Formally, a filter is defined in terms of a Set and a Set of Subsets of . Then is called a filter if
Informally, a filter is a function or procedure which removes unwanted parts of a signal. The concept of filtering and filter functions is particularly useful in engineering. One particularly elegant method of filtering Fourier Transforms a signal into frequency space, performs the filtering operation there, then transforms back into the original space (Press et al. 1992).
See also Savitzky-Golay Filter, Wiener Filter
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T.
``Digital Filtering in the Time Domain.'' §13.5 in
Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England:
Cambridge University Press, pp. 551-556, 1992.