In this paper we describe a new family of smooth power complementary windows which exhibit a very high level of localization in both time and frequency domain. This window family is parameterized by a "smoothness quotient". As the smoothness quotient increases the window becomes increasingly localized in time (most of the energy gets concentrated in the center half of the window) and frequency (far field rejection becomes increasing stronger to the order of 150 dB or higher). A closed form solution for such window function exists and the associated design procedure is described. The new class of windows is quite attractive for a number of applications as switching functions, equalization functions, or as windows for overlap-add and modulated filter banks. An extension to the family of smooth windows which exhibits improved near-field response in the frequency domain is also discussed. More information is available at http://www.atc-labs.com/technology/misc/windows.
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