State-space Filter Structures Research Articles

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

This paper considers the problem of synthesizing the finite-word-length (FWL) two-dimensional (2-D) state-space filter structures with minimum weighted sensitivity. Two kinds of frequency-weighted sensitivity measures, one based on a mixture of L/sub 1//L/sub 2/ norms and the other a pure L/sub 2/ norm, are defined in place of the usual sensitivity measure and an upper bound expressed in terms of 2D weighted Gramians is used to evaluate the weighted L/sub 1//L/sub 2/ mixed sensitivity. A simple technique is then developed for obtaining a set of filter structures with very low weighted L/sub 1//L/sub 2/-sensitivity. In this connection, the optimal coordinate transformation is characterized in a closed form. Next, an iterative procedure is proposed to obtain the optimal coordinate transformation that minimizes the weighted L sensitivity measure. Once the initial value is given, the estimate at each iteration can be calculated analytically. Finally, two numerical examples are given to illustrate the utility of the proposed technique.

Synthesis of 2-D state-space filter structures with low frequency-weighted sensitivity

Based on the Roesser (1975) local state-space (LSS) model, new measures are introduced to describe over a particular frequency region the sensitivities of a two-dimensional (2-D) transfer function with respect to state-space parameters. The overall sensitivity derived from these measures is called the frequency weighted sensitivity and is evaluated using 2-D generalized controllability and observability Gramians that are newly defined for 2-D state-space digital filters. Then, 2-D filter structures that minimize the frequency weighted sensitivity are synthesized for two cases of no constraint and scaling constraints on the state variables. These 2-D filter structures can also be optimized with respect to the scaling parameters in the latter case. An example is given to illustrate the utility of the proposed technique.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>