Strong COLA

An overly strong (but sufficient) condition is to require that the window transform be bandlimited consistent with downsampling by :

This condition is sufficient, but not necessary, for perfect OLA reconstruction. Strong COLA implies weak COLA, but it cannot be achieved exactly by finite-duration window functions.

When either of the strong or weak COLA conditions are met, we have

That is, the overlap-add of the window at hop-size is equal numerically to the dc gain of the window divided by .

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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.