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- A perfect reconstruction (PR) filter bank is any filter bank
whose reconstruction is the original signal, possibly delayed, and
possibly scaled by a constant.
- In this context, critical sampling (also called
``maximal downsampling'') means that the downsampling factor is the
same as the number of filter channels. For the STFT, this implies
(with
for Portnoff windows).
- The short-Time Fourier transform (STFT) is a PR filter bank
whenever the constant-overlap-add (COLA) condition is met by the
analysis window
and the hop size
. However, only the
rectangular window case with no zero-padding is critically sampled
(OLA hop size = FBS downsampling factor =
).
- Advanced audio compression algorithms (``perceptual audio
coding'') are based on critically sampled filter banks, for obvious
reasons.
- Important Point: We normally do not require
critical sampling for audio analysis, effects, and music
applications. We normally only need it when compression is a
requirement.
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Download JFB.pdf
Download JFB_2up.pdf
Download JFB_4up.pdf
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