Performance analysis of a new structure for digital filter implementation

It is well known that for a digital filter of order n the number of nontrivial parameters in the classical optimal state-space realizations is proportional to n². In this paper, a new structure is proposed for digital filter implementation. This structure possesses 5n-1 nontrivial parameters and is shown to be equivalent to the discrete-time counterpart of the well-known orthonormal ladder filter. A new property of this ladder filter is revealed. The performance of the proposed structure is analyzed. Expressions for evaluating the sensitivity measure and the roundoff noise gain are derived. A numerical example is presented to illustrate the design procedure. Simulations show that the performance of the proposed structure is almost the same as that of the fully parameterized optimal realizations