The digital prolate spheroidal window

The optimal window, the time limited sequence whose energy is most concentrated in a finite frequency interval, is related to a particular discrete prolate spheroidal sequence. The optimal window is actually a family of windows with many degrees of freedom. The Kaiser (1974) window is an approximation to this optimal window. Kaiser used this approximation because the standard method employed to compute the optimal window is numerically ill-conditioned. We show the actual optimal window can be efficiently computed by using an alternative formulation of the discrete prolate spheroidal sequences. We then give a set of design formulas to generate the optimal window for the desired window length, mainlobe width, and relative peak sidelobe height.