## Abstract

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 language | English |
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Pages (from-to) | 375-389 |

Number of pages | 15 |

Journal | Mathematics of Control, Signals, and Systems |

Volume | 8 |

Issue number | 4 |

DOIs | |

State | Published - 1 Dec 1995 |

## Keywords

- 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