Financial support provided by Purdue through University Fellowships and the National Science Foundation under grant ECS83-06235 is greatly appreciated.


Median filters are a special class of ranked order filters used for smoothing signals. These filters have achieved- success in speech processing, image processing, and other impulsive noise environments where linear filters have proven inadequate. Although the implementation of a median filter requires only a simple digital operation, its properties are not easily analyzed. Even so, a number of properties have been exhibited in the literature. In this thesis, a new tool, known as threshold decomposition is introduced for the analysis and implementation of median type filters. This decomposition of multi-level signals into sets of binary signals has led to significant theoretical and practical breakthroughs in the area of median filters. A preliminary discussion on using the threshold decomposition as an algorithm for a fast and parallel VLSI Circuit implementation of ranked filters is also presented* In addition, the theory is developed both for determining the number of signals which are invariant to arbitrary window width median filters when any number of quantization levels are allowed and for counting or estimating the number of passes required to produce a root- i.e. invariant signal, for binary signals. Finally, the analog median filter is defined and proposed for analysis of the standard discrete median filter in cases with a large sample size or when the associated statistics would be simpler in the continuum

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