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Nonlinear Filters with Symmetry Constraints


R. Pearson

IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing (NSIP), Antalya, Turkey

Nonrecursive digital filters are popular because they are inherently stable, unlike their recursive counterparts, and have been shown to be effective in a wide variety of situations. For example, Astola and Kuosmanen describe $20$ different classes of nonrecursive filters cite{astola97}, many of which are included in the general class of nonlinear smoothing filters considered by Mallows cite{mallows80}. This paper defines three classes of nonrecursive filters based on symmetry restrictions and explores some of the consequences of these restrictions. Specific examples of each class are presented, general procedures are given for constructing new filters in each class from known examples, and the influence of these symmetries on root sequences is examined.


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