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

Authors
  • Wang, Guoqiu1
  • Chen, Yong1, 2
  • Yi, Dingxun1
  • 1 Hunan Normal University, Changsha, 410081, China , Changsha (China)
  • 2 Anhui Normal University, Wuhu, 241002, China , Wuhu (China)
Type
Published Article
Journal
Circuits, Systems, and Signal Processing
Publisher
Springer US
Publication Date
Sep 27, 2019
Volume
39
Issue
5
Pages
2533–2549
Identifiers
DOI: 10.1007/s00034-019-01273-0
Source
Springer Nature
Keywords
License
Yellow

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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