Two-dimensional schur algorithm

Kayran A. H., Kucuk U., Parker S.

MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING, vol.9, no.1, pp.7-37, 1998 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 1
  • Publication Date: 1998
  • Doi Number: 10.1023/a:1008247520626
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.7-37
  • Keywords: 2-D spectral estimation, 2-D Schur and Levinson recursion, 2-D quarter-plane lattice filters, 2-D gapped functions, 2-D normal equations, LINEAR PREDICTION, AUTO-CORRELATION, 2-D, ENTROPY, FIELDS
  • Istanbul Technical University Affiliated: Yes


In this paper, a novel 2-D Schur algorithm is developed as a natural extension of the 1-D Schur recursion. This lattice structure is based on Parker and Kayran's four-field lattice approach. Starting with given 2-D autocorrelation samples, four quarter-plane gapped functions are generated. Their linear combination is used to satisfy gap conditions and calculate 2-D lattice parameter reflection factors for the first stage. In order to determine the growing number of 2-D reflection coefficients at succesive stages, appropriately defined auxiliary gapped functions are introduced after the first order. The theory has been confirmed by computer simulations. In addition to developing the basic theory, the presentation includes a comparison between the proposed 2-D lattice structure and other existing four-field lattice structures.