In the Fourier transform, the first null after the main lobe occurs at formula_4 which is just formula_5 in units of N (DFT "bins"). As "α" increases, the main lobe increases in width, and the side lobes decrease in amplitude.   = 0 corresponds to a rectangular window. For large the shape of the Kaiser window (in both time and frequency domain) tends to a Gaussian curve.  The Kaiser window is nearly optimal in the sense of its peak's concentration around frequency "0".