How we perceive non-linear distortions

Pinox67

Member
2017-01-20 8:25 pm
Roma
I am a SW engineer with the hobby of audio reproduction.
I have no in-depth experience with regards to electronics, but in the group I attend I have a couple of friends who build amplifiers (both solid-state and tube) for the local market (I live in Italy). Having measuring instruments, computer skills, and an acoustically treated room for music listening, I help them fine-tune their creations. I was also lucky enough to measure and listen to dozens of preamps from many brands, so, after some years of experience, I ventured into the difficult task of better correlating measurements to listening tests, also considering psychoacoustic effects in the equation (yes, very challenger!). This is based on the great work done by people like GedLee, Nelson Pass and Bob Katz.

The study I'm conducting with personal resources is in this thread.
In this following post I explain the rationales better.
Finally, the state of the study (still ongoing) is here and additional explanations here.

Some aspects are very technical, but I hope they can be understood by people with not too much knowledge of acoustics and electronics.
I would like to have comments/suggestions on the subject.
 
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After years of dabbling with the occasional multi-way speaker design, I ventured into amplifier design, and here are a couple of things I've noticed so far...

There seems to have been a bit of a "cold war" going on with current feedback vs voltage feedback and variations thereof. There is plenty of evidence that current steering, which what tubes usually do actually allows speakers to produce much lower THD. Even class-A transistor amps cannot be guaranteed to work one way or the other without looking at the schematic layout. Sometimes, they are 'correct' (says me) with open-drain / current steering. Other times, the output is a unit gain buffer and/or uses voltage feedback.

But I guess it's human nature that when people have already built something, they don't like being told that they were mistaken in some way. Especially if they have already spent years and 100s of hours designing class AB amplifiers with <0.01% distortion, only to have some guy on the internet claim that they've done something backwards. Or that the 0.01% buried inside the amplifier is meaningless when the way it was achieved causes THD from the speaker load to go up from 0.1% to 1%.

E.g.: that force applied to the voice coil is proportional to Current x turns x magnetic field strength.
That delayed energy from the cone flexing as well as air pressure and box vibrations displace the coil, and that these laggy vibrations should be allowed to ring freely (dissipated naturally by the air load and mechanical damping) and that the corresponding delayed voltages that appear should not be short-circuited with a low output impedance.

Or telling people that short-circuiting the coil does not damp it or absorb vibrations. Rather, it tends to reflect echoes in much the same way that an immovable concrete wall causes balls thrown at it to bounce right back.

That attempting some kind of back-EMF 'control' of the speaker cone does not work because of the delay. That delays change the phase of the signal. Therefore, negative feedback is incapable of stopping them, unless it is somehow intelligently filtered in an active speaker setting. Depending on factors entirely out of an amplifier designer's control, a speaker builder could use a 6" woofer and build a box with 20cm walls and a certain set of resonant frequencies. Or they could build another loudspeaker with a different set of resonant frequencies.

Depending on whether voltage feedback is attempting to correct a frequency node or an anti-node, the phase could be shifted anywhere from 0 or 360 degrees, to 180 or 270 degrees. Nearly all of the low THD claims that I've seen, rely on unrealistic assumptions that the speaker connected is not actually a transducer, and that it won't produce any voltages. Not least, distorted voltage echoes.

If we accept that if a speaker has relatively high THD, inherently, then we should also accept that repeated voltage to motion to voltage to motion (etc....) conversions should be kept to a minimum. Low output resistance / voltage feedback attempts to maximise voltage regulation, with the side effect that it also makes a mess of stored energy, recursively adding more harmonics and secondary distortions. Then people blame speakers for being unusable above a certain frequency because of cone-breakup. No, a poorly suited amplifier made a mess of cone break-up.

Then it's possible to see the earlier premises in a different light.

Perhaps it's not so much that harmonic distortion is "subjectively appealing", but that perhaps a design with an otherwise mediocre 0.1% THD may actually produce far less of the other types of distortion that only appear once a practical speaker is connected?


Real life examples:
People routinely add L-pads and series resistance to their tweeters to dial back sensitivity, and they admire the improved sound as a matter of course. But then they attribute the subjective improvement in tone to a mundane change in EQ, not realising that most of the difference was probably the reduced THD.
 

Pinox67

Member
2017-01-20 8:25 pm
Roma
For a person who tries to reason with a scientific approach, audio is probably one of the most mysterious and fascinating disciplines one can deal with. There is a lot of subjectivity in the audio as the characteristics that the waveform of a sound must have to make it more "pleasant" and "realistic" than others have not yet been rigorously defined. The reasons are in the complexity of the devices in the production / reproduction chain and in the psychoacoustic component involved, which makes it difficult to establish well quantifiable and absolute results. Probably there will never be, but this does not prevent us from deepening where possible little explored aspects to arrive at a greater understanding.

