Asymptotic distribution of a discrete transform of an arbitrarily sampled homogeneous random field

Multidimensional sampling of real data, e.g., in space and time, often requires observations at non-uniformly spaced intervals. A discrete transform of a multidimensional stationary stochastic process transforms a multivariate problem into an asymptotically univariate one if the spacing is uniform in at least one dimension. For both uniform and non-uniform sampling and a model of ‘signal’ imbedded in a ‘noise’ process, asymptotic normality and independence justifies statistical testing in each cell of the transformed domain of the hypothesis ‘noise alone’ versus the alternate ‘signal plus noise’.