IEICE TRANSACTIONS on Fundamentals
Design of Two Channel Biorthogonal Graph Wavelet Filter Banks with Half-Band Kernels
Summary :
In this paper, we propose a novel design method of two channel critically sampled compactly supported biorthogonal graph wavelet filter banks with half-band kernels. First of all, we use the polynomial half-band kernels to construct a class of biorthogonal graph wavelet filter banks, which exactly satisfy the PR (perfect reconstruction) condition. We then present a design method of the polynomial half-band kernels with the specified degree of flatness. The proposed design method utilizes the PBP (Parametric Bernstein Polynomial), which ensures that the half-band kernels have the specified zeros at λ=2. Therefore the constraints of flatness are satisfied at both of λ=0 and λ=2, and then the resulting graph wavelet filters have the flat spectral responses in passband and stopband. Furthermore, we apply the Remez exchange algorithm to minimize the spectral error of lowpass (highpass) filter in the band of interest by using the remaining degree of freedom. Finally, several examples are designed to demonstrate the effectiveness of the proposed design method.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.9 pp.1743-1750
- Publication Date
- 2017/09/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E100.A.1743
- Type of Manuscript
- Special Section PAPER (Special Section on Signal Processing on Irregular Sampling Grids)
- Category
Authors
Xi ZHANG
University of Electro-Communications
Keyword
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Xi ZHANG, "Design of Two Channel Biorthogonal Graph Wavelet Filter Banks with Half-Band Kernels" in IEICE TRANSACTIONS on Fundamentals,
vol. E100-A, no. 9, pp. 1743-1750, September 2017, doi: 10.1587/transfun.E100.A.1743.
Abstract: In this paper, we propose a novel design method of two channel critically sampled compactly supported biorthogonal graph wavelet filter banks with half-band kernels. First of all, we use the polynomial half-band kernels to construct a class of biorthogonal graph wavelet filter banks, which exactly satisfy the PR (perfect reconstruction) condition. We then present a design method of the polynomial half-band kernels with the specified degree of flatness. The proposed design method utilizes the PBP (Parametric Bernstein Polynomial), which ensures that the half-band kernels have the specified zeros at λ=2. Therefore the constraints of flatness are satisfied at both of λ=0 and λ=2, and then the resulting graph wavelet filters have the flat spectral responses in passband and stopband. Furthermore, we apply the Remez exchange algorithm to minimize the spectral error of lowpass (highpass) filter in the band of interest by using the remaining degree of freedom. Finally, several examples are designed to demonstrate the effectiveness of the proposed design method.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.1743/_p
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@ARTICLE{e100-a_9_1743,
author={Xi ZHANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Design of Two Channel Biorthogonal Graph Wavelet Filter Banks with Half-Band Kernels},
year={2017},
volume={E100-A},
number={9},
pages={1743-1750},
abstract={In this paper, we propose a novel design method of two channel critically sampled compactly supported biorthogonal graph wavelet filter banks with half-band kernels. First of all, we use the polynomial half-band kernels to construct a class of biorthogonal graph wavelet filter banks, which exactly satisfy the PR (perfect reconstruction) condition. We then present a design method of the polynomial half-band kernels with the specified degree of flatness. The proposed design method utilizes the PBP (Parametric Bernstein Polynomial), which ensures that the half-band kernels have the specified zeros at λ=2. Therefore the constraints of flatness are satisfied at both of λ=0 and λ=2, and then the resulting graph wavelet filters have the flat spectral responses in passband and stopband. Furthermore, we apply the Remez exchange algorithm to minimize the spectral error of lowpass (highpass) filter in the band of interest by using the remaining degree of freedom. Finally, several examples are designed to demonstrate the effectiveness of the proposed design method.},
keywords={},
doi={10.1587/transfun.E100.A.1743},
ISSN={1745-1337},
month={September},}
Copy
TY - JOUR
TI - Design of Two Channel Biorthogonal Graph Wavelet Filter Banks with Half-Band Kernels
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1743
EP - 1750
AU - Xi ZHANG
PY - 2017
DO - 10.1587/transfun.E100.A.1743
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2017
AB - In this paper, we propose a novel design method of two channel critically sampled compactly supported biorthogonal graph wavelet filter banks with half-band kernels. First of all, we use the polynomial half-band kernels to construct a class of biorthogonal graph wavelet filter banks, which exactly satisfy the PR (perfect reconstruction) condition. We then present a design method of the polynomial half-band kernels with the specified degree of flatness. The proposed design method utilizes the PBP (Parametric Bernstein Polynomial), which ensures that the half-band kernels have the specified zeros at λ=2. Therefore the constraints of flatness are satisfied at both of λ=0 and λ=2, and then the resulting graph wavelet filters have the flat spectral responses in passband and stopband. Furthermore, we apply the Remez exchange algorithm to minimize the spectral error of lowpass (highpass) filter in the band of interest by using the remaining degree of freedom. Finally, several examples are designed to demonstrate the effectiveness of the proposed design method.
ER -
English
