A New Property of Optimal Realizations of CRSD 2-D Digital Filters and Its Application to the Direct Spatial-Domain Design

ZHAO Qiangfu  Masayuki KAWAMATA  Tatsuo HIGUCHI  

IEICE TRANSACTIONS (1976-1990)   Vol.E69   No.10   pp.1084-1092
Publication Date: 1986/10/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: System Theory

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On the basis of the controllability gramians, the observability gramians and the second order modes, this paper shows that optimal realizations (filter structures having minimum roundoff noises) of quarter-plane-causal, recursive and separable in denominator 2-D digital filters (CRSD filters for short) are scaled and rotated balanced realizations. Two applications of this relation are given. The first one gives a simple proof of the absence of overflow oscillations in optimal realizations. The second one, which is the main result of this paper, gives a direct design method of CRSD filters in the spatial domain. This method simplifies traditional two-step design (approximation and synthesis) into a one-step design with much less computational complexity. Resulting filters of this direct design method can approximate given 2-D impulse responses closely. In addition, they are always guaranteed to be stable, nearly optimal with respect to roundoff noise and free of overflow oscillations. The efficiency of the direct design method is shown by numerical examples.