A Rethink of THD/THD+N (or why both tell us almost nothing)

Discussion in 'Audio Science' started by ChaChaRealSmooth, Jul 6, 2020.

  1. Royaume

    Royaume Rando

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    Pls fix sarcasm detector. Is there anything wrong with the unironic content of my post?
     
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  2. Lyander

    Lyander Too sensitive for SBAF

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    @Royaume While this information certainly may help curb the gormless zealotry surrounding THD, your last post read very much as if it merely wanted to replace THD with TAD; more representative of what humans hear it may be, but it does still go against the forum's general stance on not relying too heavily on measurements, specifically ones that seek to oversimplify things to their likely detriment.

    Also something something something religion is a touchy subject etc.; mayhap that was not the best way to galvanise the masses. I'm not going so far as to tell you to fuck off, but I do agree with @Elnrik that this shouldn't be taken quite so seriously. Let people like what they like, as there's no real benefit to losing sleep over something that isn't life-critical.

    Thank you for sharing that though!
     
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  3. ultrabike

    ultrabike Measurbator - Admin

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    Moved THD posts here.
     
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  4. Degru

    Degru Rando

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    I think a classic example of this is the "grainy" mids on hd6x0; the harmonic distortion graph shows up very clean in that region, but compare it to a pair of Stax for example with something like metal and it's night and day (note I haven't had much experience with 6x0 on very high end source gear tho). Transients are basically sharp, irregular waveforms as are commonly present in music. IMD/multitone tests are looking for additional distortions when playing multiple tones that aren't present when playing those tones individually.

    I think the crux of the matter is that real music waveforms aren't pure sine waves and can't be reasonably defined by simple mathematical equations, so depending on tests that derive all of their data from reproduction of a simple sine wave is incomplete and misleading.
     
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  5. Royaume

    Royaume Rando

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    Hahaha, yeah I didn't expect that kind of reaction from Elnrik at all. I'll be more tactful in future lol

    Personally I have actually lost sleep over the fact that literally billions of people are feeding their earholes with poopoo and causing themselves hearing damage etc. In general the audio industry is in a bad place. Isn't that what this thread is about? Trying to address ASR because they are the audio equivalent of eating toothpaste?

    Wrt measurements, I can entirely understand not taking the current suite of measurements seriously, because of their limited capacity to tell us anything. But surely, if we had some very good measurements which characterised the behaviour of audio equipment, would we not pay better attention to them?

    Edit: Thanks for your encouraging response.
     
  6. Biodegraded

    Biodegraded Friend

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    This stuff was also discussed in @ChaChaRealSmooth 's THD thread.

    Edit: And here we all are :)
     
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  7. purr1n

    purr1n Finding his inner redneck

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    Understanding distortion is complex: https://www.superbestaudiofriends.o...hd-n-or-why-both-tell-us-almost-nothing.9544/

    When it comes to this, there is no single number distilled that tells us everything. It's odd, but sometimes distortion comparisons are best used when applied from like to like gear. For example, comparing R2R to R2R DACs, or SET to SET, or Class AB to Class AB.

    Distortion patterns are useful for identifying / confirm audio topologies - there are usually telltale patterns - and be extension kind of sound.

    Case 1 above is a prime example of the near (not total) uselessness of SINAD measurements when it comes amps. Amir couldn't hear the "horrible" 50db SINAD amp in the JBL LSR305. Transducer distortion will always be the weakest link.
     
  8. ultrabike

    ultrabike Measurbator - Admin

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  9. Royaume

    Royaume Rando

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    Ah, thanks for explaining @Degru
    I completely agree that testing methodology is rather limited, and fails to completely capture the behaviour of audio reproduction devices. However, mathematically, between FR and phase we have all the information required for perfect reconstruction of the original signal. So if we have a complete map of harmonic distortion with respect to frequency, we should have a good idea of how the device will behave given some input signal. We are missing phase information but the song almost certainly starts at 0 displacement. We have also not accounted for potential non-linearity. Test tones are all normalised to the same level, but we can expect harmonic distortion to rise non-linearly. We could account for this by plotting distortion against both level and frequency (lots of testing) for an even better model.

    On the whole, TAD is a huge improvement on THD and I think it is worth raising awareness of the major shortcomings of THD compared to TAD.
     
