Audibility thresholds of amp and DAC measurements

[j_j]

I literally wrote "most real-life music fragments are not just sums of long-running perfect sinusoids with unchanging amplitudes".

Except they are.
Enough of this nonsense.

 

[captainbeefheart]

In fact Linkwitz did a lot of testing of speaker distortion with impulse waveforms.

Yikes!!

I try and stress this point often when people get really hung up on the electronics aspect, the transducer is by far the weak link in the chain on so many regards. Just awful compared to the accuracy we can get with the electronics side, yet it still sounds amazing to me. So ya I joke at the minuscule changes people make like swapping fuses and hear a difference, their speakers must be the most accurate speakers we have never seen before.

 

[Sergei]

That argument pops up far too often, it's an old standby argument for the believers.

"We don't listen to sine waves, music signals are much more complex"

To be fair it is higher math and not generally taught in high school unless you are in advanced classes which let's be honest here, the folks that took these classes moved on to higher education anyway. Or some people really like math and learned it on their own, that's fine also it greatly helps understand complex concepts. It goes back to the age old question, is math something we discovered or is math a human construct to help better understand the world around us? It doesn't matter, math rules

I was in the top 5%, per finals results, in both university classes I took that dealt, among other things, with Linear Time-Invariant Systems Theory (LTS), of which Fourier transform is a part. Not to mention other university math education needed to get a graduate degree in Physics.

Compared to Quantum Electrodynamics, LTS Theory is simple. I believe I know where my mathematical understanding limits are. I believe that the basic math underlying LTS is well within my limits, even though some highly specialized topics within that theory are quite sophisticated, and I didn't study them all.

The real-life problem I encounter over and over again is that some audio practitioners take LTS Theory as a gospel, literally treating it as a sacrosanct religion. In reality, it is a beautiful set of theoretical abstractions, describing some real-life systems with sufficient precision, under specific circumstances.

This theory has its limitations. It fails to explain, for instance, why professional studios prefer 192/24 representation for their masters, whereas 48/16 shall be seemingly sufficient per LTS Theory. Of why large enough number of listeners are attracted to vinyl media, despite it being "inferior" per LTS Theory.

Those limitations were constraining for the work I do, so I had to go beyond LTS Theory. I got answers to lots of questions that are not resolvable if one stays within the LTS paradigm. The set of questions around the distortions audibility thresholds being one of them.

 

[Beave]

This is weird.

 

[pkane]

I literally wrote "most real-life music fragments are not just sums of long-running perfect sinusoids with unchanging amplitudes".

Fourier transform and the Sampling theorem apply everywhere, including in mammalian cochlea and to any and all music and to every sound that was ever created. There's nothing in human anatomy that violates a mathematical truth.

If you're saying that cochlea doesn't use FT/FFT for processing, then sure, we can all agree to that. But this doesn't excuse it from obeying reality, and having to deal only with signals that can be equivalently represented as a sum of perfect sine waves. Every one of them. No exceptions. That's because all finite bandwidth signals are. This is proven beyond any shadow of a doubt; this is not one of those "maybe we don't know something yet” cases.

I was in the top 5%, per finals results, in both university classes I took that dealt, among other things, with Linear Time-Invariant Systems Theory (LTS), of which Fourier transform is a part. Not to mention other university math education needed to get a graduate degree in Physics.

Compared to Quantum Electrodynamics, LTS Theory is simple. I believe I know where my mathematical understanding limits are. I believe that the basic math underlying LTS is well within my limits, even though some highly specialized topics within that theory are quite sophisticated, and I didn't study them all.

The real-life problem I encounter over and over again is that some audio practitioners take LTS Theory as a gospel, literally treating it as a sacrosanct religion. In reality, it is a beautiful set of theoretical abstractions, describing some real-life systems with sufficient precision, under specific circumstances.

This theory has its limitations. It fails to explain, for instance, why professional studios prefer 192/24 representation for their masters, whereas 48/16 shall be seemingly sufficient per LTS Theory. Of why large enough number of listeners are attracted to vinyl media, despite it being "inferior" per LTS Theory.

