Duality of COLA and Nyquist Conditions

Let $\hbox{\sc Cola}(N)$ denote constant overlap-add using hop size $N$ . Then we have (by the Poisson summation formula Eq.(8.30))

$$\begin{eqnarray*} w &\in& \hbox{\sc Nyquist}(N) \Leftrightarrow W \in \hbox{\sc Cola}(2\pi/N) \qquad \hbox{(FBS)} \\ [10pt] w &\in& \hbox{\sc Cola}(R) \Leftrightarrow W \in \hbox{\sc Nyquist}(2\pi/R) \qquad \hbox{(OLA)} \end{eqnarray*}$$