#### 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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System Diagram of the Running-Sum Filter Bank

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Strong COLA