No ill intent.
It is a statistical thing related to the DNA analogy. An allele is a single genetic characteristic that has a finite probability of occurring in a population, say 0.01. With a 0.01 there is a 1 in 100 chance of that characteristic being in a single sample. Now we find a second allele with the same 0.01 probability of occurring in a population. The probability of both characteristics showing up in a single sample is =0.01*0.01= to 1 in 10,000. Add only 2 more characteristics, for a total of 4 with the same probability of 0.01 of being in a single sample the probability of all 4 characteristics showing up in a single sample climbs to 1 in 100,000,000. (=0.01*0.01*0.01*0.01) This puts the chances of winning the LOTTO into perspective.
Back to higher order distortion products: if 1 Higher Order Distortion Product has a 1 in 10 chance to sound a particular way, add 3 more HODP’s and you have a 1 in 100,000,000 of having a particular sound, we could say a 1 in 100,000,000 chance of sounding bad. (Your Mileage May Vary.)
While I am at it, pick a brand any brand and model all with the same CD + horn/waveguide they will have the same brand name HODP Profile.
Now you have it.
Thanks DT
GedLee,
I was hoping that you would be more forthcoming with what you know. Often you start off by telling people that they will not be able to understand. Other times you say, I know but I’m not telling.
Hello All,
Post number 1 gives us a spread sheet to calculate Gm; a weighted harmonic metric. The data; the magnitude and phase of the harmonic are entered and the output is Gm. Thank you for this spreadsheet.
There must be FFT’s floating around that are the source of the data used to calculate Gm.
I would be interested in seeing your FFT’s, I suspect there are visual patterns in the FFT’s.
When the weather permits I will go out in the back and do some measurements.
Thanks DT
I was hoping that you would be more forthcoming with what you know. Often you start off by telling people that they will not be able to understand. Other times you say, I know but I’m not telling.
Hello All,
Post number 1 gives us a spread sheet to calculate Gm; a weighted harmonic metric. The data; the magnitude and phase of the harmonic are entered and the output is Gm. Thank you for this spreadsheet.
There must be FFT’s floating around that are the source of the data used to calculate Gm.
I would be interested in seeing your FFT’s, I suspect there are visual patterns in the FFT’s.
When the weather permits I will go out in the back and do some measurements.
Thanks DT
I have never not answered a reasonable question by a reasonable person. I do warn people that many things are difficult to understand, but never said "that they will not be able to understand."
Hello,
GedLee,
I will aspire to ask reasonable questions and be a reasonable person. As to understanding, you often send people off to read your work. To answer my own questions I have downloaded chapters of your book; Chapter 10 “Distortion”and Chpter 12 “Measurments”. So far, background and foundation building information sort of stuff. I bought a hard copy of your book; it is going on the shelf in the acoustics section. (No question now)
mbrennwa,
You are all over my meaning, “visual patterns”.
Hope that you don’t mind that I post one of your visuals here. Your FaitalPro visual looks to have a pattern of peaks and valleys that may even be brand and model specific. I am thinking that type of data would look really impressive in a waterfall type graphic spilling down the diminishing input voltages.
Thanks DT
Attachments
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That sounds good.
It seems to me to be a reasonable expectation that people read what is already available if that answers their questions, rather than my repeating the same answers that have already been discussed.
I do not answer questions sent to be directly, I ask that they post the question to DIY so that I can answer it there. This turns some people off, but hey, I get tired of answering the same questions over and over and over and ... .
I'm digging up an old thread here with a lot of admission and humility:
1) I took math in college. I didn't hate it. I didn't suck at it. But to say I was a mathematician is a far cry from reality. Moreso, it's been about 15 years since I have done anything other than simply use Mathcad to crunch some integrations. So, in my current state... yea, I suck at math.
2) I have read over these works a number of times over the last 10 years. Trying to think of how I could implement the Gm metric in to what I do with testing drive units and loudspeakers. Every few years I come back to the topic, read it, get dissuaded either by the ability of myself to calculate the metric, or by the applicability of the metric in general; after all, many feel distortion is a "non-issue" at all. So, that doesn't give me a lot of motivation.
Enter my 4th round of "hey, I wonder..." and here I am, again. And I have to think, surely I can do this. Surely I can take my data and find a way to provide the Gm metric in my results.
Rather than give up before I start, I figure I need to give this a go. So, I am soliciting help - albeit with cautious optimism.
