Symmetric delay factorization: generalized framework for paraunitary filter banks

The Symmetric Delay Factorization (SDF) is introduced in 1] for synthesizing linear phase paraunitary lter 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 valid for a larger class of paraunitary lter banks, and for an arbitrary (even and odd) number of channels. The approach presented here provides a unifying framework for linear phase paraunitary lter banks including linear phase Lapped Orthogonal Transforms (LOT) and for cosine-modulated lter banks, this for an arbitrary number of channels (odd or even). This approach opens new perspectives in the design of time-varying lter 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.