On the construction of window functions with constant-overlap-add constraint for arbitrary window shifts

In this paper we present a construction method for window functions with constant-overlap-add (COLA) constraint for spectral analysis-synthesis with a given percentage of window overlap. The window functions are derived from the shortest possible COLA window i.e., the rectangular window. The construction method allows to adjust the side-lobe fall-off and to fulfill the COLA constraint for arbitrary window shifts. The procedure results in a family of window functions which includes some well known members (the Bartlett and the Hann window) for 50% overlap.