The tapering of a sampled signal prior to a transformation being applied in order to reduce the effect of any discontinuities at the edges. This is achieved in practice by multiplying the portion of the time domain signal to be transformed by a window function, which is equivalent to convolution in the frequency domain. When, for example, a Fourier transform is being applied, the choice of a suitable window is made as a compromise between keeping local spreading of individual spectral components to a minimum as well as keeping spectral spreading elsewhere low. A number of window functions have been proposed, which are defined for

and zero elsewhere (see table).