Filter

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 offiltering and filter functions is particularly useful in engineering. One particularly elegant method offiltering Fourier Transforms a signal into frequency space, performs the filteringoperation 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.

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