Not that I pretend to know much theory -- but I think these filters don't
add up simply because they're not designed to do so. If one wants these
filters to add up he has to patch them in some way. But at this stage it's
already complicated by the uncooperative design.
Some observation on phase and group delays in this context: 1+z^-1 and
1-z^-1 add up; so do 1/(1+0.5z^-1) and 0.5z^-1/(1+0.5z^-1). They all shift
phases but their sums don't, because they are designed to add up.
xue
-----Original Message-----
From: Theo Verelst
Sent: Thursday, February 28, 2013 1:30 PM
To: music-dsp@music.columbia.edu
Subject: Re: [music-dsp] crossover filtering for multiband application
About the multi band filtering:
- *All* filtering you can do, either analog or digital, will
inevitably have phase shifting as a consequence, no matter what people
will try to tell you about correcting networks (check out the theory and
preferably do your homework: ALWAYS is ALWAYS. And "zero phase" is a
term from Control Theory, not filter theory, which REALLY means
something else than "zero phase shift" in general)
- *All* filters, analog (all the well known filter kinds with the well
known names since early radio technology in the 1900s), and digital, be
it Finite or Infinite impulse response (of course "linear"), are far
from orthogonal, and also are mostly far from adding up to the original
signal when combined+inverted. Check it out, and beware why all the
stuff about amplifiers and audio production never much gets there where
it sounds great: it's a complicated problem where most of the people
working this way have little knowledge of even the most basic theories.
- *Almost all* digital filters being in use and talked about here will
have very serious, measurable and audible sampling issues. Really, a
44.1kHz sampled digital signal processing system reproducing a 1 kHz
wave with only 45 samples IS GOING TO DISTORT (unles you know exactly
what you are doing and/or the system isn't causal (or has very long
delay)), and WILl HAVE very serious non-linearities, in most cases
discussed here.
- *Even if* you make a sort of partially (please, check out the theory
and compute you filter amplitude and phase response (MATLAB/Octave
graphs for all I care), and be a bit honest) phase corrected and
somewhat amplitude and squared amplitude "adding up" filter bank in
digital, or in some cases in (more or less linear) analog form, YOU WILL
GET GROUP DELAY issues. ***ALLWAYS*** ... (unless you do other work too,
and know things about the signals you're going to send through the
system, etc.)
No that I like to be the theoretical spoilsport, but unless I observer
more theoretically and practically interesting constructions and
synthetic considerations which can work, the whole field of DSP seems to
be very inviting for generation after generation of quacksalvers, trying
to come across as relevant. This is not very useful, unless people like
their hobby-ing around, of course, no scientific problem with that, but
making things work at a serious EE level is very little served by all
the considerations I've seen here, except of course some subjects get
mentioned, which of course is fine.
So don't be fooled too much by fancy DSP language or grand filter type
names: it isn't easy to built a working multi-compression system,
ESPECIALLY if yo want it to sound good, comply with certain loudness
controlling rules, and work on general signals.
It is possible to create a nice filter bank and get work done by it, to
have a digital workstation do multi-compression on it's synthesized
voices, and to put a CD or other recording through a radio type of
multi-band processor, but in most cases, there are things known about
the signals that go through such machinery, and it every case ot pays to
not forget the main theories at hand, which amoung other things say: the
higher the sampling rate, the more apt (not "the more complicated", but
often "the more natural", as in forming a parallel with mechanical
systems) and of course the more accurate bits being used, the better the
result will sound!
Regards,
T. Verelst
P.S. I'm aware of the many caps here, but seriously, I've observed DSP
stuff for decades, and can't help feeling there's a great need for
theory. I made well working low distortion, low order Butterworth analog
filter bands for my monitoring systems, 30 band double multi-compressed
recording path DSP from Ladspa blocks running at 192kHz/32bit, sampling
distortion averaging signals paths with mastering effects, and very
successful synthesizer multi and single compressed sounds (a.o. with a
Kurzweil), so I know stuff can be done with good sounding results, but
the directions of many hakl-scientific approaches usually falls through
as insufficient.
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