- Extract the
th windowed frame of data
(assuming a length
- 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 .
COLA constraint becomes
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
Overlap-Add (OLA) Interpretation of the STFT
Length L FIR Frame Filters