Abstract
The rank ordering of samples is widely used in robust signal processing. Recent advances have combined the rank ordering of samples with the natural time or spatial ordering of the observations through fuzzy set theory. This has lead to a novel set of signal processing tools, namely fuzzy time–rank (TR) relations, fuzzy time and rank ordered samples, and fuzzy time and rank indices. This paper reviews the fundamentals in this emerging area and presents two new algorithms: the fuzzy rank conditioned median filter, which is a generalization of the rank conditioned median filter, and the fuzzy rank order detector, which may be viewed as an extension of the maximum rank sum receiver. The superior performance of both algorithms is demonstrated in image processing and communications applications.
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