Hi, Klaus.
>From the top of my head, maybe something like this:
import("stdfaust.lib");
avg(t, x) = fi.pole(p, (1 - p) * x) // 1-pole lowpass as average
with {
p = exp((((-2.0 * ma.PI) / t) / ma.SR));
};
var(t, x) = avg(t, (x - avg(t, x)) ^ 2); // variance
sd(t, x) = sqrt(var(t, x)); // standard deviation
cov(t, x1, x2) = avg(t, (x1 - avg(t, x1)) * (x2 - avg(t, x2))); //
covariance
corr(t, x1, x2) = cov(t, x1, x2) / max(ma.ma.EPSILON, (sd(t, x1) * sd(t,
x2))); // correlation
t = .1; // averaging period in seconds
correlate_meter(x,y) = x,y <: x , attach(y, (corr(t) :
hbargraph("corr",-1,1))) : _,_;
correlate_correct(t,l,r) = (l + r) * mSmoo + l * stSmoo , (l + r) * mSmoo +
r * stSmoo
with {
th = .001;
isMono = (corr(t,l,r) > (1 - th)) | ((corr(t,l,r) < th) & ((avg(t, l * l) <
th) | ((avg(t, r * r) < th))));
mSmoo = avg(t, isMono);
stSmoo = 1.0 - mSmoo;
};
process = _,_ : correlate_meter : correlate_correct(t);
I think that several non-mono cases can result in a correlation that is
close to zero so I'd add another condition to check if either of the two
channels is really quiet.
Ciao,
Dr Dario Sanfilippo
http://dariosanfilippo.com
On Mon, 9 Aug 2021 at 09:44, Klaus Scheuermann <kla...@posteo.de> wrote:
> Dear Julius, dear Dario,
>
> thanks - again !
>
> @Julius:
> ba.if(1 > corr(t,l,r) > 0 , l, (l+r))
>
> was my clumsy way of saying 'if corr is smaller than 1 AND greater than
> 0'. Or if you turn it around 'if corr ==0 OR corr ==1'. What would be the
> most elegant way to do this in faust?
> You are right about the L == -R case... I did not look into out-of-phase
> cases yet. Probably then the condition should be 'if corr nears -1 OR 0 OR
> 1', right?
>
> @Dario, the code works very nicely and the smoothing sounds delicious ;)
> By explaining my clumsy ba.if statement, you will understand, that I'd
> like mono-left and mono-right (which result in corr=0) to be centered, too.
> If corr nears 0 or 1, the result should be in the center. Same question:
> how to do an elegant OR condition?
>
> Another thing I was thinking about is, if it makes more sense to convert
> the stereo signal to M-S and regulate the S channel for mono or stereo. But
> it's probably the same result as smoothing between l+r,l+r and l,r.
>
> Cheers,
> Klaus
>
> On 09.08.21 00:56, Dario Sanfilippo wrote:
>
> Hi, Klaus; nice to hear from you, Julius. :)
>
> As Julius points out, I also think that you'd need less demanding
> thresholds: even for identical channels, the average using a one-pole lp
> will oscillate and it might not be reliable if checking against the corner
> case.
>
> I'd go with something like this, but Julius also has a point about
> phase-inverted mono signals. Also, you may want to normalise when you sum L
> and R. It was necessary to guard against division by 0 too. I've included a
> smoother to avoid clicks when switching.
>
> I've tested that with your audio example and it's all mono except mono-left,
> mono-right, and stereo. Is that correct?
