Choice of WOLA Window

The synthesis window in weighted overlap-add is typically chosen to be the same as the input window, in which case the COLA constraint becomes

$$\zbox{\sum_m w^2(n-mR) = \hbox{constant}}$$

We can say that $R$ -shifts of the window $w$ in the time domain are power complementary (power-partition of unity), whereas for OLA they were amplitude complementary.