||In this thesis, a fuzzy one-mean filtering (FOMF) algorithm is developed which is derived from the Fuzzy c-Means Algorithm when the number of means is one. The FOMF algorithm can be viewed as a kind of weighted mean filter having fuzzy membership values as its weighting coefficients. During the course of studying FOMF, we find that the filters can be applied to a wide range of digital signal and image processing. These include decimation, interpolation, equalization, and noise smoothing. By suitable selection of parameters, FOMF can be configured as an arithmetic mean, or to become a median filter. With some modification, FOMF algorithm can be reconfigured to become FOM derivative filter (FOMDF) which can detect discontinuities of signals in noisy environment better than traditional techniques.