The problem of one dimensional and two dimensional digital filtering in a finite field is studied, with emphasis on the two dimensional case. The problem is formulated in terms of a study of polynomials and rational functions with coefficients belonging to a finite field. For purposes of illustration only binary digital filters are considered but the results obtained extend quite easily to any finite field, GF(q). The main thrust is directed towards a study of the structure and properties of the impulse response of such filters.
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- Digital Filters;
- Rational Functions;
- Periodic Variations;
- Electronics and Electrical Engineering