Orthogonal decompositions of 2-D nonhomogeneous discrete random fields

Joseph M. Francos, Boaz Porat, A. Zvi Meiri

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Imposing a total-order on a two-dimensional (2-D) discrete random field induces an orthogonal decomposition of the random field into two components: A purely-indeterministic field and a deterministic one. The purely-indeterministic component is shown to have a 2-D white-innovations driven moving-average representation. The 2-D deterministic random field can be perfectly predicted from the field's "past" with respect to the imposed total-order definition. The deterministic field is further orthogonally decomposed into an evanescent field, and a remote past field. The evanescent field is generated by the columnto-column innovations of the deterministic field with respect to the imposed nonsymmetrical-half-plane total-ordering definition. The presented decomposition can be obtained with respect to any nonsymmetrical-half-plane total-ordering definition, for which the nonsymmetrical-half-plane boundary line has rational slope.

Original languageEnglish
Pages (from-to)375-389
Number of pages15
JournalMathematics of Control, Signals, and Systems
Issue number4
StatePublished - 1 Dec 1995


  • Deterministic random fields
  • Evanescent random fields
  • Purely-indeterministic random fields
  • Total-order
  • Two-dimensional (2-D) nonhomogeneous random fields
  • Wold decomposition

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Control and Optimization
  • Applied Mathematics


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