Symmetric delay factorization: generalized framework for paraunitary filter banks

TitleSymmetric delay factorization: generalized framework for paraunitary filter banks
Publication TypeJournal Article
Year of Publication1999
AuthorsRault, P., and C. Guillemot
JournalSignal Processing, IEEE Transactions on
Pagination3315 -3325
Date Publisheddec.
Keywordschannel bank filters, complete symmetric delay factorization, data compression, delays, extended tapped transform, filter banks design, finite-duration signals, finite-size lattice structures, generalized framework, generalized tapped orthogonal transforms, image coding, image compression, lattice filters, lattice structures, linear phase filters, linear-phase lapped orthogonal transforms, linear-phase paraunitary filter banks, matrix algebra, minimal delay factorization, modulated lapped transform, modulation, network synthesis, nonlinear functions, nonlinear phase basis functions, nonlinear-phase paraunitary filter banks, object-based coding, orthogonal matrices, paraunitary cosine modulated filter banks, polyphase transfer matrix decomposition, real-valued coefficients, region based coding, symmetric delay factorization, time-bounded filter banks, time-varying filter banks, time-varying filters, transform coding, uniform order filter length, video coding, video compression

The symmetric delay factorization (SDF) was introduced to synthesize linear-phase paraunitary filter banks (LPPUFBs) with uniform order (i.e., filter length equal to NM for arbitrary N) and real-valued coefficients. The SDF presents the advantage of decomposing the polyphase transfer matrix (PTM) into only orthogonal matrices, even at the boundary of finite-duration signals, simplifying significantly the design of time-bounded filter banks (TBFBs) or of time-varying filter banks (TVFBs). However, the symmetric delay factorization applies only to LPPUFBs. On the other hand, lattice structures, as well as finite-size lattice structures, are proposed for classes of nonlinear-phase paraunitary filter banks, as the modulated lapped transform (MLT) and the extended tapped transform (ELT). This paper describes a new minimal and complete symmetric delay factorization valid for a larger class of paraunitary filter banks, encompassing paraunitary cosine modulated filter banks, with nonlinear phase basis functions, as well as for a set of LPPUFBs including the linear-phase lapped orthogonal transforms (LOTs) and the generalized tapped orthogonal transforms (GenLOTs). The derivations for filter banks with even and odd numbers of channels are formulated in a unified form. This approach opens new perspectives in the design of time-varying filter banks used for image and video compression, especially in the framework of region or object-based coding


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