Multidimensional orthogonal filter bank characterization and design using the Cayley transform

Jianping Zhou, Minh N. Do, Jelena Kovačević

Research output: Contribution to journalArticlepeer-review


We present a complete characterization and design of orthogonal infinite impulse response (IIR) and finite impulse response (FIR) filter banks in any dimension using the Cayley transform (CT). Traditional design methods for one-dimensional orthogonal filter banks cannot be extended to higher dimensions directly due to the lack of a multidimensional (MD) spectral factorization theorem. In the polyphase domain, orthogonal filter banks are equivalent to paraunitary matrices and lead to solving a set of nonlinear equations. The CT establishes a one-to-one mapping between paraunitary matrices and para-skew-Hermitian matrices. In contrast to the paraunitary condition, the para-skew-Hermitian condition amounts to linear constraints on the matrix entries which are much easier to solve. Based on this characterization, we propose efficient methods to design MD orthogonal filter banks and present new design results for both IIR and FIR cases.

Original languageEnglish (US)
Pages (from-to)760-769
Number of pages10
JournalIEEE Transactions on Image Processing
Issue number6
StatePublished - Jun 2005


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

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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