A state-space approach to orthogonal digital filters for VLSI implementation

An algorithm for designing orthogonal digital filters using a purely state-space approach is developed. The algorithm consists of three parts: (i) orthogonal embedding, (ii) transformation of the embedded orthogonal transition matrix to the extended upper Hessenberg form, and (iii) factorization of this new form into into (2n+1) Givens rotations. Appropriately interconnecting the rotors leads to the pipelined orthogonal filter structure. As a consequence of this approach, an essentially orthogonal structure is obtained for the inverse filter, and only one Givens rotor gets replaced by a hyperbolic rotor.<>