>
> import("stdfaust.lib");
> avg(t, x) = fi.pole(p, (1 - p) * x) // 1-pole lowpass as average
> with {
> p = exp((((-2.0 * ma.PI) / t) / ma.SR));
> };
> var(t, x) = avg(t, (x - avg(t, x)) ^ 2); // variance
> sd(t, x) = sqrt(var(t, x)); // standard deviation
> cov(t, x1, x2) = avg(t, (x1 - avg(t, x1)) * (x2 - avg(t, x2))); //
> covariance
> corr(t, x1, x2) = cov(t, x1, x2) / max(ma.ma.EPSILON, (sd(t, x1) * sd(t,
> x2))); // correlation
> t = .5; // averaging period in seconds
> correlate_meter(x,y) = x,y <: x , attach(y, (corr(t) :
> hbargraph("corr",-1,1))) : _,_;
> correlate_correct(t,l,r) = (l + r) * mSmoo + l * stSmoo , (l + r) * mSmoo
> + r * stSmoo
> with {
> isMono = corr(t,l,r) > .999;
> mSmoo = avg(.05, isMono);
> stSmoo = 1.0 - mSmoo;
> };
> process = _,_ : correlate_meter : correlate_correct(t);
>
> Ciao,
> Dr Dario Sanfilippo
> http://dariosanfilippo.com
>
>
> On Mon, 9 Aug 2021 at 00:25, Julius Smith <julius.sm...@gmail.com> wrote:
>
>> And of course I mean "cross-correlation coefficient"
>>
>> On Sun, Aug 8, 2021 at 3:22 PM Julius Smith <julius.sm...@gmail.com>
>> wrote:
>>
>>> Hi Klaus,
>>>
>>> I am late to this (just read some of the thread with interest), and I
>>> have a question: what do you mean by "1 > corr(t,l,r) > 0" ? It appears to
>>> be "parsed" left to right, so that the 2nd ">" only sees "1>0" most (all?)
>>> of the time, which is always true (1) of course (so no "else" activated).
>>> Maybe you want something like "abs(corr(t,l,r)) > 0.95" ? (i.e., 95%
>>> correlation deemed to be "panned mono"). I'm taking the absolute value
>>> because I assume you don't care if the left channel is merely the negative
>>> of the right (unless that's an accepted cheezy "stereoizer" of sorts).
>>>
>>> FYI, this is what we call a time-domain "normalized cross-correlation"
>>> or "correlation coefficient" measurement (official buzzwords)
>>>
>>> Cheers,
>>> Julius
>>>
>>>
>>> On Sun, Aug 8, 2021 at 10:07 AM Klaus Scheuermann <kla...@posteo.de>
>>> wrote:
>>>
>>>> Dear Dario,
>>>>
>>>> cool, your corr function gives me the desired results. At least when
>>>> feeding it to a meter.
>>>>
>>>> Here is my test audio which contains vocals in mono-mid, mono-left,
>>>> mono-right, mono-half-left, mono-half-right, stereo:
>>>> https://cloud.4ohm.de/s/y9oZzqFGyrZT5ej
>>>> For mono-mid, mono-half-left, mono-half-right it shows 1.
>>>> For mono-left, mono-right it shows 0.
>>>> For stereo it shows values between 0 and 1.
>>>>
>>>> I would like to detect mono signals that are not exactly in the middle
>>>> and put them there. Stereo signals should be unchanged.
>>>>
>>>> My code is here, but for some reason it does not work correctly.
>>>> Especially when corr shows 0, ba.if does not go to the else-path.
>>>>
>>>> import("stdfaust.lib");
>>>> avg(t, x) = fi.pole(p, (1 - p) * x) // 1-pole lowpass as average
>>>> with {
>>>> p = exp((((-2.0 * ma.PI) / t) / ma.SR));
>>>> };
>>>> var(t, x) = avg(t, (x - avg(t, x)) ^ 2); // variance
>>>> sd(t, x) = sqrt(var(t, x)); // standard deviation
>>>> cov(t, x1, x2) = avg(t, (x1 - avg(t, x1)) * (x2 - avg(t, x2))); //
>>>> covariance
>>>> corr(t, x1, x2) = cov(t, x1, x2) / (sd(t, x1) * sd(t, x2)) : _ ; //
>>>> correlation
>>>> t = 0.5; // averaging period in seconds
>>>> correlate_meter(x,y) = x,y <: x , attach(y, (corr(t) : hbargraph("corr"
>>>> ,-1,1))) : _,_;
>>>> correlate_correct(t,l,r) = ba.if(1 > corr(t,l,r) > 0 , l, (l+r)) ,
>>>> ba.if(1 > corr(t,l,r) > 0 , r, (l+r));
>>>> process = _,_ : correlate_meter : correlate_correct(t);
>>>>
>>>> Am I doing the ba.if wrong?
