### WOLA Processing Steps

The sequence of operations in a WOLA processor can be expressed as follows:- Extract the
th windowed frame of data
,
(assuming a length
causal window
and hop
size
).

- Take an FFT of the
th frame translated to time zero,

, to produce the th spectral frame

, . - Process as desired to produce .
- Inverse FFT to produce , .
- Apply a
*synthesis window*to to yield a*weighted*output frame , . - Translate the th output frame to time as and add to the accumulated output signal .

(9.44) |

#### 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

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Overlap-Add (OLA) Interpretation of the STFT

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Length L FIR Frame Filters