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

Abstract

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.

Document Details

Document Type
Technical Report
Publication Date
May 03, 1974
Accession Number
AD0779874

Entities

People

  • David A. Swick

Organizations

  • United States Naval Research Laboratory

Tags

DTIC Thesaurus Topics

  • Coefficients
  • Covariance
  • Data Science
  • Fast Fourier Transforms
  • Information Processing
  • Information Science
  • Mathematics
  • Nonuniform
  • Observation
  • Two Dimensional

Fields of Study

  • Engineering

Readers

  • Approximation Theory.

Technology Areas

  • Space