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help a student please (dBFS and loudness measures)!

Reply #25
I'm curious as to exactly what the OP means when he refers to symmetric/asymmetric variables.

I'll cop up to statistics not being a strong suit of mine, and thinking of RMS as a variance measure is something I had not thought of before, and is kind of cute - it adds an interesting interpretation to eg the RMS value of a square wave. It also has absolutely zilch to do with loudness measurement or even the entire field of power measurement.

The math behind traditional RMS and/or Fourier analysis might be the same if interpreted in a statistical context, but for the life of me, I can't think of a single useful piece of information you could obtain by that line of analysis that you couldn't obtain otherwise. Now that I think about it more, the only reason RMS figures are even used in engineering is because a) they allow the reduction of sinusoidally driven systems to dc systems, and b) rms power figures allow relatively easy manipulation/summation. That's it. And Parseval's Theorem is pretty fundamental to understanding both. And b) in particular is the key link between RMS figures and volume, and from there, loudness.

It's not that most "engineers" have problems with "probability theory". IMNSHO, It's that probability theory is, in this context, a stupid way of thinking about real problems that yields no conceptual insight. It makes about as much sense as studying number theory with Roman numerals.

Maybe his prof has some insightful statistical interpretation to make on audio datasets. I dunno. I'm not disputing that the OP's field of study is worthwhile. But I'd expect physics majors to actually comprehend engineering before trying to take their place above us on the totem pole.

help a student please (dBFS and loudness measures)!

Reply #26
It's not that most "engineers" have problems with "probability theory". IMNSHO, It's that probability theory is, in this context, a stupid way of thinking about real problems that yields no conceptual insight. It makes about as much sense as studying number theory with Roman numerals.

Maybe his prof has some insightful statistical interpretation to make on audio datasets. I dunno. I'm not disputing that the OP's field of study is worthwhile. But I'd expect physics majors to actually comprehend engineering before trying to take their place above us on the totem pole.


A "physics major" who is now in grad school would most likely not say anything as err... non-perceptive  as "quantum mechanics is a good example of a stochastic process" (Nelson notwithstanding).

But who knows, I've heard worse.

help a student please (dBFS and loudness measures)!

Reply #27
I'm curious as to exactly what the OP means when he refers to symmetric/asymmetric variables.


Just a guess: maybe titox means unsymmetric = having nonzero DC offset?

Then yes, sure, strictly speaking RMS only makes sense when DC offset = 0.

But for an engineer it's quite trivial, it's an implicit assumption: either your signal has no DC offset to start with, or DC offset is negligibly small (as with most useful audio signals), or you simply compensate for the nonzero offset (if there is any) as the first step before doing anything with the signal.

help a student please (dBFS and loudness measures)!

Reply #28
I'm curious as to exactly what the OP means when he refers to symmetric/asymmetric variables.


Just a guess: maybe titox means unsymmetric = having nonzero DC offset?

Then yes, sure, strictly speaking RMS only makes sense when DC offset = 0.

No. RMS(1) = 1. The RMS value is completely well-defined for DC signals. That's the whole point - RMS measurements allow AC signals to be treated as if they were DC signals.

help a student please (dBFS and loudness measures)!

Reply #29
No. RMS(1) = 1. The RMS value is completely well-defined for DC signals. That's the whole point - RMS measurements allow AC signals to be treated as if they were DC signals.

Well, RMS is well-defined as a function. but it doesn't make much sense if you don't compensate for DC offset.

To be a useful measure, RMS should produce either signal power (in its physical meaning) or a measure of variance (in its mathematical meaning, 2nd "moment" or whatever it's called in statistics). This is only true when DC offset is zero.

help a student please (dBFS and loudness measures)!

Reply #30
Actually, RMS measurement of a signal with a DC offset makes perfect sense if what you are interested in is the power that will be dissipated by a resistor when that signal is applied to it. The power is the RMS voltage squared divided by the resistance, regardless of the DC offset.

In the case of audio signals the audible volume calculation should, as you say, not include the offset.

help a student please (dBFS and loudness measures)!

Reply #31
Actually, RMS measurement of a signal with a DC offset makes perfect sense if what you are interested in is the power that will be dissipated by a resistor


Ah, yes, you are right, of course.

Indeed I was thinking more of power ~ loudness and all that. 

/Edit: The OP was interested in loudness.

help a student please (dBFS and loudness measures)!

