2-D LMA Filters--Design of Stable Two-Dimensional Digital Filters with Arbitrary Magnitude Function--
Summary :
This paper proposes a technique for designing two-dimensional (2-D) digital filters approximating an arbitrary magnitude function. The technique is based on 2-D spectral factorization and rational approximation of the complex exponential function. A 2-D spectral factorization technique is used to obtain a recursively computable and stable system with nonsymmetric half-plane support from the desired 2-D magnitude function. Since the obtained system has an exponential function type transfer function and cannot be realized directly in a rational form, a class of realizable 2-D digital filters is introduced to approximate the exponential type transfer function. This class of filters referred to as two-dimensional log magnitude approximation (2-D LMA) filters can be viewed as an extension of the class of 1-D LMA filters to the 2-D case. Filter coefficients are given by the 2-D complex cepstrum coefficients, i.e., the inverse Fourier transform of the logarithm of the given magnitude function, which can be efficiently computed using 2-D FFT algorithm. Consequently, computation of the filter coefficients is straightforward and efficient. A simple stability condition for the 2-D LMA filters is given. Under this condition, the stability of the designed filter is guaranteed. Parallel implementation of the 2-D LMA filters is also discussed. Several examples are presented to demonstrate the design capability.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E75-A No.2 pp.240-246
- Publication Date
- 1992/02/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Digital Image Processing
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Takao KOBAYASHI, Kazuyoshi FUKUSHI, Keiichi TOKUDA, Satoshi IMAI, "2-D LMA Filters--Design of Stable Two-Dimensional Digital Filters with Arbitrary Magnitude Function--" in IEICE TRANSACTIONS on Fundamentals,
vol. E75-A, no. 2, pp. 240-246, February 1992, doi: .
Abstract: This paper proposes a technique for designing two-dimensional (2-D) digital filters approximating an arbitrary magnitude function. The technique is based on 2-D spectral factorization and rational approximation of the complex exponential function. A 2-D spectral factorization technique is used to obtain a recursively computable and stable system with nonsymmetric half-plane support from the desired 2-D magnitude function. Since the obtained system has an exponential function type transfer function and cannot be realized directly in a rational form, a class of realizable 2-D digital filters is introduced to approximate the exponential type transfer function. This class of filters referred to as two-dimensional log magnitude approximation (2-D LMA) filters can be viewed as an extension of the class of 1-D LMA filters to the 2-D case. Filter coefficients are given by the 2-D complex cepstrum coefficients, i.e., the inverse Fourier transform of the logarithm of the given magnitude function, which can be efficiently computed using 2-D FFT algorithm. Consequently, computation of the filter coefficients is straightforward and efficient. A simple stability condition for the 2-D LMA filters is given. Under this condition, the stability of the designed filter is guaranteed. Parallel implementation of the 2-D LMA filters is also discussed. Several examples are presented to demonstrate the design capability.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e75-a_2_240/_p
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@ARTICLE{e75-a_2_240,
author={Takao KOBAYASHI, Kazuyoshi FUKUSHI, Keiichi TOKUDA, Satoshi IMAI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={2-D LMA Filters--Design of Stable Two-Dimensional Digital Filters with Arbitrary Magnitude Function--},
year={1992},
volume={E75-A},
number={2},
pages={240-246},
abstract={This paper proposes a technique for designing two-dimensional (2-D) digital filters approximating an arbitrary magnitude function. The technique is based on 2-D spectral factorization and rational approximation of the complex exponential function. A 2-D spectral factorization technique is used to obtain a recursively computable and stable system with nonsymmetric half-plane support from the desired 2-D magnitude function. Since the obtained system has an exponential function type transfer function and cannot be realized directly in a rational form, a class of realizable 2-D digital filters is introduced to approximate the exponential type transfer function. This class of filters referred to as two-dimensional log magnitude approximation (2-D LMA) filters can be viewed as an extension of the class of 1-D LMA filters to the 2-D case. Filter coefficients are given by the 2-D complex cepstrum coefficients, i.e., the inverse Fourier transform of the logarithm of the given magnitude function, which can be efficiently computed using 2-D FFT algorithm. Consequently, computation of the filter coefficients is straightforward and efficient. A simple stability condition for the 2-D LMA filters is given. Under this condition, the stability of the designed filter is guaranteed. Parallel implementation of the 2-D LMA filters is also discussed. Several examples are presented to demonstrate the design capability.},
keywords={},
doi={},
ISSN={},
month={February},}
Copy
TY - JOUR
TI - 2-D LMA Filters--Design of Stable Two-Dimensional Digital Filters with Arbitrary Magnitude Function--
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 240
EP - 246
AU - Takao KOBAYASHI
AU - Kazuyoshi FUKUSHI
AU - Keiichi TOKUDA
AU - Satoshi IMAI
PY - 1992
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E75-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 1992
AB - This paper proposes a technique for designing two-dimensional (2-D) digital filters approximating an arbitrary magnitude function. The technique is based on 2-D spectral factorization and rational approximation of the complex exponential function. A 2-D spectral factorization technique is used to obtain a recursively computable and stable system with nonsymmetric half-plane support from the desired 2-D magnitude function. Since the obtained system has an exponential function type transfer function and cannot be realized directly in a rational form, a class of realizable 2-D digital filters is introduced to approximate the exponential type transfer function. This class of filters referred to as two-dimensional log magnitude approximation (2-D LMA) filters can be viewed as an extension of the class of 1-D LMA filters to the 2-D case. Filter coefficients are given by the 2-D complex cepstrum coefficients, i.e., the inverse Fourier transform of the logarithm of the given magnitude function, which can be efficiently computed using 2-D FFT algorithm. Consequently, computation of the filter coefficients is straightforward and efficient. A simple stability condition for the 2-D LMA filters is given. Under this condition, the stability of the designed filter is guaranteed. Parallel implementation of the 2-D LMA filters is also discussed. Several examples are presented to demonstrate the design capability.
ER -
English
