Specific Windows

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Recall that the rectangular window transform is $\hbox{\sc Nyquist}(2\pi/M)$ , implying the rectangular window itself is $\hbox{\sc Cola}(M)$ , which is obvious.
The window transform for the Hamming family is $\hbox{\sc Nyquist}(4\pi/M)$ , implying that Hamming windows are $\hbox{\sc Cola}(M/2)$ , which we also knew.
The rectangular window transform is also $\hbox{\sc Nyquist}(K2\pi/M)$ for any integer $1\leq K\leq M/2$ , implying that all hop sizes given by for $K=1,2,\ldots,M/2$ are COLA.
Because its sidelobes are the same width as the sinc sidelobes, the Hamming window transform is also $\hbox{\sc Nyquist}(K2\pi/M)$ ,for any integer $2\leq K\leq M/2$ , implying hop sizes are good, for $K=2,\ldots,M/2$ . Thus, the available hop sizes for the Hamming window family include all of those for the rectangular window except one ().

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.

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