Optimal FWL design of state-space digital systems with weighted sensitivity minimization and sparseness consideration

Abstract

The ontimal finite word leneth (FWL) state-space arithmetical ooeration. The first effect is usuallv measured bv digital system design problem is investigated. Instead of the a global sensitivity measure of the filter function usual sensitivity measure, it is argued that it may be desirable to w,r,t. all the parameters [31-[51, the other by the minimize a frequency weighted sensitivity measure over all similarity transformations. The set of optimal realizations minimiz-noise gain and [' I. ing this weighted sensitivity is completely characterized, and an In [3], a global sensitivity measure of the transfer function algorithm is proposed to find the optimal solution set. It is w.r.t. the parameters of the state-space model was proposed shown that a subset of the optimal realization set consists of by ~~~~~~~~l~ and ~h i~l~. and a reasonable easily sparse Schur realizations, whose actual sensitivity (taking into computable upper bound for this measure was studied. It was account the zero elements) is even smaller than the theoretical minima! ss-xitivity. Some nicr properties of the schur realiza-shown in [51 that the realizations that minimize the upper tiuns are !!iscussed. A numerical exarnule that confirms the bound also minimize the sensitiv~ty measure ~tseif aid that, theoretical results is given.

An analytical approach for the synthesis of two-dimensional state-space filter structures with minimum weighted sensitivity

“…A closedform solution that is optimal in a certain sense is obtained. The 1-D version of this closed-form solution turns out to be more efficient than the one proposed in [5]. Notice that the closed-form solution reported in [5] is restrictive and only exists under a certain constraint.…”

“…The 1-D version of this closed-form solution turns out to be more efficient than the one proposed in [5]. Notice that the closed-form solution reported in [5] is restrictive and only exists under a certain constraint. Third, an iterative procedure is presented to find the optimal coordinate transformation that minimizes the weighted -sensitivity measure.…”

“…An analytical method will be developed for obtaining such a matrix . The problem of iteratively minimizing (17) with respect to for any nonsingular that is not block diagonal has been solved in [5]. However, apart from whether the matrix is block diagonal or not, the two problems mentioned above are similar, yet different.…”

“…Notice that (53) can be considered to be an extension of the 1-D closed-form solution reported in [5] to the 2-D case. In Corollary 2 it is mentioned that (53) can be derived from (37) as a special case for the system such that (42) is satisfied.…”

“…Moreover, has the single extremum (24) which is independent of . 1 Noting that has the unique solution [5] (25) where and are symmetric, the matrix is given by (26) and is described by (27) P P P b = (1=)P P P satisfies P P P b K K K o1 P P P b = K K K c2 . Indeed, P P P 01 b = P P P 01 and…”