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Complete Factorization of the 2m-Band Paraunitary Polyphase Matrix with Multiple Centers of Symmetry

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A Correction to this article was published on 30 October 2019

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Abstract

The design of filter banks with multiple centers of symmetry is very difficult. In this paper, a space decomposition of an orthogonal projection matrix is studied. This decomposition plays a key role in a new complete factorization theory. In addition, the concept of a minimal starting block matrix is proposed and is used to establish a new factorization of a 2m-band paraunitary polyphase matrix with multiple centers of symmetry. This factorization has the completeness property. The different possible forms of the minimal starting block matrix, which lead to the different types of filter banks, are obtained. Through different combinations of minimal starting block matrices and orthogonal projection matrices, the general solutions of a 2m-band paraunitary system with multiple centers are obtained theoretically. The four-band issue is discussed in detail as an example.

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  • 30 October 2019

    The original version of the article unfortunately contained an error in article.

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Authors and Affiliations

  1. Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, China

    Guoqiu Wang, Yong Chen & Dingxun Yi

  2. School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241002, China

    Yong Chen

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  1. Guoqiu Wang
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Correspondence to Yong Chen.

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Wang, G., Chen, Y. & Yi, D. Complete Factorization of the 2m-Band Paraunitary Polyphase Matrix with Multiple Centers of Symmetry. Circuits Syst Signal Process 39, 2533–2549 (2020). https://doi.org/10.1007/s00034-019-01273-0

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