Window function Wikipedia. In signal processing, a window function also known as an apodization function or tapering function1 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 waveformdata sequence 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. In typical applications, the window functions used are non negative, smooth, bell shaped curves. 2 Rectangle, triangle, and other functions can also be used. 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, and, more specifically, that the function goes sufficiently rapidly toward zero. 3ApplicationseditApplications of window functions include spectral analysismodificationresynthesis,4 the design of finite impulse response filters, as well as beamforming and antenna design. Spectral analysiseditThe Fourier transform of the function cos t is zero, except at frequency. However, many other functions and waveforms do not have convenient closed form transforms. Alternatively, one might be interested in their spectral content only during a certain time period.
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