  10. Royaume

    Royaume Rando

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    Also, about the example you mentioned. The harmonic distortion graph might appear clean, but typically unpleasant characteristics such as "grain" are due to high order distortion. How many harmonic components were on the graph? At 400Hz, there are 49 harmonics in the audio band! An extreme example, but the point stands. As I mentioned above, between FR and phase, we have fully described the signal, so is something is audible, you will find it in measurements. You just need to know where to look. I suspect that much of what is "immeasurable" is actually present as very low level high order distortion.
     
  11. Royaume

    Royaume Rando

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    Cheever actually addresses this point in his paper. I'm not sure I can explain it, but he gave some kind of mathematical derivation which I believe showed THD and IMD to be equivalent?

    Again I don't think that there is information which distortion plots does not capture from a theoretical standpoint. I think that other measurements are just different ways of displaying the data.
     
  12. Royaume

    Royaume Rando

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    Wow! Thanks @ultrabike for moving the posts to this goldmine of a thread. Also thanks @Biodegraded for linking @Zampotech s post. How did I not find this sooner?

    Since discovering this flaw with THD I have become a big fan of some kind of weighting system. The BBC's n^2 weighting is interesting but Dan Cheever's paper leads me to believe that the more extreme n^4 weighting is more appropriate as it better matches the harmonic envelope of the ear.
     
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  13. atomicbob

    atomicbob dScope Yoda

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    @Royaume Congratulations on taking steps forward, away from concepts of using THD and THD+N numbers as any sort of figure of merit.

    Now for some further reading look at these two:
    https://www.superbestaudiofriends.o...-of-6-amps-thd-n-and-thd-specifications.6194/
    https://www.superbestaudiofriends.org/index.php?threads/shortest-way-51-technical-measurements.8387/

    Read the entirety of the first post for the SW51+ technical measurements, especially the part about 4+HD+N. Now imagine graphing a sweep over frequency, instead of a single number at some frequency, as another step forward. Even better, two tone FFT sweeps with a 3D display of the FFT. And still this is only representative of static component behavior. Dynamic performance is not well represented at this time in measurements, though some insight may be attained from square wave response.

    *edited for grammatical clarity*
     
    Last edited: Oct 21, 2020
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  14. purr1n

    purr1n Finding his inner redneck

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    Again, bad idea to take a single number distilled from many other numbers.

    Using this method, many R2R DACs would sound like shit, (or at least "grainy") but they don't.

    ADD EXAMPLE

    Measurements of one of the smoothest more liquid sounding DACs I have ever heard in my life:
    https://www.superbestaudiofriends.o...ream-dac-awesomesauce.8493/page-2#post-279357
     
    Last edited: Oct 21, 2020
  15. Royaume

    Royaume Rando

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    Thanks @atomicbob , I was searching for quite a long time.
    Ah, the 4+HD+N crap factor is a neat trick. :headbang:

    Wait, R2R DACs cointain lots of high order distortion? I know delta sigma DACs do, thanks to filtering and such, but I thought R2R were more similar to tube gear in that they tend to have significant levels of lower order harmonics but not much high order stuff.

    Certainly the transducer will dominate the amplifier in terms of THD as it is currently measured. However, Cheever suggests that the amplifier is more often the worse offender since it is likely to have higher TAD due to the weighting of higher order components. I have no idea if this is true or not, but it seems possible with certain SS designs. Could he be right? Do you think the amplifier could degrade the audio more than the transducer/room?

    @atomicbob would it be possible to calculate TAD for a few amplifiers/dacs and see if it corelates well with members subjective rankings? It seems fascinating to me! Cheever claims to have done this with a small number of amps (5 or 6 or something) and then tested them with a live microphone feed from a piano in a separate room. He claims that the ranking matched perfectly with subjective evaluation.
    There are very clear instructions on pages 41 through 44 of the paper for calculating TAD. Could you take a look and confirm that no more measurements are required than for standard THD?
    Let me know if I'm being annoying:D

    https://next-tube.com/articles/Cheever/cheever.pdf
     
  16. ultrabike

    ultrabike Measurbator - Admin

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    R2R have a lot of unfiltered images.

    Delta sigma does not have high order distortion. It is modulated quantization noise. The difference is that in general, non-linear distortion is somewhat correlated to the signal. Noise is not. And because it's not, it may be perceived a bit differently. Not only that, the modulated noise is not necessarily sinusoidal even if the input signal is. Again, it's modulated quantization noise.

