Quote from: dwoz on 2010-03-21 01:23:23

Ethan's conjecture is that the stacking of component characteristic is a myth, because it can be simply eliminated by applying a single inverse "value" of the characteristic, to the summed master.

In this definition, he elaborates by saying that if a component put a 3dB 'bump' at a certain frequency, and you used that component on 10 tracks, then you don't need to remove 30dB of "bump" from the master, but only 3dB.  So far so good.  But then he pollutes this by saying that you can completely compensate using one 3dB inverse function. 

That's the rub!  you can NOT completely compensate!  Because it's non-linear!!!!!

I don't follow here.  If you have a summer with N inputs, and the identical linear filter in each of the N paths leading to the summer, then barring nonlinearity you can (conceptually) move that linear filter after the summer.  This assumes no limiters. compressors, clipping op-amps or other grossly nonlinear devices in the chain between the filter and the summer.  If that linear filter is minimum-phase, then its inverse is stable and you can correct for the filter's inclusion with a single filter at the summer output that implements the reciprocal of the transfer function of the original filter.

Quote from: dwoz on 2010-03-21 01:23:23

Also, it isn't just frequency and amplitude where f(x) can manifest.  Imagine that you have a component that acts as an all-pass, but has a non-linear phase response.  Stack those puppies up and try to apply an inverse.  Not gonna happen!

The issue there is that analog all-pass filters are non-minimum phase devices, so their inverse is unstable.  That's why you can't in general compensate for their effects in an exact way.

Quote from: dwoz on 2010-03-21 01:23:23

the important thing here is the realize that you must be EXTREMELY careful how you generalize a statement.  You can take a perfectly true fact, and make it false by applying it too broadly.

This points out the need to qualify one's statements.  As above, the filter must be linear and minimum-phase and all the components in each path from the filter to the summer must be linear for the correction to work.  So generalizing is not always possible.  Yet you're also getting on Ethan's case for qualifying his statements.  You're telling him, in effect, that he shouldn't qualify his statements, nor should he generalize them.

Actually, you apparently follow quite well.  I agree completely with your characterization, EXCEPT that you're not describing a real-world system, but a hypothetical one, that you'd be hard pressed to discover in actual use.

It doesn't NEED to be minimum-phase, but that would be nice.  It just needs to be linear phase as well as frequency and amplitude linear.

I'll give an example.  I have a hypothetical component that is frequency linear.  It demonstrates THD + IMD of 0.000002 %.  (again, I DID say hypothetical).  But that component has a non-linear phase response.  So, it tests VERY well.  It's spec looks BEAUTIFUL.  But it cannot have it's phase non-linearity removed once summed with other tracks.

The phase problem in the source has been turned into a frequency problem in the sum.  And it's dynamic, so we're "screwed".

Quote from: dwoz on 2010-03-21 02:08:58

I'll give an example.  I have a hypothetical component that is frequency linear.  It demonstrates THD + IMD of 0.000002 %.  (again, I DID say hypothetical).  But that component has a non-linear phase response.  So, it tests VERY well.  It's spec looks BEAUTIFUL.  But it cannot have it's phase non-linearity removed once summed with other tracks.

Are you talking about just a single filter in one branch of the summer?  I'm not sure.  What I'm talking about is an identical filter in each path to the input of the summer.  In the scenario I'm talking about, the phase nonlinearity of said filter is a non-issue.  In fact, all lumped-parameter analog filters have nonlinear phase response.  In my scenario, minimum-phase is the only requirement to be able to correct for the filter's presence.  But again, I'm assuming an identical filter in each branch.  If that's different from what you're assuming, please spell out what's different.

Quote from: dwoz on 2010-03-21 02:08:58

The phase problem in the source has been turned into a frequency problem in the sum.  And it's dynamic, so we're "screwed".

I don't follow.  Please spell out as specifically as possible the scenario you're referring to.  Also, as someone else mentioned, it would help to know which position in Ethan's video you're referring to.  I downloaded it but haven't looked at it since shortly after he first released it.

Actually, you apparently follow quite well.  I agree completely with your characterization, EXCEPT that you're not describing a real-world system, but a hypothetical one, that you'd be hard pressed to discover in actual use.

I'm sorry, I'm talking about a more real-world extension of your hypothetical.  Instead of "component", use the word "filter" as you have.  But back to the "real world" issue...As soon as you introduce a reactive impedance into your circuit, I think you give up the ability to talk about minimum-phase AND frequency magnitude.  Thus, only in the hypothetical world can you both have your cake and eat it too.