Those limitations were constraining for the work I do, so I had to go beyond LTS Theory. I got answers to lots of questions that are not resolvable if one stays within the LTS paradigm. The set of questions around the distortions audibility thresholds being one of them.

Just wow…. I wonder how the other 95% of your class are doing if you were in the top 5.

 

[Blumlein 88]

This theory has its limitations. It fails to explain, for instance, why professional studios prefer 192/24 representation for their masters, whereas 48/16 shall be seemingly sufficient per LTS Theory. Of why large enough number of listeners are attracted to vinyl media, despite it being "inferior" per LTS Theory.

Well professional studios overwhelmingly use 44.1 khz /24 bit or 48 khz/24 bit for recording, mixing, mastering everything.

 

[dc655321]

Those limitations were constraining for the work I do, so I had to go beyond LTS Theory. I got answers to lots of questions that are not resolvable if one stays within the LTS paradigm. The set of questions around the distortions audibility thresholds being one of them.

It’s common to resolve seemingly correct answers in the absence of critical review.
Were your discoveries part of your entrepreneurial work?

 

[Sergei]

Fourier transform and the Sampling theorem apply everywhere, including in mammalian cochlea and to any and all music and to every sound that was ever created. There's nothing in human anatomy that violates a mathematical truth.

No, the Fourier Transform and the Sampling theorem are not applicable everywhere. Formally, they are only applicable to signals with unlimited duration, sampled with unlimited precision.

There is a classic theorem in LTS Theory, proving that every time-limited signal has infinite, that is practically incalculable, spectrum.

There is a set of other theorems, in more contemporary LTS Theory, proving that sampling in the presence of noise or with limited precision renders the Sampling Theorem inoperable.

In practice, if a signal is a mix of nearly perfectly stable sinusoids with long enough duration, sampled in a competent enough way, the spectrum can be calculated with sufficient enough precision.

But! Here's a paper explaining that such signals are only a subset of what mammalian hearing system evolved to decode: https://redwood.berkeley.edu/wp-content/uploads/2020/08/lewicki2002.pdf.

The paper is rather technical, yet it basically says that there are three broad classes of sounds the hearing system evolved to be optimized for:

(a) Animal vocalizations.
(b) Speech.
(c) Natural sounds.

Only the animal vocalizations are suited for decoding by a mechanism resembling, yet not exactly equivalent, to Fourier transform. The other two classes of sounds are processed quite differently.

I like music pieces that contain all three classes of sounds.

I have to admit though, that with the advent of MP3 and other lossy formats based on harmonic decomposition, the music mixes seemingly consisting only of animal vocalizations became more prevalent

If you're saying that cochlea doesn't use FT/FFT for processing, then sure, we can all agree to that. But this doesn't excuse it from obeying reality, and having to deal only with signals that can be equivalently represented as a sum of perfect sine waves. Every one of them. No exceptions. That's because all finite bandwidth signals are. This is proven beyond any shadow of a doubt; this is not one of those "maybe we don't know something yet” cases.

Even morphologically, the mammalian hearing system has elements and structures explicitly optimized for detecting non-harmonic components, typical of natural sounds. For instance: https://pubmed.ncbi.nlm.nih.gov/11976365/.

Interestingly enough, going beyond the LTS theory explains yet another interesting phenomenon: a seemingly unreasonable popularity and high residual prices of vintage "overkill" power amplifiers, with their huge banks of PSU capacitors, and totally insane slew rates.

Turns out, such amplifiers better deal with the non-harmonic components, back then much more prevalent in what used to be widely popular music. Lovers of such vintage music can more readily satisfy their thirst for faithful music reproduction of their favorite music pieces using those monster amplifiers.

 

[pma]

Gentlemen, do not feed the Trolls, please.