From your experience, if I understand correctly, the distortions you are referring to are generated in the interaction between the power amp and the loudspeakers. The former are not always able to correctly control the mechanical vibrations of the cones returned in voltage to the power amp, and this creates potentially audible distortion. So, even if a given power amp has higher distortions than another (resulting from dummy resistive load), this could still induce a more linear behaviour in a real speaker (with "live" load), and therefore greater fidelity in listening, because its internal design (the internal feedback strategy) is different.
An interesting and entirely reasonable hypothesis, considering that even here for this interface, where usually the main parameter is the Damping Factor, there is no clarity or agreement in the community: low, but not too much (in tube amps), or high (only possible with solid state amps).
It would be nice to be able to measure these effects… have you ever thought about setting up any ad-hoc tests?

However, there are other elements in the field. In the interface between power amp and preamp, or the latter and a DAC, the effects you are talking about are not present. Yet, by switching only the preamp or the DAC in a given chain, the sound can change considerably. Here I think the game is dominated by non-linear distortions, once the other parameters are "normal".
Now the point is that some distortions (I'm studying that of the preamps) improve the listening pleasure. If this improvement derives from the loudspeaker which is indirectly induced to behave in a more linear way also in this case, or due to the our ear masking effect, it could be a further element of investigation. Maybe it's a combination of both… increasingly difficult!

I must say that in favor of the first hypothesis there are already precedents in the DACs, well studied and probably little known. Simplifying as much as possible, in these devices the heart section of the signal conversion from digital to analog shows two types of distortions that are not found in analog devices.
The first is caused by inaccuracies on the clock time axis. This type of distortion, known as Jitter, has been well studied and now seems to have been outdated. The second, less known, is the one on the axis of levels in volts. For example, when you pass from the numeric input value 100 to 101, I expect an increase of let's say 1mV at the output; from 101 to 102 I expect the same 1mV increase and so on with all other intervals. In reality, things are different… There are conversion errors, for which the same differences in numerical values in the input do not give the same difference in voltage at the output. This problem is known as differential non-linear distortion and all DACs are affected. Difficult to measure; however, it introduces distortions that make the signal tiring and hard (especially at higher levels).

Two are the classic strategies to reduce the problem. The first involves the use of multiple DAC chips in parallel, mediating the output of each. Of course, it is a bit expensive solution... The other is to act on the digital oversampling filters, that should introduce samples that generate in the final signal ultrasonic frequency components. These have the ultimate effect of simulating the presence of multiple DAC chips, and thus of assisting in more linear behaviour. This is the main reason why digital filters with slow roll-off, theoretically less correct than those with fast roll-off (that do not introduce ultrasonic components), sound better.

Hence, injecting something "foreign" to the original signal ("good" distortions) helps the DAC to contain less pleasant distortions.
 
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It would be nice to be able to measure these effects… have you ever thought about setting up any ad-hoc tests?

However, there are other elements in the field. In the interface between power amp and preamp, or the latter and a DAC, the effects you are talking about are not present. Yet, by switching only the preamp or the DAC in a given chain, the sound can change considerably. Here I think the game is dominated by non-linear distortions, once the other parameters are "normal".
Now the point is that some distortions (I'm studying that of the preamps) improve the listening pleasure. If this improvement derives from the loudspeaker which is indirectly induced to behave in a more linear way also in this case, or due to the our ear masking effect, it could be a further element of investigation. Maybe it's a combination of both… increasingly difficult!

I must say that in favor of the first hypothesis there are already precedents in the DACs, well studied and probably little known. Simplifying as much as possible, in these devices the heart section of the signal conversion from digital to analog shows two types of distortions that are not found in analog devices.
The first is caused by inaccuracies on the clock time axis. This type of distortion, known as Jitter, has been well studied and now seems to have been outdated. The second, less known, is the one on the axis of levels in volts. For example, when you pass from the numeric input value 100 to 101, I expect an increase of let's say 1mV at the output; from 101 to 102 I expect the same 1mV increase and so on with all other intervals. In reality, things are different… There are conversion errors, for which the same differences in numerical values in the input do not give the same difference in voltage at the output. This problem is known as differential non-linear distortion and all DACs are affected. Difficult to measure; however, it introduces distortions that make the signal tiring and hard (especially at higher levels).

