New approach to the design of linear phase biorthogonal filter banks

Takayuki Nagai, Masaaki Ikehara

Research output: Contribution to journalArticle

Abstract

In this paper, a novel way to design biorthogonal filter banks and wavelets is proposed. Perfect reconstruction (PR) filter banks are roughly separated into orthogonal (paraunitary) and biorthogonal filter banks. Biorthogonal filter banks have more degrees of freedom than orthogonal ones. Thus they have been thoroughly studied, and several design methods have been reported. Almost all of these methods, however, require a nonlinear programming technique with constraints. This is because biorthogonal filter banks, unlike the orthogonal ones, do not have a complete lattice structure except for the two-channel case. We therefore consider a simple design method which only requires that we solve a linear equation iteratively. In the proposed method, the least square error of the PR condition is minimized so as to avoid using the nonlinear programming technique. It is shown that a PR system can be obtained.

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Filter banks
Nonlinear programming
Linear equations

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

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title = "New approach to the design of linear phase biorthogonal filter banks",
abstract = "In this paper, a novel way to design biorthogonal filter banks and wavelets is proposed. Perfect reconstruction (PR) filter banks are roughly separated into orthogonal (paraunitary) and biorthogonal filter banks. Biorthogonal filter banks have more degrees of freedom than orthogonal ones. Thus they have been thoroughly studied, and several design methods have been reported. Almost all of these methods, however, require a nonlinear programming technique with constraints. This is because biorthogonal filter banks, unlike the orthogonal ones, do not have a complete lattice structure except for the two-channel case. We therefore consider a simple design method which only requires that we solve a linear equation iteratively. In the proposed method, the least square error of the PR condition is minimized so as to avoid using the nonlinear programming technique. It is shown that a PR system can be obtained.",
author = "Takayuki Nagai and Masaaki Ikehara",
year = "1999",
month = "7",
doi = "10.1002/(SICI)1520-6440(199907)82:7<21::AID-ECJC3>3.0.CO;2-7",
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volume = "82",
pages = "21--29",
journal = "Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)",
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AB - In this paper, a novel way to design biorthogonal filter banks and wavelets is proposed. Perfect reconstruction (PR) filter banks are roughly separated into orthogonal (paraunitary) and biorthogonal filter banks. Biorthogonal filter banks have more degrees of freedom than orthogonal ones. Thus they have been thoroughly studied, and several design methods have been reported. Almost all of these methods, however, require a nonlinear programming technique with constraints. This is because biorthogonal filter banks, unlike the orthogonal ones, do not have a complete lattice structure except for the two-channel case. We therefore consider a simple design method which only requires that we solve a linear equation iteratively. In the proposed method, the least square error of the PR condition is minimized so as to avoid using the nonlinear programming technique. It is shown that a PR system can be obtained.

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