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This paper proposes a realization of a two-dimensional adaptive state-space filter for parallel processing using state-space model with a general form. For the modeling of the filter, a generalized model realized for parallel processing is used and the conventional denominator-separation type model is extended. Further, the LMS (Least Mean Square) algorithm is used to construct an adaptive algorithm and its processing speed and computational effort are evaluated. By means of this method, the hardware content can be reduced while the processing speed is maintained almost the same as in the complete generalized model. Finally, in order to verify the effectiveness of the present method, an example is presented in which a two-dimensional adaptive filter is applied to the spatial domain design as a system identification problem. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(1): 46–57, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10019

This paper introduces the parallel processing into the separable-denominator 3-D adaptive state-space filter, and discusses a realization method which is suited to the high-speed processing. the LMS (least-mean-square) algorithm is used as the adaptive algorithm, and the parallel processing-oriented structure of the separable-denominator 3-D filter is used as the filter model. The parallel processing-oriented structure of the 3-D adaptive state-space filter is obtained by extending the adaptive algorithm of the 2-D state-space adaptive filter to the above 3-D structure. the proposed algorithm is evaluated in this paper in terms of the time required for the filtering and the coefficient update, as well as the number of multipliers (adders). Finally, the proposed adaptive filter is applied to the design of the 3-D state-space digital filter, and the effectiveness of the algorithm is demonstrated.

This paper considers the realization of three-dimensional (3-D) adaptive separable-denominator state-space filters suitable for parallel processing. The least mean squares (LMS) algorithm is used to adjust the filter parameters. First, a 3-D local state-space model which is separable in the denominator is realized in a parallel form. Next, the LMS algorithm is employed to adjust the filter parameters in the parallel form. In addition, the computational time and the number of multipliers (adders) required for the realization are estimated. Finally, in a numerical example, the present adaptive filter is applied to the problem of designing a 3-D digital filter in the spatial domain.