In signal processing, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval. For instance, a function that is constant inside the interval and zero elsewhere is called a rectangular window, which describes the shape of its graphical representation. When another function or a signal (data) is multiplied by a window function, the product is also zero-valued outside the interval: all that is left is the part where they overlap; the "view through the window". Applications of window functions include spectral analysis, filter design, and beamforming.
A more general definition of window functions does not require them to be identically zero outside an interval, as long as the product of the window multiplied by its argument is square integrable, that is, that the function goes sufficiently rapidly toward zero.
In typical applications, the window functions used are non-negative smooth "bell-shaped" curves, though rectangle, triangle, and other functions are sometimes used.
Read more about Window Function: Applications, Window Examples, Comparison of Windows, Overlapping Windows, Two-dimensional Windows
Famous quotes containing the words window and/or function:
“It is a pleasure to stand upon the shore, and to see ships tossed upon the sea: a pleasure to stand in the window of a castle, and to see a battle and the adventures thereof below: but no pleasure is comparable to standing upon the vantage ground of truth ... and to see the errors, and wanderings, and mists, and tempests, in the vale below.”
—Francis Bacon (1561–1626)
“Morality and its victim, the mother—what a terrible picture! Is there indeed anything more terrible, more criminal, than our glorified sacred function of motherhood?”
—Emma Goldman (1869–1940)