Convergence of the Multidimensional Minimum Variance Spectral Estimator for Continuous and Mixed Spectra

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A proof of the pointwise convergence of the multidimensional minimum variance spectral estimator as the region of data support becomes infinite is given. It is shown that an octant is sufficient to ensure that the minimum variance spectral estimator will converge to the true power spectral density. The proof is valid for 1-D, multidimensional, continuous, and mixed spectra. Another useful result is that a normalized minimum variance spectral estimator can be defined to indicate sinusoidal power for processes with a mixed spectrum. Finally, upper and lower bounds on the continuous portion of the spectral estimate are given. </para>