Reply #32
First of all I am sorry, I was probably too much arrogant in my last post, but in a sense I am a bit puzzled how 'mathematical' concepts are wrongly used by practitioners and audio engineers.

I want to stress here that I don't have any argument against RMS as a mesure of power in electrical signals at fixed frequency. There is a physical argument because you do RMS in that case. In fact for DC

P = V^2/R

by analogy in the AC case you take the integral (wrt to time) of squares, and the RMS is just the sample analog of that integral, and from here you have all the theory of  square-integrable functions which also make Fourier theory much easier. Not only, if the integrand is square-integrable you have that the RMS converges in probability to the integral
I mentioned above.  This is simple probability theory which anyone working with SAMPLES should know. 

What I am saying is that I find RMS not suitable for measuring music power. End in fact,  it can be easily shown that the the RMS is not a good sample analog of what RMS measures in that case of the pure sinus signals (like mains AC).  If you understand concepts like  as-convergence and p-convergence  I can tell you why.



The math behind traditional RMS and/or Fourier analysis might be the same if interpreted in a statistical context, but for the life of me, I can't think of a single useful piece of information you could obtain by that line of analysis that you couldn't obtain otherwise.


that's the main problem: you talk about samples ignoring probability theory, that's funny.

Now that I think about it more, the only reason RMS figures are even used in engineering is because a) they allow the reduction of sinusoidally driven systems to dc systems, and b) rms power figures allow relatively easy manipulation/summation. That's it. And Parseval's Theorem is pretty fundamental to understanding both. And b) in particular is the key link between RMS figures and volume, and from there, loudness.


the reason why RMS measurement is central is because it is easy to deal with square-integrable function and Hilbert Spaces.


It's not that most "engineers" have problems with "probability theory". IMNSHO, It's that probability theory is, in this context, a stupid way of thinking about real problems that yields no conceptual insight. It makes about as much sense as studying number theory with Roman numerals.



Now I am tempted to become arrogant again. I am really impressed with this... Now I understand why most modern recordings simply don't sound good. You pretend to deal with sampling just ignoring probability and elementary statistic concepts. Congratulations.


... But I'd expect physics majors to actually comprehend engineering before trying to take their place above us on the totem pole.



I am almost on the way to finish  my PhD in physics, my undergrad  major was in math.  Anyway,  just a last comment regarding physics.  Quantum physics has to do with stochastic processes (as almost all modern physics). Just let us go back to  one of the pillars of quantum mechanics:  Schrödinger equation. The time evolution of a quantum state  can be described by the so called "Schrödinger equation" (where the Hamiltonian total energy  operator generates time paths). Now an important ingredient of the equation is  the wave function, ie the probability amplitude for different system configurations. The wave function is a probability density function. Statistics played an important (if not prominent) role in the last century of science and there are  three main fields which opened questions for probability theorists and statisticians: (in order of importance) Physics, Genetics and Economics. 

I hope this help,
Jp









help a student please (dBFS and loudness measures)!

Reply #33
I am almost on the way to finish  my PhD in physics, my undergrad  major was in math.  Anyway,  just a last comment regarding physics.  Quantum physics has to do with stochastic processes (as almost all modern physics). Just let us go back to  one of the pillars of quantum mechanics:  Schrödinger equation. The time evolution of a quantum state  can be described by the so called "Schrödinger equation" (where the Hamiltonian total energy  operator generates time paths). Now an important ingredient of the equation is  the wave function, ie the probability amplitude for different system configurations. The wave function is a probability density function. Statistics played an important (if not prominent) role in the last century of science and there are  three main fields which opened questions for probability theorists and statisticians: (in order of importance) Physics, Genetics and Economics.


Yes, you're far too arrogant and assume too much, too. The wavefunction is most definitely not a probability density function; it is the square of its absolute value that is a pdf. And that has many effects, one of which being that you cannot formulate quantum mechanical dynamics as a "usual" stochastic process. Look at attempts to formulate quantum mechanics "classically" (Bohm, Nelson, Bell will be useful names, not that I am an expert on this stuff) and you will see it is not an easy problem.

Compare this to the Boltzmann equation, for instance, which does indeed describe the time evolution of the pdf for a classical system.

Or if you disagree, I am sure PRL will be more than happy to accept your groundbreaking new formulation of quantum mechanics as a classical, local stochastic theory, complete with explanation as to why, if this is possible, the Bell inequalities hold.

