Hann-Poisson (``No Sidelobes'')

$$w(n) = \frac{1}{2}\left[1 + \cos\left(\pi\frac{n}{(M-1)/2}\right)\right] e^{-\alpha\frac{\vert n\vert}{(M-1)/2}}$$

• Poisson window times Hann window
  (exponential times raised cosine)
• ``No sidelobes'' for $\alpha\geq 2$
• Valuable for ``hill climbing'' optimization methods
  (gradient-based)

Matlab:

function [w,h,p] = hannpoisson(M,alpha)
%HANNPOISSON  - Length M Hann-Poisson window 

Mo2 = (M-1)/2; n=(-Mo2:Mo2)';
scl = alpha / Mo2;
p = exp(-scl*abs(n));
scl2 = pi / Mo2;
h = 0.5*(1+cos(scl2*n));
w = p.*h;