On 12/04/2016 10:26 AM, Evan Balster wrote:
I haven't yet come across an automated process for designing
high-quality pinking filters, so if someone can offer one up I'd also
love to hear about it!
Last time that I checked (about a year and a half ago) the following
was the best reference that I could find. Unfortuately I'm not yet
sufficiently initiated to follow the Hardy-space methods.
"Simulation of Fractional-Order Low-Pass Filters"
Thomas Hélie (IRCAM)
IEEE/ACM TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING, VOL.
22, NO. 11, NOVEMBER 2014
Abstract:
"""
The attenuation of standard analog low-pass filters
corresponds to a multiple value of decibels per octave. This
quantified value is related to the order of the filter. The issue
addressed here is concerned with the extension of integer orders
to non integer orders, such that the attenuation of a low-pass filter
can be continuously adjusted. Fractional differential systems are
known to provide such asymptotic behaviors and many results
about their simulation are available. But even for a fixed cutoff
frequency, their combination does not generate an additive group
with respect to the order and they involve stability problems. In
this paper, a class of low-pass filters with orders between 0 (the
filter is a unit gain) and 1 (standard one-pole filter) is defined to
restore these properties. These infinite dimensional filters are not
fractional differential but admit some well-posed representations
into weighted integrals of standard one-pole filters. Based on this,
finite dimensional approximations are proposed and recast into the
framework of state-space representations. A special care is given
to reduce the computational complexity, through the dimension
of the state. In practice, this objective is reached for the complete
family, without damaging the perceptive quality, with dimension
13. Then, an accurate low-cost digital version of this family is
built in the time-domain. The accuracy of the digital filters is
verified on the complete range of parameters (cutoff frequencies
and fractional orders). Moreover, the stability is guaranteed, even
for time-varying parameters. As an application, a plugin has been
implemented which provides a new audio tool for tuning the cutoff
frequency and the asymptotic slope in a continuous way. As a
very special application, choosing a one-half order combined with
a low cutoff frequency (20 Hz or less), the filter fed with a white
noise provides a pink noise generator.
"""
There is an AES paper by the same author:
http://dl.acm.org/citation.cfm?id=2693064
HTH,
Ross.
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