#### Choice of WOLA Window

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

 (9.45)

We can say that -shifts of the window in the time domain are power complementary, whereas for OLA they were amplitude complementary.

A trivial way to construct useful windows for WOLA is to take the square root of any good OLA window. This works for all non-negative OLA windows (which covers essentially all windows in Chapter 3 other than Portnoff windows). For example, the root-Hann window'' can be defined for odd by

Notice that the root-Hann window is the same thing as the MLT Sine Window'' described in §3.2.6. We can similarly define the root-Hamming'', root-Blackman'', and so on, all of which give perfect reconstruction in the weighted overlap-add context.

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Strong COLA