Dual of Constant Overlap-Add

In this section, we will derive the Fourier dual of the Constant OverLap-Add (COLA) condition for STFT analysis windows (discussed in §6.1). Recall that for perfect reconstruction using a hop-size of samples, the window must be . We will find that the equivalent frequency-domain condition is that the window transform must have spectral zeros at all frequencies which are a nonzero multiple of . Following established nomenclature for filter banks, we will say that such a window transform is .

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Subsections

• Poisson Summation Formula
• Frequency-Domain COLA Constraints
  • Strong COLA
  
  
• PSF Dual and Graphical Equalizers
• PSF and Weighted Overlap Add
• Example COLA Windows for WOLA

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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.