where is acyclic in this context. Stated as a procedure, we have the following steps in an overlap-add FFT processor:
- Extract the th length frame of data at time .
- Shift it to the base time interval (or ).
- Optionally apply a length analysis window (causal or zero phase, as preferred). For simple LTI filtering, the rectangular window is fine.
- Zero-pad the windowed data out to the FFT size (a power of 2), such that , where is the FIR filter length.
- Take the -point FFT.
- Apply the filter frequency-response as a windowing operation in the frequency domain.
- Take the -point inverse FFT.
- Shift the origin of the -point result out to sample where it belongs.
- Sum into the output buffer containing the results from prior frames (OLA step).
A second condition is that the analysis window be COLA at the hop size used:
Poisson Summation Formula
Example of Overlap-Add Convolution