Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation

Note 25. Kaiser Windows

One way to structure the window optimization problem is to find the particular time-limited function having the minimum energy outside the main lobe of its frequency response. The solution to this problem, found by Slepian and Pollak [1], involves prolate spheroidal wave functions. Kaiser [2, 3] found an approximate solution that is simpler to compute than the exact solution of Slepian and Pollak. The continuous-time form of the Kaiser window and its frequency response are listed in Math Box 25.1. The specification of the continuous-time window is such that it spans a time interval of (N – 1)T. This span is equivalent to saying that the continuous-time window begins at the time corresponding to sample –(N – 1)/2 and ends ...