Quaternionic building block for paraunitary filter banks

This paper presents a new, motivated by the theory of hypercomplex numbers, approach to the design of paraunitary filter banks. Quaternion multiplication matrices related to 4D hyperplanar transformations turn out to be usable in the factorization of orthogonal matrices, as an extension and alternative for commonly met Givens rotations. The corresponding building block is suitable for design parameterization and efficient implementation of lossless lattices with 4 or more channels. Novel quaternion-based mutations of known filter banks are proposed and the theory is supported with design examples.