Symmetrie delay factorization: A generalized theory for paraunitary filter banks

The Symmetric Delay Factorization (SDF) is introduced in [1] for synthesizing linear phase paraunitary filter banks and is applied successfully in [2] for designing Time Varying Filter Banks (TVFB). This paper describes a minimal and complete generalized symmetric delay factorization theory valid for a larger class of paraunitary filter banks. The approach presented here provides a unifying framework for linear phase paraunitary filter banks including linear phase Lapped Orthogonal Transforms (LOT) and for cosine-modulated filter banks, this for an arbitrary number of channels (odd or even). This generalized theory 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. The generalized symmetric delay factorization relying on lattice structure representations leads also naturally to fast implementation algorithms.