Actually if you are interested and not just trying to show off, there is a nice and clear book by Isham explaining where all these problems in QM come from.

Also, "there are  three main fields which opened questions for probability theorists and statisticians" is not the same as "those three fields have to do with stochastic processes". Most of my colleagues (ie, those who did not happen to need to know) have very little idea of what a stochastic process is, who Ito and Stratonovich are etc, and they have no problem in their professional life. It's just not that important (sometimes it is as a tool though). Anyway this is not the place to discuss the relevance and importance of probability theory to physics (short version: of course it is important, but beyond the basics, very little heavy machinery from probability theory is actually used in physics, in comparison to fields like mathematical finance etc--let's not get into why and which is most successful in practice  ).

But seriously, read your posts. Do you have any idea how arrogant you come across as? And ignorant, I am sorry to say (well actually I'm not sorry, insulting random groups of people about mathematical ineptitude while claiming knowledge you blatantly don't have ranks very high of my list of irritants). And this is after asking for help. Brilliant.

If you always write like this, I'd love to be a referee your first publication

help a student please (dBFS and loudness measures)!

Reply #34
Yes, you're far too arrogant and assume too much, too. The wavefunction is most definitely not a probability density function; it is the square of its absolute value that is a pdf.


Oh I am sorry, in the hurry I forgot to write  "square of the absolute value".

Actually if you are interested and not just trying to show off, there is a nice and clear book by Isham explaining where all these problems in QM come from.



You mean Chris Isham from Imperial College London? I know that book, I had some classes with Dolnick Sorkin and  he suggested that book. Of course you can look  at QM from several angles.  From what I understand you are talking about what is called the "Copenhagen-interpretation". Well, even though I studied in UK and US, I find the Russian  school more interesting, and the Russian school produced very good representation of QM via stochastic processes. And I understand why is that: Russians, starting form Kolmogorov, mastered probability theory.  Anyway, It can be shown that an elementary quantum systems can be described  as a non-Markovian stochastic process and  this  eliminates some mysterious characteristics of QM in the classical Copenhagen view.



... Most of my colleagues (ie, those who did not happen to need to know) have very little idea of what a stochastic process is, who Ito and Stratonovich are etc, and they have no problem in their professional life. It's just not that important (sometimes it is as a tool though).




If we are talking about *scientific meaning* of RMS in sampled signals we should know  elementary statistic, then you can still use the RMS in your professional life and being happy. 


But seriously, read your posts. Do you have any idea how arrogant you come across as? And ignorant, I am sorry to say (well actually I'm not sorry, insulting random groups of people about mathematical ineptitude while claiming knowledge you blatantly don't have ranks very high of my list of irritants). And this is after asking for help. Brilliant.

If you always write like this, I'd love to be a referee your first publication



Well I was told that there are  referees like you, but with my first paper I was lucky enough to get good referees' reports. 

See, I don't know what you do in your life (I hope you are not into the academics though!), but this section of the forum is named "scientific discussion",  so it's quite irritating that people talk about samples without any idea of what sampling is.

Now I understand why digital recordings rarely sound good... too much sloppiness. With this I would like to shut down the discussion, I should go to do more serious things.

Best
Jp




help a student please (dBFS and loudness measures)!

Reply #35
titox.  You are paranoid.

It may be because of the language ( You say you preffer the Russian school, maybe it's because you are russian).

Sampling can mean too many things, and you want to keep on the statistical meaning of it.

Since you don't want to continue, the conversation can be considered closed. Not the topic, though.

help a student please (dBFS and loudness measures)!

Reply #36
Yes, you're far too arrogant and assume too much, too. The wavefunction is most definitely not a probability density function; it is the square of its absolute value that is a pdf.


Oh I am sorry, in the hurry I forgot to write  "square of the absolute value".
Quote
If I were you I'd be sorry for not realizing the significance of this...


Actually if you are interested and not just trying to show off, there is a nice and clear book by Isham explaining where all these problems in QM come from.



You mean Chris Isham from Imperial College London? I know that book, I had some classes with Dolnick Sorkin and  he suggested that book. Of course you can look  at QM from several angles.  From what I understand you are talking about what is called the "Copenhagen-interpretation". Well, even though I studied in UK and US, I find the Russian  school more interesting, and the Russian school produced very good representation of QM via stochastic processes. And I understand why is that: Russians, starting form Kolmogorov, mastered probability theory.  Anyway, It can be shown that an elementary quantum systems can be described  as a non-Markovian stochastic process and  this  eliminates some mysterious characteristics of QM in the classical Copenhagen view.


