Akimitsu Doi

2-D adaptive state-space filters based on the Fornasini-Marchesini second model

Based on the Fornasini-Marchesini second model, a technique is developed for implementing two-dimensional (2-D) adaptive state-space filters. First, the relationship between the coefficient sensitivities and the intermediate transfer functions is investigated for the Fornasini-Marchesini second model. A least mean square (LMS) adaptive algorithm is then presented by using new systems that generate the gradient signals. Finally, a 2-D adaptive line enhancer is constructed by using the 2-D adaptive state-space filter to illustrate the utility of the proposed technique.

Error spectrum shaping in three-dimensional recursive digital filters

Error spectrum shaping is considered in 3-D recursive digital filters. A technique is developed for obtaining the optimal error feedback (EFB) coefficients that minimize the noise variance at the filter output. A detail discussion on the use of symmetry and antisymmetry of the EFB coefficients is also presented. The proposed technique relies on the use of the Lagranges multiplier method. Moreover, the suboptimal EFB with integer coefficients is constructed by using a least-squares discrete-space optimization algorithm. Finally, a numerical example is given to illustrate the utility of the proposed technique.

Design of Multidimensional Separable-Denominator DigitalFilters in the Spatial Domain

Based on a concept of minimal decomposition and balanced realization, a novel technique is developed for designing multidimensional (M-D) separable-denominator digital filters in the spatial domain. This is done by decomposing a desired M-D FIR filter into M parts and by representing it by a cascade connection of M 1-D filters. The minimal decomposition treated here can be viewed as an extension of that in 2-D separable-denominator case in some sense. However, the proposed technique differs from the existing one even in 2-D case and is simpler. Two numerical examples are also given to illustrate the utility of the proposed technique. The amount of calculation required here is relatively small and the stability of the filter is always guaranteed.

A spatial-domain technique for the design of 3-D separable-denominator state-space digital filters

In this paper, a technique for designing 3-D separable-denominator state-space digital filters is developed. The design process is divided into two phases. First, the coefficient matrices related to stability are constructed for the filter to be stable by using alternating variable method. Next, the other matrices are obtained by solving linear equations. These phases are repeated until there is no significant change in the squared error function. Finally, a numerical example is shown to illustrate the utility of the proposed technique.

Design of multidimensional separable-denominator digital filters in the spatial domain

Based on a concept of minimal decomposition and balanced realization, a novel technique is developed for designing multidimensional (M-D) separable-denominator digital filters in the spatial domain. This is done by decomposing a desired M-D FIR filter into M parts and by representing it by a cascade connection of M 1-D filters. The minimal decomposition treated here can be viewed as an extension of that in 2-D separable-denominator case in some sense. However, the proposed technique differs from the existing one even in 2-D case and is simpler. The amount of calculation required here is relatively small and the stability of the filter is always guaranteed.

A technique for the design of 2-D recursive digital filters with guaranteed stability

In the present technique, the denominator and numerator in the filter are designed separately and recursively. First, the denominator coefficients, derived from the stable matrix of the Roesser model (the Fornasini-Marchesini second model), are found by minimizing a performance index through the alternating variable method. The numerator coefficients are then determined analytically by solving linear simultaneous equations. The above process will be repeated until there is negligible change in the objective function. Finally, a numerical example is given to illustrate the utility of the proposed technique.

Joint optimization of high-order error feedback and realization for roundoff noise minimization in state-estimate feedback controllers

Joint optimization of high-order error-feedback and state-space realization to minimize roundoff noise at the output of a closed-loop system with a state-estimate feedback controller subject to l2-scaling constraints is investigated. The problem is converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained optimization problem at hand is then solved iteratively by employing an efficient quasi-Newton algorithm with closed-form formulas for key gradient evaluation. A numerical example is presented to illustrate the utility of the proposed technique.

Design of adaptive state-space digital filters using stable filter structures

A new technique for designing adaptive state-space digital filters using stable filter structures is developed. First, the coefficient sensitivities are related to intermediate transfer functions in order to generate gradient signals. Next, the LMS algorithm is applied to construct adaptive state-space digital filters with new systems to generate gradient signals. To illustrate the validity of the proposed technique, a numerical example is given. In the example, the comparison between the proposed and conventional adaptive filters is presented

A design technique of 2-D separable-denominator state-space digital filters via projection

This paper treats a design technique for 2-D state-space digital filters based on model reduction of 2-D FIR filters. An IIR filter is derived by a matrix projection of original FIR filter and the coefficient matrices are optimized by iterative algorithm. A numerical example is shown to illustrate the validity of the proposed technique.

Minimization of weighted sensitivity for 2-D state-space digital filters described by the Fornasini-Marchesini second model

This paper considers the problem of minimizing the weighted coefficient sensitivity for 2-D state-space digital filters described by the Fornasini-Marchesini (F-M) second model. First, a simple technique is presented for obtaining a set of filter structure with very low weighted L/sub 1//L/sub 2/-sensitivity. Next, an iterative procedure is applied to obtain the optimal coordinate transformation that minimizes the weighted L/sub 2/-sensitivity measure. This is based on the matrix Riccati differential equation. Finally, a numerical example is given to illustrate the utility of the proposed technique.