DIRECT DESIGN OF SEPARABLE DENOMINATOR 3-D STATE-SPACE DIGITAL FILTERS.

This paper studies the design problem of causal, recursive and separable denominator (CRSD) 3-D state-space digital filters. A balanced approximation method and a synthesis method of optimal realizations of CRSD 3-D digital filters are proposed by introducing the concept of characteristic filters. Then, a simple equivalent relation between balanced realizations and optimal realizations of CRSD 3-D digital filters is revealed. Using this relation and the balanced approximation method, this paper proposes a spatial-domain direct design method of CRSD 3-D digital filters. This design method can perform approximation and synthesis of CRSD 3-D digital flters simultaneously. It results in stable state-space digital filters which are nearly optimal with respect to roundoff noise, and free of overflow oscillations. The efficiency of direct design method is shown by a numerical example.