Spectral estimation of irregularly sampled multidimensional processes by generalized prolate spheroidal sequences

A nonparametric spectral estimation method is presented for bandlimited random processes that have been sampled at arbitrary points in one or more dimensions. The method makes simultaneous use of several weight sequences that depend on the set of sampling point, the signal band, and the frequency band being analyzed. These sequences are solutions to a generalized matrix eigenvalue problem and are termed generalized prolate spheroidal sequences, being extensions of the familiar discrete prolate spheroidal sequences. Statistics of the estimator are derived, and the tradeoff among bias, variance, and resolution is quantified. The method avoids several problems typically associated with irregularly sampled data and multidimensional processes. A related method is suggested that has nearly as good performance while requiring significantly fewer computations