Re: [music-dsp] Can anyone figure out this simple, but apparently wrong, mixing technique?

[gjberchin]

>>Message: 1
>>Date: Sat, 10 Dec 2016 14:31:37 -0500
>>From: "robert bristow-johnson" 
>>To: music-dsp@music.columbia.edu
>>Subject: [music-dsp] Can anyone figure out this simple, but apparently
>>  wrong, mixing technique?
>
>>it's this Victor Toth 
>>article:?http://www.vttoth.com/CMS/index.php/technical-notes/68 and it 
>>doesn't seem to make sense to me.
>>
>>it doesn't matter if it's 8-bit offset binary or not, there should not be a 
>>multiplication of two signals in the definition.
>>i cannot see what i am missing. ?can anyone enlighten me?

Search for "automixer". The author is not mixing individual samples, he
is using observed signal magnitudes (that have time constants associated
with them) to determine desired signal magnitudes, and from those
desired magnitudes he is calculating channel gains.

At least I hope that's what he's doing.

I implemented "Dugan" automixers while at Altec Lansing; also one or two
of my own that addressed some of the Dugan shortcomings. Alas, they
never made it to market.

Greg

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Re: [music-dsp] Iterative decomposition of an arbitrary frequency response by biquad IIR

[gjberchin]

On Wed, 05 Mar 2014 12:11:23 -0500, Marco Lo Monaco wrote:

Ciao Greg,
any chances to download your paper somewhere? I am also interested in it :)

Marco, I'm sending it to the email address listed in your message.
Others, please send me email if you want copies. I receive Music-DSP in
digest form, and frankly I don't always read the whole thing, so I might
miss your request.

Greg

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Re: [music-dsp] crossover filtering for multiband application

[gjberchin]

On Tue, 26 Feb 2013 17:35:56 -0500, James C Chandler Jr wrote:

The parallel config I'd been thinking about, inspired by your diagrams, would 
be
slightly different--

For instance in your figure 8-7 Three-way crossover, substitute an AllPass2 
for
your LP2 in the Low output. 

And in your figure 8-10 Four-way crossover, substitute an AllPass2 for HP2 in
the High output, and also substitute an Allpass2 for your LP2 in the Low 
output. 

I do not understand why you would want to do this. While it will provide you
with your desired constant transition band slopes, the responses will no
longer sum to allpass.

The preliminary result (barring foolish mistakes)-- A parallel configuration
using one fourth order highpass and one fourth order linkwitz riley lowpass 
for
each midband, and one highpass in the high band, and one lowpass in the low
band-- It does show symmetrical band skirts between the bandpass interior
sections. They mix surprisingly flat, but not exactly so. There are slight
deviations. It mixes together unity-gain at very high and very low frequencies
but gradually accumulates about a half dB gain nearing the center of the audio
spectrum.

What you describe is exactly what I would expect with the LP filters and HP
filters replaced by AP filters.

On the other hand, trying a binary-tree with the same assortment of filters--
The binary-tree did not show perfectly symmetrical band skirts (as expected),
though the skirts are fairly symmetrical. The big surprise-- This binary-tree
with non-symmetrical band skirts-- It mixes ruler flat over the entire audio
spectrum! That is non-intuitive and I want to experiment more with the
spreadsheet to better understand it. 

It is non-intuitive, but it is mathematically correct.

With the binary-tree crossover network, the mid-band gain of each bandpass
section is almost the same but not quite. With the binary-tree crossover
network, adjacent bands' gains at each crossover frequency are almost 
identical
but not quite. However, the entire tree mixes flat anyway, at least in the
spreadsheet. Interesting as I didn't expect it to work that way.

That might be due to slight differences in the positioning of the cutoff
frequencies -- are they *exactly* one octave apart? 

For most people's use of hard limiters as in-line effects, a multiband hard
limiter might be a weird animal? 

Yes, very much so. I only used a limiter example because it was the simplest
way to demonstrate my point about the effects at the crossover frequencies. I
don't think I've ever actually seen a multiband limiter in practice.

Because if a limiter has been inserted to avoid clipping in the broadband
signal, then merely limiting each band could never guarantee absence of 
clipping
after the bands are summed back together?

Yes, but the same applies to a multiband compressor, to a lesser extent.

What configuration makes sense to you, which would be transparent flat when
dynamics are not applied, but would do the right thing to signals near 
crossover
points?

You'd have to run two parallel paths -- a traditional crossover that sums to
unity gain, to separate the audio signal; and a non-traditional bandsplitter in
which the frequency bands overlap, for analysis of the audio signal. 

