Hop Sizes for WOLA

In the weighted overlap-add method, with the synthesis (output) window equal to the analysis (input) window, we have the following modification of the recommended maximum hop-size table:

L In and Out Window (Length $ M$ ) $ R_{\hbox{max}}$ $ R_{\hbox{\hbox{\sc Cola}}}$
1 Rectangular ($ L=1$ ) M/2 M
2 Generalized Hamming ($ L=2$ ) M/6 M/3
3 Blackman Family ($ L=3$ ) M/10 M/5
L $ L$ -term Blackman-Harris M/(4L-2) M/(2L-1)
Note that the following properties hold as before in the OLA case:
  • $ R_{\hbox{max}}$ is equal to $ 2\pi$ divided by the main-lobe width in ``side lobes'', while

  • $ R_{\hbox{\hbox{\sc Cola}}}$ is $ 2\pi$ divided by the first notch frequency in the window transform (lowest available frame rate at which all frame-rate harmonics are notched).

  • For windows in the Blackman-Harris families, and with main-lobe widths defined from zero-crossing to zero-crossing, $ R_{\hbox{\hbox{\sc Cola}}} = 2 R_{\hbox{max}}$ .


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Hamming Overlap-Add Example
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Properly Anti-Aliasing Window Transforms