The original Csound source has a set of coefficients for this type of
hilbert transform but they don't say how the coefficients were derived
and the performance is fairly lackluster. The only reference I've come
across for this was Olli Niemitalo's:
http://yehar.com/blog/?p=368
He gives a bit of theory, but the filter pair he provides doesn't give
great performance.
I was able to use Olli's filter as a starting point for optimization of
a higher order AP set that gave almost 20dB better image rejection. I
interpolated the originals to a higher order and then used simulated
annealing with a cost function that included the bandwidth and image
rejection. Rather brute-force, but it worked.
Eric
On 02/04/2017 04:32 PM, robert bristow-johnson wrote:
hey guys,
what's the best online reference you can tell me for theory and practice
of designing APF pairs with ± 45° phase (+ a linear phase that
represents causality delay) to result in a Hilbert pair for audio
processing. i know how to do this for FIR and to use half-band
symmetry, but i wanna make a MATLAB program where i can specify order
and come up with an optimal pair of IIR APFs that have virtually 90°
phase difference over the widest possible frequency range. also some
discussion of error metric would be good (how do we decide what is
"optimal"?). eventually, i wanna compare computational effort with the
half-band FIR Hilbert transformer.
anyone have a good, definitive reference?
thanks.
--
r b-j r...@audioimagination.com
"Imagination is more important than knowledge."
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