Here is what I have access to:
I can take the data and dump it out in text file. I can read it in to MATLAB. Thing is... what data do I need? Is the HD data adequate (as it yields the fundamental and the HD orders; I need to go higher than 5th, I am sure). I also have a way to dump the stimulus as a .txt file so I can use that as well. And then after I get the data, I need to do something with it which involves the calculations. I am hopeful someone here would be willing to work with me so that I can take the tools I already have and use the data generated from them to provide us with not just the standard HD data but also a graphic with the Gm included. I really want to improve our understanding and the usefulness of the data. If you guys think incorporating the Gm metric is a valid way of doing that then I'm game. If, however, we are still at the point where "eh, distortion isn't a big issue" then that's fine, too.
Any help is appreciated.
- Erin
Here is an example of the data I already provide. I can go at least to 9th order, and I think I can go higher than that but I'll have to double check.
1) I took math in college. I didn't hate it. I didn't suck at it. But to say I was a mathematician is a far cry from reality. Moreso, it's been about 15 years since I have done anything other than simply use Mathcad to crunch some integrations. So, in my current state... yea, I suck at math.
2) I have read over these works a number of times over the last 10 years. Trying to think of how I could implement the Gm metric in to what I do with testing drive units and loudspeakers. Every few years I come back to the topic, read it, get dissuaded either by the ability of myself to calculate the metric, or by the applicability of the metric in general; after all, many feel distortion is a "non-issue" at all. So, that doesn't give me a lot of motivation.
Enter my 4th round of "hey, I wonder..." and here I am, again. And I have to think, surely I can do this. Surely I can take my data and find a way to provide the Gm metric in my results.
Rather than give up before I start, I figure I need to give this a go. So, I am soliciting help - albeit with cautious optimism.
Here is what I have access to:
- KLIPPEL hardware and software. I use the NFS for speaker measurements. I can pretty easily gather anechoic harmonic distortion data at varying levels. In fact, I do this already for my loudspeaker tests (examples provided below). I sweep for HD at 86dB @ 1m and 96dB @ 1m. If you want to see an example of my testing, here is a link to the Kef R3 review I completed last month:Kef R3 Bookshelf Speaker Review
- I can generate IMD but that's a lot harder as there is no way for me to do so without going outdoors and that creates its own set of issues.
- MATLAB. I can code stuff up. I'm not the best developer... but I make do. You can find some examples on my site.
I can take the data and dump it out in text file. I can read it in to MATLAB. Thing is... what data do I need? Is the HD data adequate (as it yields the fundamental and the HD orders; I need to go higher than 5th, I am sure). I also have a way to dump the stimulus as a .txt file so I can use that as well. And then after I get the data, I need to do something with it which involves the calculations. I am hopeful someone here would be willing to work with me so that I can take the tools I already have and use the data generated from them to provide us with not just the standard HD data but also a graphic with the Gm included. I really want to improve our understanding and the usefulness of the data. If you guys think incorporating the Gm metric is a valid way of doing that then I'm game. If, however, we are still at the point where "eh, distortion isn't a big issue" then that's fine, too.
Any help is appreciated.
- Erin
Here is an example of the data I already provide. I can go at least to 9th order, and I think I can go higher than that but I'll have to double check.
An externally hosted image should be here but it was not working when we last tested it.
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Then take a look at MATAA. It's basically an audio test system for GNU Octave (or Matlab).
MATAA has a function to measure GedLee metric, see here: mataa/mataa_measure_GedLee.m at master * mbrennwa/mataa * GitHub
Much of the code is concerned with plotting the intermediate steps of the GedLee stuff, but you might be able to extract the stuff that is interesting for your needs.
Here is an example of how I used MATAA to measure the GedLee metric for two different woofers.
Erin
I couldn't open you attachment.
For loudspeakers I do think that we will find that any "good" loudspeaker will not have enough nonlinear distortion to be a real concern. Gm will probably work on smaller loudspeakers that can distort significantly within their operating intentions, but larger pro ones likely won't.
Still, if you'd like some help let me know, but I think that mbreewa has the right approach.
I couldn't open you attachment.
For loudspeakers I do think that we will find that any "good" loudspeaker will not have enough nonlinear distortion to be a real concern. Gm will probably work on smaller loudspeakers that can distort significantly within their operating intentions, but larger pro ones likely won't.
Still, if you'd like some help let me know, but I think that mbreewa has the right approach.
Earl, sorry, the link was bad. I've provided new examples below.
I did check my most recent measurement and found the Klippel software will measure out to the 24th harmonic.
