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Design of Two Channel Biorthogonal Graph Wavelet Filter Banks with HalfBand Kernels
Xi ZHANG
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E100A
No.9
pp.17431750 Publication Date: 2017/09/01
Online ISSN: 17451337 Type of Manuscript: Special Section PAPER (Special Section on Signal Processing on Irregular Sampling Grids) Category: Keyword: graph signal processing, graph wavelets, biorthogonal graph filter bank, polynomial halfband kernel, Remez exchange algorithm, flatness,
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Summary:
In this paper, we propose a novel design method of two channel critically sampled compactly supported biorthogonal graph wavelet filter banks with halfband kernels. First of all, we use the polynomial halfband 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 halfband kernels with the specified degree of flatness. The proposed design method utilizes the PBP (Parametric Bernstein Polynomial), which ensures that the halfband 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.

