Overlap-Save Method

The OverLap-Save (OLS) method, unlike OLA, uses no zero padding to prevent time aliasing. Instead, it

1. discards output samples corrupted by time aliasing each frame, and
2. overlaps the input frames by the same amount.

• In general, if the input frame size is $M=N$ and the FIR filter length is $L<N$ , then after convolution, $L-1$ samples of the output are invalid due to time aliasing

• For causal filters of length $L$ :
  • The invalid samples are the first $L-1$ samples of each length $N$ inverse FFT, because these samples are computed using time-aliased samples from the end of the length $N$ FFT input frame

  • Therefore, the input signal should have at least $L-1$ leading zeros

  • The hop size is set to $R=N-L+1$ so that the last $L-1$ samples of frame 1 become the first segment of frame 2. These samples have already been output from frame 1 and can now be overwritten by time aliasing by the processing of frame 2.

  • The length $N$ blocks overlap by $L-1$ samples. $L-1$ samples from the previous block are ``saved'' rather than reread from disk--hence the name ``OverLap Save (OLS)''.

• For anticausal filters:
  • The invalid samples are at the end of the frame
  • The input signal needs no leading zeros
  • The hop size is again $R=N-L+1$
  • Samples 0 through $R-1$ are written out, ignoring the last $L-1$ samples corrupted by time aliasing

• For general non-causal FIR filters, there are bad samples at the beginning and end of each inverse FFT.

• The overlap-save method is generally somewhat more efficient than the overlap-add method because it does not use zero padding, and there is no overap-add on output

• Exercise: Compare the computational complexities of overlap-add and overlap-save for the case $N=M+L-1$ , where $M$ is the frame length, $L$ is the filter length, and $N$ is the FFT size. Show that zero-phase filters yield the most efficient overlap-save scheme for a given filter length $L$ .