Takao Hinamoto

Synthesis of 2-D state-space digital filters with low sensitivity based on the Fornasini-Marchesini model

The balanced realization and low-sensitivity structure of two-dimensional recursive digital filters are considered in the framework of the Fornasini-Marchesini local state-space model. A procedure is introduced for the balanced realization of 2-D recursive digital filters. The sensitivities of a 2-D transfer function are investigated with respect to the coefficients in the local state-space model. The overall sensitivity is evaluated using the 2-D controllability and observability Gramians. The filter structure reducing the overall sensitivity is synthesized for two cases: one free from l/sub 2/ scaling constraints on the state variables and the other under the scaling constraints. These filter structures are shown to be closely related to the balanced realization. An example is given to illustrate the utility of the proposed technique. >

Canonic Form State Space Realization of Two Dimensional Transfer Functions having Separable Denominator

In this paper a procedure is developed for the computation of a state space realization from two dimensional transfer functions with separable denominator. The procedure relies on a canonic form for the state space realization.

A generalized on the study synthesis of 2-D state-space digital filters with minimum roundoff noise

The Fornasini-Marchesini local state-space (LSS) model is used as the basis for a novel expression for the output-noise variance due to roundoff together with an I/sub 2/ scaling on the state variables. An optimal Fornasini-Marchesii LSS model structure is then synthesized that minimizes the output noise due to roundoff, subject to an l/sub 2/ scaling constraint. The synthesis utilizes a 2-D similarity transformation matrix that is not block-diagonal, but general. This requires solving only one optimization problem. Some constraints imposed on the Fornasini-Marchesini LSS model and the 2-D similarity transformation yield the results obtained with the Roesser LSS model. The proposed synthesis theory is therefore quite general and simple. An example is given to illustrate its utility. >

A novel 2-D adaptive filter based on the 1-D RLS algorithm

This paper proposes a novel two-dimensional (2-D) adaptive filter by applying a 1-D recursive least-squares (RLS) algorithm along both horizontal and vertical directions. The relation of the proposed algorithm to a usual 2-D RLS algorithm are investigated. A method that employs a priori estimation error is also considered to accelerate the convergent rate of the algorithm. The proposed filter has a good performance in nonstationary case, and the accuracy of convergence is better than in the existing 2-D least mean square (LMS) adaptive filters. The amount of computations required for the proposed algorithm are relatively small. Finally, an example is given to illustrate the utility of the proposed filter.

Spatial-domain design of a class of two-dimensional recursive digital filters

This paper presents a technique for designing a class of two-dimensional (2-D) recursive digital filters, and also proposes a new state-space model for the 2-D recursive digital filters. The technique is applicable to the design of both quarter-plane causal filters and 2-D weakly causal filters. The filter is designed in terms of a canonic form state-space model, as well as a transfer function. The design is based upon minimization of the sum of squared differences between the desired and actual 2-D impulse responses over a finite interval. The test of stability for such filters is easy.

The Fornasini-Marchesini model with no overflow oscillations and its application to 2-D digital filter design

Based on a two-dimensional (2-D) local state-space (LSS) model that was proposed by E. Fornasini and G. Marchesini (Math. Syst. Theory, vol.12, p.59-72, 1978), a new condition for 2-D discrete systems to be asymptotically stable is introduced. This condition is more general than that based on the Roesser LSS model and includes the latter as a special case. A necessary and sufficient condition for 2-D discrete systems to be asymptotically stable is given in detail, without loss of generality. A criterion that sufficiently guarantees the absence of overflow oscillations in the Fornasini-Marchesini model is shown. The asymptotic stability condition is incorporated in the 2-D filter design.<<ETX>>

The use of strictly causal filters in the approximation of two-dimensional asymmetric half-plane filters

This paper considers the problem of approximating twodimensional (2-D) asymmetric half-plane digital filters using strictly causal filters. A technique is developed by means of certain mapping techniques and singular value decomposition of two finite Hankel matrices. First, a given impulse response over an asymmetric half-plane is transferred into the open first quadrant via an invertible mapping. Second, the data in the transformed domain (open first-quadrant) are approximated by a strictly causal separable-denominator recursive filter using singular value decomposition. Finally, the resultant filter is transferred back to the original coordinates. Since the resulting filter is simpler than a causal filter being separable in the denominator, the implementation is advantageous in addition to having a very easy stability check. Two examples are presented to illustrate the utility of the proposed technique.

Observers for a class of 2-D filters

In this paper, a 2-D observer is proposed for 2-D systems of the Fornasini-Marchesini type. Conditions are given for the existence of the proposed observer where both the case of known and unknown boundary conditions are considered. Design equations are developed for calculation of the observer matrices. Conditions are also given for being able to choose the form of the observer in the simple form for 2-D systems proposed by Attasi. Finally, it is shown how the proposed observer can be used in a feedback scheme to stabilize a 2-D filter having a state-space model of the Attasi type.

Approximation and minimum roundoff noise synthesis of 3-d separable-denominator recursive digital filters

Abstract In respect to a state-space model for causal three-dimensional (3-D) recursive digital filters, a necessary and sufficient condition is derived for a 3-D separable-denominator recursive model to be separately locally controllable and separately locally observable. To approximate a given 3-D digital filter by a 3-D separable-denominator recursive model, a technique is developed via singular value decomposition of three finite Hankel matrices. The resulting 3-D separable-denominator recursive model is advantageous to the computational speed and implementation cost in addition to the ease of stability testing. A roundoff noise analysis and a scaling on state variables are discussed for 3-D separable-denominator recursive models. A technique is then presented for the synthesis of an optimal 3-D separable-denominator recursive model which minimizes the output noise due to roundoff subject to a scaling condition on the state variables. Finally, two examples are given to illustrate the utility of the proposed techniques.

Minimization of sensitivity for MIMO linear discrete-time systems under scaling constraints

The minimization of the coefficient sensitivity and roundoff noise of multi-input/ multi-output linear discrete-time systems under scaling constraints of the dynamic range is discussed. After considering the scaling of the dynamic range, scaled system structures are synthesized in order to minimize the coefficient sensitivity. Then after analysing the roundoff noise, scaled system structures are synthesized to minimize the coefficient sensitivity and roundoff noise simultaneously. The synthesized system structures are also optimized with respect to the scaling parameter. In addition, an efficient algorithm is given for computing the controllability and observability gramians of multi-input/multi-output linear discrete-time systems. Finally, a numerical example is solved to illustrate the utility of the proposed theory.