 

[j_j]

If you're saying that cochlea doesn't use FT/FFT for processing, then sure, we can all agree to that. But this doesn't excuse it from obeying reality, and having to deal only with signals that can be equivalently represented as a sum of perfect sine waves. Every one of them. No exceptions. That's because all finite bandwidth signals are. This is proven beyond any shadow of a doubt; this is not one of those "maybe we don't know something yet” cases.

You might notice the advice given to me a few notes earlier in this thread by SIY. You may also have noticed that he's trying to shift the area of debate after having been found far afield in one subject. I have to conclude that in fact he is trolling for some purpose. As with most problems, the appropriate framework for one part of an analysis may not be the best for another, but there has been ample discussion of partial loudnesses elsewhere on this board to address the straw-man references that were made to LTI systems.

So, I agree, but I suspect there's little point of debating when we see deliberate subject shifts and evasion at every turn. I think we can all understand where this is headed when he denies Gauss's convergence theorem for the integral form of the Fourier Transform. Perhaps a discussion of L1 vs. L2 errors might be in order.

 

[j_j]

Yikes!!

I try and stress this point often when people get really hung up on the electronics aspect, the transducer is by far the weak link in the chain on so many regards. Just awful compared to the accuracy we can get with the electronics side, yet it still sounds amazing to me. So ya I joke at the minuscule changes people make like swapping fuses and hear a difference, their speakers must be the most accurate speakers we have never seen before.

In many ways yes, this is quite the truth.

There is, however, one other major loss of information, that being in the reduction to 2, 4, 5, 7, whatever channels. That's insurmountable in current reproduction technologies. 2 channel, in particular, ignores work from the 1930's.

 

[DualTriode]

....

There is, however, one other major loss of information, that being in the reduction to 2, 4, 5, 7, whatever channels. That's insurmountable in current reproduction technologies. 2 channel, in particular, ignores work from the 1930's.

You are completely lost and off topic.

The topic is the audibility thresholds of defects in amplifiers and DAC.

Math is a set of tools, not the topic.

You make me want to go pick up a Double Jack.

DT

 

[SIY]

Gentlemen, do not feed the Trolls, please.

Crank, not troll.

 

[abm0]

There is, however, one other major loss of information, that being in the reduction to 2, 4, 5, 7, whatever channels. That's insurmountable in current reproduction technologies. 2 channel, in particular, ignores work from the 1930's.

I don't know, it's pretty surmountable according to dr. Griesinger, and he doesn't ignore that work from the 30s.

 

[captainbeefheart]

I hit my head earlier so I might not be all there today lol. Ouch!!

I am trying to make sense of his argument that Fourier doesn't explain all things we hear, as he said only animal vocalization. Maybe we need a thought experiment to make the distinction simpler for us all to be on the same page?

So, assume we have a system that is described with a known differential equation, let say for example that we have a common RLC circuit. Also assume that a common switch is used to switch ON or OFF the circuit. Now if we want to study the circuit in the sinusoid steady state we have to use Fourier transform. Otherwise, if our analysis include the switch ON or switch OFF the circuit we have to implement the Laplace transformation for the differential equations.

 

[SIY]

I am trying to make sense of his argument that Fourier doesn't explain all things we hear...

Why?

 

[captainbeefheart]

Why?

I have no idea. I suppose I'm trying to get where he is coming from.

I did injure my head so I'm probably just not thinking correctly. Ignore anything silly I say for a while or I'll just step away from the conversation lol.

 

[SIY]

I have no idea. I suppose I'm trying to get where he is coming from.

I did injure my head so I'm probably just not thinking correctly.

The latter is a good start toward the former.

 

[pma]

Crank, not troll.

I am not a native speaker, Sir. Can’t see a tiny difference.

 

[j_j]

You are completely lost and off topic.

The topic is the audibility thresholds of defects in amplifiers and DAC.

Math is a set of tools, not the topic.

You make me want to go pick up a Double Jack.

Apparently you don't believe that some kinds of distortion can actually mitigate the losses one gets by reducing to two channels? And that can read directly on amplifier performance and perception of amplifiers that are "not that good" in certain ways.

Suit yourself.