From Audacity-Nyquist Digest, Vol 15, Issue 6:
> Don't blame the math. All of the common linear
filters
> can be represented in a mathematically equivalent
form
> using FFTs. That means if you do it right you should
get
> the same results. The artifacts usually come from
using
> intuition to invent filters in FFT (spectra) space
rather
> than going back to filter theory and doing the math.
Well, I think this needs some clarification too:
I believe that the statement (above) is true if you can take
a DFT of
the entire input signal, but that might be computationally
impractical
and numerically inaccurate. Assuming you need to use an
overlap/add STFT
approach, there is no mathematical equivalent to IIR filters
(which are
common linear filters) because the infinite response would
not be
contained within a finite window. FIR filters can always be
implemented
in a mathematically equivalent way (ignoring any numerical
issues)
through fast convolution based on overlap add/overlap save
algorithms.
-Roger
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