A state-space approach to orthogonal digital filters

Abstract

An algorithm for designing multi-input multi-output (MIMO) orthogonal digital filters is developed using a state-space approach. The algorithm consists of three parts: (i) orthogonal embedding, (ii) transformation of the embedded orthogonal transition matrix to the α-extended upper Hessenberg form; and (iii) factorization of this new form into Givens (planar) rotations. Appropriately interconnecting the rotors leads to the pipelined orthogonal filter structure. As a consequence of the approach, for the single-input, single-output (SISO) case, an essentially orthogonal structure is obtained for the inverse filter; only one of the Givens rotors is replaced by a hyperbolic rotor.