IEICE TRANSACTIONS on Fundamentals
Analysis and Minimization of Roundoff Noise for Generalized Direct-Form II Realization of 2-D Separable-Denominator Filters
Summary :
Based on the concept of polynomial operators, this paper explores generalized direct-form II structure and its state-space realization for two-dimensional separable-denominator digital filters of order (m, n) where a structure with 3(m+n)+mn+1 fixed parameters plus m+n free parameters is introduced and analyzed. An l2-scaling method utilizing different coupling coefficients at different branch nodes to avoid overflow is presented. Expressions of evaluating the roundoff noise for the filter structure as well as its state-space realization are derived and investigated. The availability of the m+n free parameters is shown to be beneficial as the roundoff noise measures can be minimized with respect to these free parameters by means of an exhaustive search over a set with finite number of candidate elements. The important role these parameters can play in the endeavors of roundoff noise reduction is demonstrated by numerical experiments.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E103-A No.7 pp.873-884
- Publication Date
- 2020/07/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2019EAP1152
- Type of Manuscript
- PAPER
- Category
- Digital Signal Processing
Authors
Takao HINAMOTO
Hiroshima University
Akimitsu DOI
Hiroshima Institute of Technology
Wu-Sheng LU
University of Victoria
Keyword
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Takao HINAMOTO, Akimitsu DOI, Wu-Sheng LU, "Analysis and Minimization of Roundoff Noise for Generalized Direct-Form II Realization of 2-D Separable-Denominator Filters" in IEICE TRANSACTIONS on Fundamentals,
vol. E103-A, no. 7, pp. 873-884, July 2020, doi: 10.1587/transfun.2019EAP1152.
Abstract: Based on the concept of polynomial operators, this paper explores generalized direct-form II structure and its state-space realization for two-dimensional separable-denominator digital filters of order (m, n) where a structure with 3(m+n)+mn+1 fixed parameters plus m+n free parameters is introduced and analyzed. An l2-scaling method utilizing different coupling coefficients at different branch nodes to avoid overflow is presented. Expressions of evaluating the roundoff noise for the filter structure as well as its state-space realization are derived and investigated. The availability of the m+n free parameters is shown to be beneficial as the roundoff noise measures can be minimized with respect to these free parameters by means of an exhaustive search over a set with finite number of candidate elements. The important role these parameters can play in the endeavors of roundoff noise reduction is demonstrated by numerical experiments.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019EAP1152/_p
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@ARTICLE{e103-a_7_873,
author={Takao HINAMOTO, Akimitsu DOI, Wu-Sheng LU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Analysis and Minimization of Roundoff Noise for Generalized Direct-Form II Realization of 2-D Separable-Denominator Filters},
year={2020},
volume={E103-A},
number={7},
pages={873-884},
abstract={Based on the concept of polynomial operators, this paper explores generalized direct-form II structure and its state-space realization for two-dimensional separable-denominator digital filters of order (m, n) where a structure with 3(m+n)+mn+1 fixed parameters plus m+n free parameters is introduced and analyzed. An l2-scaling method utilizing different coupling coefficients at different branch nodes to avoid overflow is presented. Expressions of evaluating the roundoff noise for the filter structure as well as its state-space realization are derived and investigated. The availability of the m+n free parameters is shown to be beneficial as the roundoff noise measures can be minimized with respect to these free parameters by means of an exhaustive search over a set with finite number of candidate elements. The important role these parameters can play in the endeavors of roundoff noise reduction is demonstrated by numerical experiments.},
keywords={},
doi={10.1587/transfun.2019EAP1152},
ISSN={1745-1337},
month={July},}
Copy
TY - JOUR
TI - Analysis and Minimization of Roundoff Noise for Generalized Direct-Form II Realization of 2-D Separable-Denominator Filters
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 873
EP - 884
AU - Takao HINAMOTO
AU - Akimitsu DOI
AU - Wu-Sheng LU
PY - 2020
DO - 10.1587/transfun.2019EAP1152
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E103-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2020
AB - Based on the concept of polynomial operators, this paper explores generalized direct-form II structure and its state-space realization for two-dimensional separable-denominator digital filters of order (m, n) where a structure with 3(m+n)+mn+1 fixed parameters plus m+n free parameters is introduced and analyzed. An l2-scaling method utilizing different coupling coefficients at different branch nodes to avoid overflow is presented. Expressions of evaluating the roundoff noise for the filter structure as well as its state-space realization are derived and investigated. The availability of the m+n free parameters is shown to be beneficial as the roundoff noise measures can be minimized with respect to these free parameters by means of an exhaustive search over a set with finite number of candidate elements. The important role these parameters can play in the endeavors of roundoff noise reduction is demonstrated by numerical experiments.
ER -
English
