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Quaternionic Lattice Structures for Four-Channel Paraunitary Filter Banks

EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 037481 (2006) Cite this article

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.

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  1. Department of Real-Time Systems, Faculty of Computer Science, Bialystok Technical University, Wiejska 45A street, Bialystok, 15-351, Poland

    Marek Parfieniuk & Alexander Petrovsky

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  1. Marek Parfieniuk
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  2. Alexander Petrovsky
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Correspondence to Marek Parfieniuk.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Parfieniuk, M., Petrovsky, A. Quaternionic Lattice Structures for Four-Channel Paraunitary Filter Banks. EURASIP J. Adv. Signal Process. 2007, 037481 (2006). https://doi.org/10.1155/2007/37481

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