ASYMPTOTICALLY OPTIMUM MULTIDIMENSIONAL FILTERING FOR SAMPLED-DATA PROCESSING OF SEISMIC ARRAYS
MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB
Pagination or Media Count:
A number of asymptotically optimum multidimensional filtering methods are investigated with the purpose of determining filtering techniques which require relatively little computing time to implement with a digital computer. In particular, the asymptotic properties of the maximum-likelihood and minimum- variance unbiased multidimensional filters are investigated in the sampleddata case. These two multidimensional filters are shown to be identical since they are both based on a conditional expectation. In addition, the martingale property of conditional expectation assures that the asymptotic properties of these multidimensional filters are well defined. An asymptotically optimum frequency domain synthesis procedure is given for two-sided multidimensional filters. This procedure is well suited to machine computation and has the advantage with respect to the exact recursive synthesis method of requiring much less computation time. A synthesis procedure for physically realizable multidimensional filters is presented which is based on a factorization of rational spectral matrices. This method is not, however, well suited to machine computation. An interpretation of optimum multidimensional filtering in terms of a frequency wavenumber space is also given.