An overly strong (but sufficient) condition is to require that the window transform be bandlimited consistent with downsampling by :
This condition is sufficient, but not necessary, for perfect OLA reconstruction. Strong COLA implies weak COLA, but it cannot be achieved exactly by finite-duration window functions.
When either of the strong or weak COLA conditions are met, we have
That is, the overlap-add of the window at hop-size is equal numerically to the dc gain of the window divided by .
Choice of WOLA Window
Example 2: Time Domain Aliasing