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
.

To obtain perfect reconstruction in the absence of spectral modifications, we require

which is true if and only if

(9.44) |

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University