WOLA Window Construction

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 includes essentially all typical windows).

• For example, the ``root-Hann window'' can be defined for odd $M$ by
  $$\begin{eqnarray*} w(n) &=& w_R(n) \sqrt{\frac{1}{2} + \frac{1}{2} \cos( 2\pi n/M) } \\ &=& w_R(n) \cos(\pi n/M), \; n= -\frac{M-1}{2},\ldots,\frac{M-1}{2} \end{eqnarray*}$$
  

• Notice that the root-Hann window is essentially the same thing as the ``MLT Sine Window'' described in the lecture on FFT windows.

• Similarly, we can define the ``root-Hamming'', ``root-Blackman'', and other windows for perfect reconstruction in the weighted overlap-add context.