This is the problem...Ethan does not cover this.  I can construct a set of files that demonstrate a stacking effect that cannot be removed via an inverse function on the sum, and this WILL be used by somebody to jam a shiv into Ethan's argument...much the way my "anonymous nym" is used to invalidate my points.  Neither are fair, but both are fair game.

I can construct a set of files that demonstrate a stacking effect that cannot be removed via an inverse function on the sum, and this WILL be used by somebody to jam a shiv into Ethan's argument.

Quote from: dwoz on 2010-03-21 02:08:58

Actually, you apparently follow quite well.  I agree completely with your characterization, EXCEPT that you're not describing a real-world system, but a hypothetical one, that you'd be hard pressed to discover in actual use.

With a couple reasonable assumptions around signal level and dither, a digital console or workstation absolutely operates as an ideal linear system.

Quote from: Notat on 2010-03-21 02:53:36

Quote from: dwoz on 2010-03-21 02:08:58

Actually, you apparently follow quite well.  I agree completely with your characterization, EXCEPT that you're not describing a real-world system, but a hypothetical one, that you'd be hard pressed to discover in actual use.

With a couple reasonable assumptions around signal level and dither, a digital console or workstation absolutely operates as an ideal linear system.

Right, and even the general run of analog consoles is very, very linear.

Quote from: dwoz on 2010-03-21 02:50:09

I can construct a set of files that demonstrate a stacking effect that cannot be removed via an inverse function on the sum, and this WILL be used by somebody to jam a shiv into Ethan's argument.

Problem is, doing such a thing in no way invalidates Ethan's argument.

My previous answer to Notat's post was deleted in the lawnmower-fest that went through this thread this morning... But I think that's a breathtaking assertion to make.  I don't agree at all.

Implication you're making is that analog console sonics are non-differentiable.  (for modern kit).    I think that's a bold statement to make that will get you in trouble later.

Quote from: Arnold B. Krueger on 2010-03-21 17:02:31

Quote from: dwoz on 2010-03-21 02:50:09

I can construct a set of files that demonstrate a stacking effect that cannot be removed via an inverse function on the sum, and this WILL be used by somebody to jam a shiv into Ethan's argument.

Problem is, doing such a thing in no way invalidates Ethan's argument.

Which argument, the argument that stacking exists, or the relativistic one of whether a given average person can hear it in a DBT?

Quote from: dwoz on 2010-03-21 17:49:18

My previous answer to Notat's post was deleted in the lawnmower-fest that went through this thread this morning... But I think that's a breathtaking assertion to make.  I don't agree at all.

Before further forking this thread to discuss mathematical precision, please do us the favor of searching the forums for previous discussions. It is a topic most of us are quite familiar with. Here's one of the more recent discussions.

Quote from: dwoz on 2010-03-21 17:49:18

Implication you're making is that analog console sonics are non-differentiable.  (for modern kit).    I think that's a bold statement to make that will get you in trouble later.

Arnold said that analog consoles are linear. Linearity doesn't say a whole lot about about how a console sounds just that it doesn't generate certain types of distortion.

...the whole argument is not around the competence of the summing, but the competence of the source.

Quote from: dwoz on 2010-03-21 02:08:58

Actually, you apparently follow quite well.  I agree completely with your characterization, EXCEPT that you're not describing a real-world system, but a hypothetical one, that you'd be hard pressed to discover in actual use.

Okay, but if one is trying to have a productive discussion, it's helpful for each side to completely understand what the other is saying.  Toward that end, it's often useful to start with an idealized scenario that everyone can agree on, then start introducing non-ideal elements one by one to get to the real-world system.

Quote from: dwoz on 2010-03-21 02:08:58

Actually, you apparently follow quite well.  I agree completely with your characterization, EXCEPT that you're not describing a real-world system, but a hypothetical one, that you'd be hard pressed to discover in actual use.

With a couple reasonable assumptions around signal level and dither, a digital console or workstation absolutely operates as an ideal linear system.

Quote from: dwoz on 2010-03-21 02:50:09

I'm sorry, I'm talking about a more real-world extension of your hypothetical.  Instead of "component", use the word "filter" as you have.  But back to the "real world" issue...As soon as you introduce a reactive impedance into your circuit, I think you give up the ability to talk about minimum-phase AND frequency magnitude.  Thus, only in the hypothetical world can you both have your cake and eat it too.

Minimum-phase is just a property that can be ascribed to some linear circuits.  This includes reactive impedances (inductance, capacitance, etc).  If it's linear, the relationship between its input and its output in the frequency domain is completely described by its transfer function.  The transfer function for such a circuit also determines its time-domain behavior.  Of course, all real-world circuits are nonlinear to some degree, but many of them, such as low-distortion op-amps and other components, can be treated as if they were linear as long as they are operated within sensible limits.

