Design of Multidimensional Digital Filters via System Balancing Concept and its CAS System

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The controllability and observability gramians are defined for multi-dimensional state-space digital filters. Using the controllability and observability gramians, balanced realizations of multi-dimensional state-space digital filters are synthesized.Sensitivity of one- and multi-dimensional state-space filters is analyzed by using the state-space description. This analysis shows that sensitivity of linear multidimensional state-space digital filters is described by their controllability gramian and the observability gramians. Sensitivity can be minimized by using equivalent transformations, and as a result minimum sensitivity of multi-dimensional state-space digital filters can be achieved when their controllability gramian and observability gramian are identical.Several design methods of multi-dimensional state-space digital filters are proposed. These methods design multi-dimensional state-space digital filters via system balancing concept, and can approximate given frequency or spatial domain specifications with very small error. The computational time for the design can be reduced to half of conventional design method by utilizing symmetries of specifications.Computer programs for multi-dimensional state-space digital filtering, system balancing, and several design methods are implemented in FORTRAN and C.