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Quaternionic Lattice Structures for Four-Channel Paraunitary Filter Banks

EURASIP Journal on Advances in Signal Processing20062007:037481

https://doi.org/10.1155/2007/37481

Received: 31 December 2005

Accepted: 9 October 2006

Published: 24 December 2006

Abstract

A novel approach to the design and implementation of four-channel paraunitary filter banks is presented. It utilizes hypercomplex number theory, which has not yet been employed in these areas. Namely, quaternion multipliers are presented as alternative paraunitary building blocks, which can be regarded as generalizations of Givens (planar) rotations. The corresponding quaternionic lattice structures maintain losslessness regardless of coefficient quantization and can be viewed as extensions of the classic two-band lattice developed by Vaidyanathan and Hoang. Moreover, the proposed approach enables a straightforward expression of the one-regularity conditions. They are stated in terms of the lattice coefficients, and thus can be easily satisfied even in finite-precision arithmetic.

Keywords

Information TechnologyBuilding BlockNumber TheoryQuantum InformationLattice Structure

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Authors’ Affiliations

(1)
Department of Real-Time Systems, Faculty of Computer Science, Bialystok Technical University, Bialystok, Poland

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Copyright

© M. Parfieniuk and A. Petrovsky. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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