Definition:
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(4.35) |
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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 [58], 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.