Optimum Filter :-

A filter is a system that is designed to process signals into those we desire. The purpose of using a filter can be various, to extract a desired signal from noisy data (measurement), to transform signals, to suppress noise, to separate two signals that are mixed in one measurement, etc. An optimum filter is such a filter used for acquiring a best estimate of desired signal from noisy measurement. It is different from the classic filters like lowpass, highpass and bandpass filters. Optimal filters are optimum because they are designed based on optimization theory to minimize the mean square error between a processed signal and a desired signal, or equivalently provides the best estimation of a desired signal from a measured noisy signal.