>>>>
>>>> Thank s very much,
>>>> Klaus
>>>>
>>>>
>>>> On 04.08.21 18:25, Dario Sanfilippo wrote:
>>>>
>>>> I had implemented a few statistics function a while back, kindly taken
>>>> from Wikipedia, and they seem to produce the expected values mentioned on
>>>> the webpage. I hope that these can be useful.
>>>>
>>>> Ciao,
>>>> Dr Dario Sanfilippo
>>>> http://dariosanfilippo.com
>>>>
>>>> import("stdfaust.lib");
>>>> avg(t, x) = fi.pole(p, (1 - p) * x) // 1-pole lowpass as average
>>>> with {
>>>> p = exp((((-2.0 * ma.PI) / t) / ma.SR));
>>>> };
>>>> var(t, x) = avg(t, (x - avg(t, x)) ^ 2); // variance
>>>> sd(t, x) = sqrt(var(t, x)); // standard deviation
>>>> cov(t, x1, x2) = avg(t, (x1 - avg(t, x1)) * (x2 - avg(t, x2))); //
>>>> covariance
>>>> corr(t, x1, x2) = cov(t, x1, x2) / (sd(t, x1) * sd(t, x2)); //
>>>> correlation
>>>> ph0 = os.phasor(2.0 * ma.PI, 200);
>>>> red = sin(ph0) + .35 * sin(ph0 * 3.0) + .91 * sin(ph0 * 5.0);
>>>> blue = sin(ph0) + .5 * sin(ph0 * 3.0) - .5 * sin(ph0 * 5.0);
>>>> red1 = sin(ph0) + sin(ph0 * 3.0);
>>>> blue1 = sin(ph0) - sin(ph0 * 3.0) / 3.0;
>>>> t = 1.0; // averaging period in seconds
>>>> process = (red , blue : corr(t)) , (red1 , blue1 : corr(t));
>>>>
>>>>
>>>>
>>>> On Wed, 4 Aug 2021 at 16:52, Klaus Scheuermann <kla...@posteo.de>
>>>> wrote:
>>>>
>>>>> Thanks Giuseppe,
>>>>>
>>>>> I checked it out, but somehow it still does not give me the desired
>>>>> result...
>>>>> I did some more research and found this, which indicates that it can
>>>>> be done with arctan more easily.
>>>>>
>>>>> The way this is done on phase (correlation) meters in audio equipment
>>>>> is rather simple:
>>>>>
>>>>> Phase = arctan(L/R)
>>>>>
>>>>> With phase of 45 or 225 = 1, and phase of 135 and 315 (-45) is -1.
>>>>>
>>>>> Essentially, the Y Axis is the L, and the X axis is the R. The phase
>>>>> is simply the polar angle of the vector between the two.
>>>>>
>>>>> This type of meters will show 1 if the signal is mono, and -1 if the
>>>>> left and right are perfectly phase inverted.
>>>>>
>>>>> Notice however, that phase meters of this type also account for the
>>>>> magnitude in the polar coordinates. So:
>>>>>
>>>>> Magnitude = (L^2 + R^2)^1/2
>>>>>
>>>>> Thus the actual meter display is a normalised version of:
>>>>>
>>>>> Correlation = Phase * Magnitude
>>>>>
>>>>> I'm not sure that satisfies your requirements, but this answers the
>>>>> question in the subject.
>>>>>
>>>>> So I transfered this to faust, but it still behaves weired...
>>>>> import("stdfaust.lib");
>>>>> phase(l,r) = (l/r) : aa.arctan;
>>>>> magnitude(l,r) = (l^2 + r^2)^1/2;
>>>>> correlate(l,r) = phase(l,r) * magnitude(l,r);
>>>>> correlate_meter(x,y) = x,y <: x , attach(y, (correlate : hbargraph(
>>>>> "corr",-1,1))) : _,_;
>>>>> process = _,_ : correlate_meter: _,_;
>>>>>
>>>>> Any ideas?
