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 [n.sup.2]. 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 in [13]. 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. Index Terms--Realizations, roundoff noise, sensitivity, structures.