Asymptotic Distribution of the Discrete Transform of a Nonuniformly Sampled Multidimensional Process.

摘要

Multidimensional discrete transforms that map arbitrarily spaced sampled data into arrays of coefficients of arbitrary basis functions were considered in a previous paper. These studies are motivated by a model of observations uniformly spaced in time obtained simultaneously at a nonuniform set of spatial points. For the uniformly spaced samples the transformation becomes the familiar discrete finite Fourier transform (DFT),and fast-Fourier-transform processing is applicable. The nonuniformly spaced samples generally require a transformation matrix that is not as highly factorable. For a two-dimensional sample space consisting of M nonuniform spatial points and N uniform temporal points,an efficient transformation is possible if M << N. Under the same assumption this two-dimensional transformation will be shown to approximately diagonalize the covariance matrix. 'Asymptotic'will refer here to the limit as N nears infinity,with M finite.