title: Multidimensional orthogonal filter bank characterization and design using the Cayley transform.
abstract: 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.
authors.affiliation: Department of Electrical and Computer Engineering, The Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. jzhou2@uiuc.edu
authors.forename: Jianping
authors.initials: J
authors.lastname: Zhou
authors.forename: Minh N
authors.initials: MN
authors.lastname: Do
authors.forename: Jelena
authors.initials: J
authors.lastname: Kovacević
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods; D012815:Signal Processing, Computer-Assisted