Algebraic Structure of Classes of Nonlinear Filters

ABSTRACT In this research paper, it is shown that the class of all Boolean rank order filters are represented using the class of all Positive Symmetric Boolean functions. Using this result, it is shown that the class of all permutation invariant filters are equivalent to the class of rank order filters. The algebraic structure of Positive Boolean symmetric functions and Positive Boolean functions is explored. Also, some basic properties of Positive Symmetric Boolean Functions are determined. It is reasoned that non-linear filters obeying threshold decomposition are a structured class of polynomial filters.