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 $R$ samples, the window must be $\hbox{\sc Cola}(R)$ . 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 $2\pi/R$ . Following established nomenclature for filter banks, we will say that such a window transform is $\hbox{\sc Nyquist}(2\pi/R)$ .