method applied to the finite Fourier transform; its statistical efficiency is typically a factor of two to three higher than that of conventional methods with the same degree of bias protection; and it separates the continuous part of the spectrum from line components. In addition, it has the major advantage that underlying assumptions can be tested. However, because higher-dimensional problems are more delicate than univariate ones, robustness and diagnostics become far from critical. Such diagnostics are illustrated by the application of multiple-window methods to analysis of data from a linear array of three-axis magnetometers