    Filtering is your friend here, since it removes out of band noise and images.

    The main problem with R2R is not the unfiltered images. It's the roll off that is also a byproduct of the sample-hold operation.

    The main problem with unfiltered delta sigma, is not the nasties out of band. Because they are out of band. It is the issues that these out of band nasties can have on equipment downstream or so. Maybe EMI if it really goes that high, but don't know, and didn't google.

    R2R is not at all similar to tube gear distortion. It just rolls off, producing likely warmer sound. Maybe some tubes produce warm sound. Many don't. Some can be bright and harsh. Varies system to system.
     
    Last edited: Oct 21, 2020
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  17. purr1n

    purr1n Finding his inner redneck

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    R2R DACs because of their operational nature (low sample rates, discrete samples) have squarish waveforms. Squarish waveforms means harmonics ad infinitum.

    You have it reversed. Delta sigma DACs might have a bit of H2 or H3, maybe a tiny dose up to H5 (none of this detectable by humans ears). They have barely any high order harmonics. For example, here is cheapo sigma-delta Modius DAC at full scale output and note crazy scale (-150db):
    [​IMG]

    We already know TAD won't correlate to subjective impressions based on the measurements here.

    Cheever could very well be correct in regards to TAD with the typical class AB solid-state amp of the 1980s when comparing to 300B SET tube amps. However, the audio world is much larger than that. I bet that for every example where TAD "works", I could show you a counter example of where TAD doesn't work. Even then, there are personal preferences. Who's to say that people may prefer the "grainer" class AB solid-state amp of the 80s over "warmpoo" 300B amps.
     
    Last edited: Oct 21, 2020
  18. atomicbob

    atomicbob dScope Yoda

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    I have a suggestion. You seem very enthusiastic, have the energy towards this topic and probably a lot more time than me. I still have a corporate gig which includes audio and acoustic measurements and takes precedence for my time. It would be a great exercise for you to perform that which you request. Here are some helpful links.
    measurements:
    https://superbestaudiofriends.org/index.php?forums/headphone-amplifier-measurements.13/
    https://superbestaudiofriends.org/index.php?forums/source-measurements.14/

    subjective evaluations:
    https://superbestaudiofriends.org/index.php?forums/headphone-amplifiers-and-combo-dac-amp-units.20/

    And to give you an idea of time required for me to produce my technical measurements per device:
    https://www.superbestaudiofriends.o...echnical-measurements.4774/page-2#post-159219

    By doing this exercise you would become more familiar with the denizens of this forum, measurements of a number of components and also learn considerably more about the various measurements used to characterize static audio component behavior.
     
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  19. Royaume

    Royaume Rando

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    Fascinating. Thanks for the explanation. Also many many thanks to you and everyone else here who maintain this site. I have spent hundreds of hours here and loved every minute of it.

    Thanks @atomicbob , I certainly am enthused. Sadly I am a penniless student and had to save for my headphone rig for a rather long time. I may end up working as a researcher in a field related to audio. Currently I am doing a machine learning project with the goal of "restoring" audio which has been compressed with a lossy codec. One day I will afford the equipment and gear to experiment with new testing methodologies. As you describe, it will be some years before we can capture the dynamic behaviour of audio devices, not just their static behaviour.
    In the meantime I might figure out exactly Cheever's scheme for calculating TAD, and write the pseudocode. It would be interesting to see how TAD compares to your 4+ HD + N as a crap factor estimation thingy.

    Thanks for everyone's input to this discussion. I will dwell on what I have learned.
     
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  20. purr1n

    purr1n Finding his inner redneck

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    @Royaume: This is the direction we are going: Distortion pattern + level

    Simplified cases below - covers most often seen cases. There are variations of these of course.
    upload_2020-10-22_9-4-6.png
    For purposes of high, med, and low level of distortion, we are talking about the device being moderately pushed, a little bit more onset of clipping.
    • High 50-60db THD
    • Med 60-80db THD
    • Low 80db+ THD
    Let's play a game. Match the letter A, B, C, D with the numbers below (one letter to many numbers).
    1. Single-Ended Triode amp
    2. Balanced ASR approved Chinese chip amp with 100db of feedback
    3. Decent Class AB amp
    4. Typical R2R DAC
    5. Modern DS DAC
    6. Well designed dynamic speaker driver
     
    Last edited: Oct 22, 2020
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