Abstract

In this research paper, threshold decomposition property (arising in the case of rank order order filters) is generalized to bipolar signals. By associating a square "threshold matrix" with a digital signal, its linear algebraic properties are investigated. Also, most general class of nonlinear filters for which the weak superposition property (based on threshold decomposition) holds (in the spirit of rank order filters) are identified. Partition theoretic interpretation of threshold decomposition is explored. It is reasoned that columnwise Boolean median filtering leads to faster implementation of median filter.