FFT Convolution Across Frames

For FIR-filtering of very long signals, the
OverLap-Add (OLA) method is often used:

• Partition the input signal into adjacent frames (i.e., using the ``rectangular window'')
• Process each frame as in the previous example
  (zero pad, FFT, window by $H$ , IFFT)
• Sum the (overlapping) frames into an
  overlap-add output buffer

Extensions:

• The FIR filter $h$ can also be broken up into frames
  • Basis for low-latency FFT convolution techniques
• Initial signal partitioning can be a more general overlap-add decomposition (e.g., Hann window with 50% overlap)
  • Needed for nonlinear STFT processing
    (not needed for simple FFT convolution)