Based on controllability gramians, observability gramians and second order modes, this paper shows that optimal realizations (filter structures having minimum roundoff noises) of quarter-plane-causal, recursive and separable in denominator 2-D digital filters (CRSD) filters are scaled and rotated balanced realizations. Two applications are given. The first gives a simple proof of the absence of overflow oscillations in optimal realizations. The second which is the main result of this paper, gives a direct design method of CRSD filters in the spatial domain. This method simplifies traditional two-step design (approximation and synthesis) into a one-step design with less computational complexity. Resulting filters of this direct design can approximate given 2-D impulse responses closely. They are always guaranteed to be stable, nearly optimal with respect to roundoff noise and free of overflow oscillations. The efficiency of the direct design method is shown by numerical examples.
|Number of pages||9|
|Journal||Transactions of the Institute of Electronics and Communication Engineers of Japan. Section E|
|Publication status||Published - 1986 Oct 1|
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