Formally, a filter is defined in terms of a Set and a Set of Subsets of . Then is called a filter if

- 1. ,
- 2. the Empty Set ,
- 3. and Implies ,
- 4. Implies .

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).

**References**

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.

© 1996-9

1999-05-26