>>>>>
>>>>> Klaus
>>>>>
>>>>> On 03.08.21 14:48, Giuseppe Silvi wrote:
>>>>>
>>>>> Hi Klaus,
>>>>> The filters are necessary to obtain a -1 +1 range, I think.
>>>>>
>>>>> import("stdfaust.lib");
>>>>>
>>>>> correlate(l,r) = l*l ,r*r , l*r : par(i,3, si.smooth(0.9)) : sqrt, sqrt,
>>>>> _ : *,_ : /;
>>>>> correlate_meter(x,y) = x,y <: x , attach(y, (correlate :
>>>>> hbargraph("corr”,-1,1)));
>>>>>
>>>>> process = correlate_meter;
>>>>>
>>>>> Try playing with the si.smooth coefficient.
>>>>>
>>>>> best,
>>>>> giuseppe
>>>>>
>>>>>
>>>>> On 3 Aug 2021, at 14:09, Klaus Scheuermann <kla...@posteo.de>
>>>>> <kla...@posteo.de> wrote:
>>>>>
>>>>> Could it be something like this?
>>>>>
>>>>> (according to the 'correct' algorithm in
>>>>> https://www.beis.de/Elektronik/Correlation/CorrelationCorrectAndWrong.html
>>>>> )
>>>>> import("stdfaust.lib");
>>>>>
>>>>> correlate(l,r) = l*l ,r*r , l*r : sqrt, sqrt, _ : *,_ : / :_;
>>>>> correlate_meter(x,y) = x,y <: x , attach(y, (correlate :
>>>>> hbargraph("corr",-1,1))) : _,_;
>>>>>
>>>>> process = _,_ : correlate_meter: _,_;
>>>>>
>>>>> I am not sure about the lowpass filters though. Maybe not needed in the
>>>>> digital domain?
>>>>>
>>>>> Also, my code only returns -1 or 1 while it should be returning a range
>>>>> of -1 and 1, right?
>>>>>
>>>>> The correlation is either expressed in % from -100% to +100% or as the
>>>>> correlation factor, which ranges from -1 to +1. Note that due to the
>>>>> correlation algorithm the level of both signals does not matter, i.e., it
>>>>> does not influence the measured result.
>>>>>
>>>>> When a mono source is used for a stereo signal both stereo channels will
>>>>> be +100% correlated. When e.g. in a stereo signal both channels contain
>>>>> completely different signals, e.g. left (and only left) is the trumpet
>>>>> and right (and only right) is the guitar these stereo channels will be 0%
>>>>> correlated. With a third instrument appearing in both channels, the
>>>>> correlation will be somewhere between 0 and +100%.
>>>>>
>>>>>
>>>>> Ideas?
>>>>> Danke :)
>>>>> Klaus
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> On 03.08.21 12:48, Klaus Scheuermann wrote:
>>>>>
>>>>> Hello List,
>>>>>
>>>>> I just wondered, if anyone has implemented a stereo audio correlation
>>>>> meter/analyser in faust?
>>>>>
>>>>> If yes - great!
>>>>> If no - I have another project :)
>>>>>
>>>>> Here is what I found about the algorithm(s):
>>>>> https://www.beis.de/Elektronik/Correlation/CorrelationCorrectAndWrong.html
>>>>>
>>>>>
>>>>> I never learned analog electronic schematics, but it seems it should not
>>>>> be extremely hard to transfer to faust.
>>>>>
>>>>> Cheers, Klaus
>>>>>
>>>>>
>>>>>
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>>>
>>>
>>> --
>>> "Anybody who knows all about nothing knows everything" -- Leonard
>>> Susskind
>>>
>>
>>
>> --
>> "Anybody who knows all about nothing knows everything" -- Leonard Susskind
>>
>
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