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window function

(windowing function)
(function with a zero value outside some specific range)

A window function (or windowing function) is a function which evaluates to zero outside a portion of its range. Window functions are used as a means of adapting another function to apply to a particular range, for use in models and analysis. A function can be multiplied by a window function to produce an adaptation of the original function which evaluates to zero outside a range of interest. A step function with values of zero or one is an obvious kind of window function, but others are adapted to preserve particular qualities or prevent particular distortions and noise (analogous to aliasing), and typically are in the general shape of a bell curve, but specifically curves that reach zero in each direction within a finite interval. An example type of windowing function used for functions of a sphere (e.g., specified by a multipole expansion) is a Slepian window function.