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Weighted Overlap Add

In the weighted overlap add (WOLA) method, we apply a second window after the inverse DFT [49] and prior to the final overlap-add to create the output signal. Such a window can be called a ``synthesis window,'' ``postwindow,'' or simply ``output window.''

Output windows are important in audio compression applications for minimizing ``blocking effects.'' The synthesis window ``fades out'' any spectral coding error at the frame boundaries, thereby suppressing audible discontinuities.

Output windows are not used in simple FFT convolution processors because the input frames are supposed to be expanded by the convolution, and a synthesis window would ``pinch off'' the ``filter ringing'' from each block, yielding incorrect results. Output windows can always be used in conjunction with spectral modifications made by means of the ``filter bank summation'' (FBS) method, which is the subject of the next chapter.

The WOLA method is most useful for nonlinear ``instantaneous'' FFT processors such as

In these and other nonlinear signal processing operations, the output window helps to suppress artifacts caused by nonlinear spectral modifications. Another common factor in these applications is that filtering effects are not desired, so no provision for ``ringing'' in the time domain is necessary. In other words, WOLA is good for ``instantaneous nonlinear spectral processing.''

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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University