Computation of a block-diagonal realization of a high-order filter via singular value decomposition

In electronic communication, a high-order filter may be realized by a state-space realization. For implementation, a canonical form is useful. In this paper, a block-diagonal state-space realization is determined by using singular value decomposition. Certain parity-orthogonal transformations are determined first which are then employed to determine a block-diagonal realization of a high-order filter. The realization can be implemented as a parallel structure of second-order networks, and is always obtainable when the spectrum of the system matrix of the state-space description is separable into distinct groups relative to the modulus of the eigenvalues-not an unusual constraint in filters. The procedure avoids the use of eigenstructure routines which are not helpful for ill-conditioned matrices. Also, the parity-orthogonal transformations share some properties of orthogonal matrices; the inverse is obtainable from the transpose. The computations are, hence, simplified. The transformations and the procedure is demonstrated by an example.