Definition:

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.3.12.

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 [52], as shown in Fig.3.13. 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 (Fig.3.12b).

Figure 3.14 also shows the slope and curvature of the Hann-Poisson window transform, but this time with increased to 3. We see that higher further smoothes the side lobes, and even the curvature becomes uniformly positive over a broad center range.

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.