A New Property of Optimal Realizations of CRSD 2-D Digital Filters and Its Application to the Direct Spatial-Domain Design
Summary :
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.
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- IEICE TRANSACTIONS on transactions Vol.E69-E No.10 pp.1084-1092
- Publication Date
- 1986/10/25
- Publicized
- Online ISSN
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- Type of Manuscript
- PAPER
- Category
- System Theory
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ZHAO Qiangfu, Masayuki KAWAMATA, Tatsuo HIGUCHI, "A New Property of Optimal Realizations of CRSD 2-D Digital Filters and Its Application to the Direct Spatial-Domain Design" in IEICE TRANSACTIONS on transactions,
vol. E69-E, no. 10, pp. 1084-1092, October 1986, doi: .
Abstract: 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.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e69-e_10_1084/_p
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@ARTICLE{e69-e_10_1084,
author={ZHAO Qiangfu, Masayuki KAWAMATA, Tatsuo HIGUCHI, },
journal={IEICE TRANSACTIONS on transactions},
title={A New Property of Optimal Realizations of CRSD 2-D Digital Filters and Its Application to the Direct Spatial-Domain Design},
year={1986},
volume={E69-E},
number={10},
pages={1084-1092},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={October},}
Copy
TY - JOUR
TI - A New Property of Optimal Realizations of CRSD 2-D Digital Filters and Its Application to the Direct Spatial-Domain Design
T2 - IEICE TRANSACTIONS on transactions
SP - 1084
EP - 1092
AU - ZHAO Qiangfu
AU - Masayuki KAWAMATA
AU - Tatsuo HIGUCHI
PY - 1986
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E69-E
IS - 10
JA - IEICE TRANSACTIONS on transactions
Y1 - October 1986
AB - 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.
ER -
English
