Frequency-wavenumber spectrum analysis using quadratic estimators

Abstract

A general representation for all non-negative, modulation invariant estimators of the frequency-wavenumber spectrum shows explicitly how the quadratic estimates are constructed from linear transformations of the array data. The windows associated with these transformations are those normally associated with 'classical' spectrum estimators. The authors present closed form representations for the moments of quadratic estimators, and show that variance decreases as the number of orthogonal windows increases. Since a time-bandwidth product bounds the number of orthogonal windows with given selectivity, the design process involves the classical issue of trading resolution and variance. With this issue in mind, the development of both separable and inseparable windows is considered.<>