Special paraunitary matrices, Cayley transform, and multidimensional orthogonal filter banks

Jianping Zhou, Minh N. Do, Jelena Kovaĉević

Research output: Contribution to journalArticlepeer-review


We characterize and design multidimensional (MD) orthogonal filter banks using special paraunitary matrices and the Cayley transform. Orthogonal filter banks are represented by paraunitary matrices in the polyphase domain. We define special paraunitary matrices as paraunitary matrices with unit determinant. We show that every paraunitary matrix can be characterized by a special paraunitary matrix and a phase factor. Therefore, the design of paraunitary matrices (and thus of orthogonal filter banks) becomes the design of special paraunitary matrices, which requires a smaller set of nonlinear equations. Moreover, we provide a complete characterization of special paraunitary matrices in the Cayley domain, which converts nonlinear constraints into linear constraints. Our method greatly simplifies the design of MD orthogonal filter banks and leads to complete characterizations of such filter banks.

Original languageEnglish (US)
Pages (from-to)511-519
Number of pages9
JournalIEEE Transactions on Image Processing
Issue number2
StatePublished - Feb 2006


  • Cayley transform
  • Filter banks
  • Multidimensional (MD) filter banks
  • Nonseparable filter design
  • Orthogonal filter banks
  • Paraunitary
  • Polyphase
  • Special paraunitary

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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