Sometimes that's easier said than done though.  One can always, and easily, come up with ways to violate this.  Put an op-amp with a gain of 40 dB into a 40 dB pad and the usable output voltage swing will be reduced by 100x.  That's just one of an infinite number of examples one can come up with.

Quote from: dwoz on 2010-03-21 02:50:09

This is the problem...Ethan does not cover this.  I can construct a set of files that demonstrate a stacking effect that cannot be removed via an inverse function on the sum, and this WILL be used by somebody to jam a shiv into Ethan's argument...much the way my "anonymous nym" is used to invalidate my points.  Neither are fair, but both are fair game.

Well, I'm an anonymous guy too, so I won't hassle you about that .

I can draw a block diagram of what I'm talking about, scan and post it so there's no confusion.  But it's tune time for me now.  I have to stop at 10:00 PM, so I've got a little less than an hour and I don't like headphones much.

The all-pass discussion is muddying things. There is a tangle of audibility of phase changes and linear system behavior.

The contention that different phase responses are indistinguishable to the ear is debatable as far as I'm concerned. Here's a paper that discusses the issue.

An all-pass is a linear operation. You can apply it at the individual channels or at the sum and you'll get the same sound. What you can't do is apply different linear processes to the individual channels and expect to find some sort of transform that you can apply at the sum to give you the same sound (or invert the individual transforms).

You're making some dangerous assumptions here.

First, you're assuming that all components will always be operated strictly within their linear region which in pro audio is not always true.

Second you're assuming that all production examples of a specific part will always adhere strictly to their published spec. In reality this is NEVER the case - there is always a tolerance range. NO GIVEN PART EVER EXACTLY MATCHES THE SPEC SHEET.

Quote from: Notat on 2010-03-21 19:52:12

Quote from: dwoz on 2010-03-21 17:49:18

Implication you're making is that analog console sonics are non-differentiable.  (for modern kit).    I think that's a bold statement to make that will get you in trouble later.

Arnold said that analog consoles are linear. Linearity doesn't say a whole lot about about how a console sounds just that it doesn't generate certain types of distortion.

Exactly.  Systems can have only 4 general kinds of signal response faults: linear distortion (frequency and/or phase response errors) , nonlinear distortion, random noise, and coherent interferring signals. There are no other known kinds of system signal response faults. The list is constrained by the 2-dimensional nature of electrical signals.  Any of them can cause a system to be readily differentiated by means of listening if they are severe enough. It is all about quantification. 

I only mentioned nonlinear distortion, so it is hard to understand how one might logically progress from my statement to a statement that system (in this case analog console) sonics are non-differentiable. Straw man, anyone? ;-)

I'm willing to stipuate that analog console sonics are often readily differentiated based on noise, interferring signals, and linear distortion.  IME one of the most common causes of  differentiatiable sonics may be frequency response variations caused by improperly centered or misdesigned or otherwise poorly implemented tone controls.  Another problem that I often observe is that it is virtually impossible to readjust the controls of an analog console so that you recreate the same mix within say +/- 0.1 dB. If you manually move the controls during the mix, then that is nearly impossible to recreate precisely as well.  Also, it is not unusual to find mic preamps (a standard component of most consoles) that relate to audible differences because they load some microphones differently in ways that affect the microphone's  frequency response. It is not uncommon to find mic preamps with with built-in fixed (butnot always well-documented) roll-offs on the order of -3 dB at 50 or 80 Hz, which can be easy to hear as well.

Doing a proper listening experiment to compare analog console sonics seems like a probable waste of time now that good digital consoles are so readily available.

Quote from: dwoz on 2010-03-21 02:08:58

Actually, you apparently follow quite well.  I agree completely with your characterization, EXCEPT that you're not describing a real-world system, but a hypothetical one, that you'd be hard pressed to discover in actual use.

With a couple reasonable assumptions around signal level and dither, a digital console or workstation absolutely operates as an ideal linear system.

Can you prove this?  It sounds like you're making a conjecture.  I know how fun that is, I am always accused of making conjecture. 

If one were to have to prove this, how would one even go about accomplishing that proof?

I must confess...I've never heard of "linear distortion".  What is it?  Isn't ALL distortion by definition non-linear?

Systems can have only 4 general kinds of signal response faults: linear distortion (frequency and/or phase response errors) , nonlinear distortion, random noise, and coherent interfering signals.