I can output the raw data in different ways:
1) absolute terms with the fundamental or
2) relative to the fundamental.
Images shown below.
Here are the text files for the above:
1) Dropbox - Fundamental + Harmonic distortion components.txt - Simplify your life
2) Dropbox - Harmonic distortion (relative).txt - Simplify your life
I have also attached the graphic of the stimulus signal as it *seems* to me that this is also needed. And, likewise have the data linked here:
Dropbox - Spectrum of stimulus.txt - Simplify your life
I did look at the above link and found the script for producing the Gedlee metric but I guess the first question I need answered is:
What do I need to get started to calculate the Gm? Is the fundamental + harmonic data all that is needed? Is the above information adequate?
Again, I apologize for what I'm sure are trivial questions but I'm trying to take this one step at a time before I start diving headfirst.
------------------
I did check my most recent measurement and found the Klippel software will measure out to the 24th harmonic.
I can output the raw data in different ways:
1) absolute terms with the fundamental or
2) relative to the fundamental.
Images shown below.
Here are the text files for the above:
1) Dropbox - Fundamental + Harmonic distortion components.txt - Simplify your life
2) Dropbox - Harmonic distortion (relative).txt - Simplify your life
I have also attached the graphic of the stimulus signal as it *seems* to me that this is also needed. And, likewise have the data linked here:
Dropbox - Spectrum of stimulus.txt - Simplify your life
I did look at the above link and found the script for producing the Gedlee metric but I guess the first question I need answered is:
What do I need to get started to calculate the Gm? Is the fundamental + harmonic data all that is needed? Is the above information adequate?
Again, I apologize for what I'm sure are trivial questions but I'm trying to take this one step at a time before I start diving headfirst.
------------------
An externally hosted image should be here but it was not working when we last tested it.
An externally hosted image should be here but it was not working when we last tested it.
An externally hosted image should be here but it was not working when we last tested it.
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To do things right you need the level and phase of each harmonic and from this you can calculate the nonlinear transfer characteristic from which Gm is derived. Swept sine won't work because you need the phase. I would do stepped sine with synchronous averaging to get above the noise floor for good resolution of the higher harmonics.
Your example above is a classic one in that the THD is almost dominated by 2nd order, which is almost inaudible. So while the THD may be high, audibility will be low. The 4th may be an issue, but it's still down 15-20 dB below the 2nd. Nothing that I see would worry me.
And I'll be honest here. When I started to research nonlinear distortion I was convinced that it was a major aspect of loudspeakers. The more I researched, the less convinced that I became, to the point where I don't consider nonlinear distortion to be a significant factor in loudspeakers (amps are another story.) I now believe that what we hear as nonlinear distortion is linear distortion through group delay. Group delay audibility increases with SPL (shown by Brian Moore.) We showed that group delay was more audible in simulations as the SPL rises. This means that what we "think" is nonlinear distortion - because its audibility increases with level just as the THD does - but, in fact, it is the ear that has a nonlinear audibility, not the loudspeaker.
This is why I stopped studying nonlinear distortion in loudspeakers.
Your example above is a classic one in that the THD is almost dominated by 2nd order, which is almost inaudible. So while the THD may be high, audibility will be low. The 4th may be an issue, but it's still down 15-20 dB below the 2nd. Nothing that I see would worry me.
And I'll be honest here. When I started to research nonlinear distortion I was convinced that it was a major aspect of loudspeakers. The more I researched, the less convinced that I became, to the point where I don't consider nonlinear distortion to be a significant factor in loudspeakers (amps are another story.) I now believe that what we hear as nonlinear distortion is linear distortion through group delay. Group delay audibility increases with SPL (shown by Brian Moore.) We showed that group delay was more audible in simulations as the SPL rises. This means that what we "think" is nonlinear distortion - because its audibility increases with level just as the THD does - but, in fact, it is the ear that has a nonlinear audibility, not the loudspeaker.
This is why I stopped studying nonlinear distortion in loudspeakers.
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Thanks for the information.
And I truly appreciate your candor.
For the longest time, I have been measuring distortion metrics because - honestly - everyone else was doing it and I thought it better to provide the data in case it might become more useful at a later point than to not provide it. I do agree with you that in the majority of cases that I measure high distortion, the issue is less to do with the audible "aggressive" or "grainy" or otherwise sound but rather mechanical issues such as port chuffing/resonance, suspension limiting, over-excursion. That sound, I have a different feeling about compression.
