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 §7.1). 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 .

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