## Hann-Poisson Window Definition: (4.35) The Hann-Poisson window is, naturally enough, a Hann window times a Poisson window (exponential times raised cosine). It is plotted along with its DTFT in Fig.3.21. The Hann-Poisson window has the very unusual feature among windows of having no side lobes'' in the sense that, for , the window-transform magnitude has negative slope for all positive frequencies , as shown in Fig.3.22. As a result, this window is valuable for hill climbing'' optimization methods such as Newton's method or any convex optimization methods. In other terms, of all windows we have seen so far, only the Hann-Poisson window has a convex transform magnitude to the left or right of the peak (Fig.3.21b). Figure 3.23 also shows the slope and curvature of the Hann-Poisson window transform, but this time with increased to 3. We see that higher further smooths the side lobes, and even the curvature becomes uniformly positive over a broad center range. ### Matlab for the Hann-Poisson Window

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;


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