No, what I am saying is a mathematical statement and has nothing to do with the copenhagen interpretation (or any interpretation). Namedropping Sorkin won't help you much.

I don't think this is the right place to go into the stochastic process approach to quantum mechanics though!

Quote
... Most of my colleagues (ie, those who did not happen to need to know) have very little idea of what a stochastic process is, who Ito and Stratonovich are etc, and they have no problem in their professional life. It's just not that important (sometimes it is as a tool though).




If we are talking about *scientific meaning* of RMS in sampled signals we should know  elementary statistic, then you can still use the RMS in your professional life and being happy. 


But seriously, read your posts. Do you have any idea how arrogant you come across as? And ignorant, I am sorry to say (well actually I'm not sorry, insulting random groups of people about mathematical ineptitude while claiming knowledge you blatantly don't have ranks very high of my list of irritants). And this is after asking for help. Brilliant.

If you always write like this, I'd love to be a referee your first publication



Well I was told that there are  referees like you, but with my first paper I was lucky enough to get good referees' reports. 

See, I don't know what you do in your life (I hope you are not into the academics though!), but this section of the forum is named "scientific discussion",  so it's quite irritating that people talk about samples without any idea of what sampling is.


I am a theoretical physicist. It would appear that at least part of the community does not agree with your views, else I'd be out of  a job

Quote
Now I understand why digital recordings rarely sound good... too much sloppiness. With this I would like to shut down the discussion, I should go to do more serious things.


So, let's see: you find yourself stuck and are forced to go to a forum and ask "I know dB are 20*log10(In/out) but I have negative numbers and I don't know what to put inside the logs!". ie, you can't think your way through this. Then you start ridiculing people who answer your question, because they are not mathematicians, and end up lecturing us on the foundations of quantum mechanics which you evidently do not understand (of course at this stage I am merely claiming this and can't prove it except to someone else who knows what I am talking about, to whom it is obvious anyway...).


help a student please (dBFS and loudness measures)!

Reply #37
Yes, you're far too arrogant and assume too much, too. The wavefunction is most definitely not a probability density function; it is the square of its absolute value that is a pdf.


Oh I am sorry, in the hurry I forgot to write  "square of the absolute value".



OK this won't achieve much but: it is crucially important that the dynamical evolution of the pdf (ie of $|\psi|^2$) is not linear, even though that of the wavefunction is. That is, it is crucially important that the wavefunction isn't a pdf, and not a trivial detail like you seem to imply.

That is actually the whole point, why the  interference effects are there and do what they do, and so on. As surely you know (this is even in Landau Lifshitz vol 3, or is that not what you meant by "Russians"?  ARE THERE OTHERS?!?!?), a 3-line calculation starts from the S eqn and results in the continuity and something like the Hamilton-Jacobi eqns plus a nonlinear term proportional $\hbar^2$. That rather screws things up if you try to formulate it as a stochastic process!

Anyway,

a) I am not an expert on this, as I am a many-body field theorist; what I'm saying is fairly basic stuff that I remember from undergraduate lectures and discussions with friends. Actually I couldn't care less about interpretations, my calculations seem to work anyway. Yes, I'm shallow
b) I am obviously wasting my time; nobody on HA cares about this, you won't suddenly say "damn you're right, I am making this up as I go along based on undergraduate lectures I heard once", and most likely I look like a total idiot for going on and on.
c) You really ought not to talk about things you don't really understand in an authoritative tone. Here you can continue arguing on and on about QM and nobody cares because, well, they don't care about QM, and anyway most can't tell whether what you say is right or wrong even if they were to care. But try to bullshit your way with people who know what you're talking about and you'll be ostracized, trust me. Nobody likes loudmouths, especially if they're empty.

And on this note, I give up! Apologies to the rest of the forum for wasting so much bandwidth

help a student please (dBFS and loudness measures)!

Reply #38
What I am saying is that I find RMS not suitable for measuring music power.
What is then - and why?

(I suppose a pre-question should be what exactly do you intend to measure, and why/when is this useful?)

Cheers,
David.


 
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