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Embedded SystemsFPGAElectronics

Spectral Audio Signal Processing
    The Filter Bank Summation (FBS) Interpretation of the Short Time Fourier Transform (STFT)
       Downsampled STFT Filter Banks
          Downsampling with Anti-Aliasing
             Hop Sizes for WOLA

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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 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}}$.

Previous: Properly Anti-Aliasing Window Transforms
Next: Constant-Overlap-Add (COLA) Cases

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About the Author: 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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