I do have a lot of anechoic data generated with the NFS. If ever you find the need or desire, I would be happy to provide you with whatever data you might find useful for any future curiosities you have in regards to your topic about group delay.
And I truly appreciate your candor.
For the longest time, I have been measuring distortion metrics because - honestly - everyone else was doing it and I thought it better to provide the data in case it might become more useful at a later point than to not provide it. I do agree with you that in the majority of cases that I measure high distortion, the issue is less to do with the audible "aggressive" or "grainy" or otherwise sound but rather mechanical issues such as port chuffing/resonance, suspension limiting, over-excursion. That sound, I have a different feeling about compression.
I do have a lot of anechoic data generated with the NFS. If ever you find the need or desire, I would be happy to provide you with whatever data you might find useful for any future curiosities you have in regards to your topic about group delay.
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This also may not be the best place to ask you but I figure I might as well ...
Would you be interested/willing to have a recorded chat about your studies in to nonlinearity that I could share on my YouTube channel? I think it would be enlightening (not just for myself) and would be a nice way to talk about the data reviewers provide and how we (I) could be missing the mark. I'm always looking to improve my understanding. If you're willing to do that, let me know and I will PM you. If not, I understand. I imagine at this point you're probably "over it".
Would you be interested/willing to have a recorded chat about your studies in to nonlinearity that I could share on my YouTube channel? I think it would be enlightening (not just for myself) and would be a nice way to talk about the data reviewers provide and how we (I) could be missing the mark. I'm always looking to improve my understanding. If you're willing to do that, let me know and I will PM you. If not, I understand. I imagine at this point you're probably "over it".
Now that is interesting. Why / how are loudspeakers and amplifiers different with non-linear distortion?
That's an easy discussion and core to the problems with THD.
The most audible form of nonlinearity will be crossover distortion. (.1% THD crossover distortion can be quite audible while 15% pure second is barely audible.) That's because it is very high order and its % level rises as the signal level lowers. This unmasks the harmonics and makes them very audible.
Feedback can also aggravate this situation because it tends to lower low order harmonics but raise the higher order ones.
Loudspeakers don't have these kinds of problems in general (of course there can be issues with a poorly made driver which can do similar things as crossover distortion, but these are rare and mostly designed out.)
Amps will almost always have some level of crossover distortion, although this too can be designed out. The problem is that crossover distortion tends to be masked in the THD + Noise sweeps that are usually used on amplifiers. Some years ago I developed the technique for synchronous averaging of a signal time-locked to the signals frequency - i.e. the wavelength of the fundamental is fitted exactly into the time window. Thus averaging will reduce the noise level with each average. This technique unmasks the harmonics from the noise at very low levels. With this technique I was able to see differences in amplifiers that appeared from the data sheets to be comparable.
Hence amps tend to always have the most audible form of nonlinearity while loudspeakers seldom do.
The most audible form of nonlinearity will be crossover distortion. (.1% THD crossover distortion can be quite audible while 15% pure second is barely audible.) That's because it is very high order and its % level rises as the signal level lowers. This unmasks the harmonics and makes them very audible.
Feedback can also aggravate this situation because it tends to lower low order harmonics but raise the higher order ones.
Loudspeakers don't have these kinds of problems in general (of course there can be issues with a poorly made driver which can do similar things as crossover distortion, but these are rare and mostly designed out.)
Amps will almost always have some level of crossover distortion, although this too can be designed out. The problem is that crossover distortion tends to be masked in the THD + Noise sweeps that are usually used on amplifiers. Some years ago I developed the technique for synchronous averaging of a signal time-locked to the signals frequency - i.e. the wavelength of the fundamental is fitted exactly into the time window. Thus averaging will reduce the noise level with each average. This technique unmasks the harmonics from the noise at very low levels. With this technique I was able to see differences in amplifiers that appeared from the data sheets to be comparable.
Hence amps tend to always have the most audible form of nonlinearity while loudspeakers seldom do.
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Well, ok, comparing just THD is another story than "non-linear distortion" in general.
I guess your point could be taken to say that the GedLee metric would be more useful to characterise amplifiers than loudspeakers, because it amplifies what the ear/brain perceive as "bad" (the crossover distortion, which not a primary issue with loudspeakers).
Since THD does not correlate with perception, the GedLee metric "would be more useful to characterize" anything, a loudspeaker or an amp. It's just that we then find that amps nonlinearities are more likely to be audible than loudspeakers.