The configuration is best described by example. Assume that two of your desired
bands extend from 500 Hz to 1000 Hz, and from 1000 Hz to 2000 Hz. Your
SEPARATION path might consist of a traditional Linkwitz-Riley crossover, in
which case filter spanning 500-1000 Hz would be down 6 dB at 1000 Hz, and the
filter spanning 100-2000 Hz would also be down 6 dB at 1000 Hz. But the bands in
your ANALYSIS path would overlap, such that the 500-1000 Hz band would be at 0
dB at 1000 Hz and attenuate as steeply as possible above that frequency.
Similarly, the 1000-2000 Hz band would be at 0 dB at 1000 Hz and attenuate as
steeply as possible below that frequency. You would use the output from the
ANALYSIS path as a sidechain to determine gains to be applied to signals in the
SEPARATION path. Afterward, you would recombine the signals in the SEPARATION
path.

One alternative that comes to mind is to use a separate non flat crossover
network to drive the side chain, so that levels are sensed in a more realistic
fashion near the crossover points? 

Exactly.

Also, with fourth-order linkwitz riley bands, a crossover network with 
NUMEROUS
fairly narrow bands would not show as much crossover point amplitude error,
compared to a multiband compressor with a small number of wide bands? 

Whether that is troublesome is a judgment call.

Greg

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[music-dsp] crossover filtering for multiband application

[gjberchin]

I am coming-in late on this discussion, so please forgive me if I miss the point
entirely, but it appears that there is some confusion about the use of allpass
compensation filters in Linkwitz-Riley crossovers.

Ok, I have some interesting results, with 3-band and 4-bands constructed
in following fashion:

split freqencies S1, S2:
S1 - LPFa, HPFb, APFc
S2 - APFa, LPFb, HPFc

--\-P-LPFa-APFa-\(P = processing)
\-P-HPFb-LPFb-\
 \-P-HPFc-APFc-+-

split freqencies S1, S2, S3:
S1 - LPFa, HPFb, APFc, APFd1
S2 - APFa1, LPFb, HPFc, APFd2
S3 - APFa2, APFb, LPFc, HPFd

--\-P-LPFa-APFa1-APFa2-\
\-P-HPFb-LPFb-APFb---\
 \-P-HPFc-LPFc-APFc---\
  \-P-HPFd-APFd1-APFd2-+-

Surprising to me was the discovery that frequency of APFs are
significant, and from what I tried the setting above worked the best -
taking freqencies of the other splits. This works very well in most
cases, however there is now a slight boost when the splits are very near:
http://i.imgur.com/nYOXkTi.jpg
The APFs are constructed as I described by the resources linked by
Joshua - a LR4 with no processing, and for all filters Q = 0.7071.
This results are an improvement, and give an idea how to make a
geneneral n-band crossover (though using n*(n-1) filters), however if
anyone knows how to avoid the slight boost, or can explain about the APF
frequencies and Q, or has different ideas how to do this altogether,
please share.

First, allow me to reference Active Realization of Multiway All-Pass Crossover
Systems by Joseph A. D’Appolito; Journal of the Audio Engineering
Society, Volume 35, Number 4, April 1987, which explains the need for the
allpass compensation.

Next allow me to direct you to pages 8-11 through 8-21 (and particularly the
bottom of page 8-20; Sum-to-Allpass Characteristics of Linkwitz-Riley
Crossovers) of http://www.electrovoice.com/downloadfile.php?i=971398 (big
download -- 13 MB).

Regarding the frequencies and quality factors (Q) of the allpass filters; they
can be determined from the sums of the lowpass and highpass transfer functions
of the particular Linkwitz-Riley crossover in use. For example, a 2nd-order LR
crossover has (normalized freq):

   1
Hlp = 
  s^2 + 2s + 1

  -s^2
Hhp = 
  s^2 + 2s + 1

Add them together and you have:

1 - s^2   -(s^2 - 1)-(s-1)(s+1)   -(s-1)
Hlp+Hhp =  =  = --- = --; an allpass filter.
  s^2 + 2s + 1   s^2 + 2s + 1(s+1)(s+1)(s+1)

Similar analysis can be performed for higher-order LR crossovers.

I hope that this is actually helpful; as I said I came to the party late so it
might have already been discussed.

Greg Berchin

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Re: [music-dsp] ITU 1770 RLB filter coefficients and biquad IIR filter

[gjberchin]

On Wed, 16 Jan 2013 06:07:51 -0500, robert bristow-johnson wrote:

if i were to try to re-calculate the coefficients, i would first factor 
out the constant gain, then factor both numerator and denominator into 
discrete-time poles and zeros.  then map those poles and zeros back to 
analog poles and zeros using, i suppose the inverse bilinear transform 
(with warping).  then re-transform back with the bilinear transform with 
the new sampling rate.

i dunno.  that's how i might approach it.

I just caught the tail end of this thread, so forgive me if this has
been mentioned before, but Frequency Domain Least Squares (FDLS) is
perfect for this application. Original IEEE article is available at
http://ieeexplore.ieee.org/xpl/login.jsp?tp=arnumber=4049924url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F79%2F4049870%2F04049924,
or directly from me. MATLAB code is available from IEEE; your choice of
MATLAB or C++ code is available directly from me. 

Greg Berchin
gjberchin (at) charter (dot) net 
(note that Reply-To: field is corrupted)

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