Two are the classic strategies to reduce the problem. The first involves the use of multiple DAC chips in parallel, mediating the output of each. Of course, it is a bit expensive solution... The other is to act on the digital oversampling filters, that should introduce samples that generate in the final signal ultrasonic frequency components. These have the ultimate effect of simulating the presence of multiple DAC chips, and thus of assisting in more linear behaviour. This is the main reason why digital filters with slow roll-off, theoretically less correct than those with fast roll-off (that do not introduce ultrasonic components), sound better.

Hence, injecting something "foreign" to the original signal ("good" distortions) helps the DAC to contain less pleasant distortions.
I have thought about adhoc tests.
Something like momentarily applying a DC voltage, and then taking snapshots of the speaker response (either mic or oscilloscope or both) vs various damping factors.

It might be that different loads are optimal for damping different frequencies.

One method of EQ tuning I've used with good success was to manually play sine waves on a keyboard. I would home-in on room resonances, and then use parametric EQ tools (like Calf on linux) to create digital notch filters, adjusting frequency, Q and depth by ear so that the subjective loudness was smoothed out. What I found was that by adding 10 ohms series resistance to the woofers (reducing the digital amp's damping factor to single digits), the notch amplitude and Q for the main resonance had to be reduced rather than increased.

I had to think about that one. Eventually I concluded that the once the energy was out in the room, the speaker was a 'node' and the cone stiffness was actually making the room more resonant. And with the woofer being the source of the sound, the added resistor helped it play a critical role as a kind of damping device.

Because of examples like that, I mostly stay away from the damping factor debate. I have another hypothesis that what some may regard as "loose, woolly" bass, is actually a reduced ability to localise the sound sources if the distortion is 'too' low, so it seems less 'tight'.

Or for that matter, a semantic issue regarding expectations. E.g.: large subwoofers with extremely powerful resonances that make the whole house shake on specific notes. But I suspect if you put an acoustic double bass, with the multipolar vibrations of it's violin body, into the same room, it will yield to that room and sound completely different.

There's so much to consider, I may follow up with another post later.
 
Interesting thoughts. Without going into details, two comments.
Firstly, the field you discuss from preamps, amps, speakers, DACs is VERY large. If you are serious about this and expect any meaningful results in this lifetime, you'd probably want to select something more narrow and focused.
Secondly, I see a mixing of technical arguments interspersed with subjective, personal observations ('sounds better'). This is a good recipe to get lost in opinions and personal views rather than rigorous engineering.

My € 0.02

Jan
 

Pinox67

Member
2017-01-20 8:25 pm
Roma
Interesting thoughts. Without going into details, two comments.
Firstly, the field you discuss from preamps, amps, speakers, DACs is VERY large. If you are serious about this and expect any meaningful results in this lifetime, you'd probably want to select something more narrow and focused.
Secondly, I see a mixing of technical arguments interspersed with subjective, personal observations ('sounds better'). This is a good recipe to get lost in opinions and personal views rather than rigorous engineering.

My € 0.02

Jan

Hi Jan,
Thanks for your suggestions. I agree, the theme is vast. The latest posts talk about how "bad" distortions are generated. As you correctly observe, they should be addressed in ad-hoc threads. In this post I address the issue of how to mask them with "good" distortions (if possible), regardless of which element of the electronic production / reproduction chain is generated. If there is any more specific section in which these aspects are discussed, let me know, I can save some time!

Regarding the observation about "sound better”. If the relationship “greater linearity" <-> “better sound” is true, what is reported succinctly on DAC is not a personal opinion, it is a fact. There are several scientific articles on differential non-linear distortion and how to contain it. If you want to start with something introductory on the subject you can read here. The debate, if anything, is on the sonic qualities of the different oversampling algorithms that inject more or less important quantities of ultrasonic energy, on which we can discuss on threads dedicated to DACs.

Pino
 
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That what is reported succinctly is invariably personal opinion.
There are very, very few well conducted and controlled tests that can be expected to objective results, not tainted by subjective, uncontrolledly outcomes.
If you want to tie technical parameters to audible results, you need to develop a trustworthy method to test for 'audibility' that takes out any personal and subjective influences.
Things like double blind tests are hard, expensive and time consuming.

Jan
 

Pinox67

Member
2017-01-20 8:25 pm
Roma
I agree Jan, objective tests are complex and long to perform (I am trying to perform them as part of my study).
However, based on your experience, "higher linearity" in our audio devices implies "better sound", where I mean quality like fidelity and realism? Or is this relationship purely subjective?
 
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The relationship between measurements of distortion and noise (i.e. 'figures of merit), and subjective perceptions of fidelity and realism is that two types of information are only partially correlated. More could be said about that of course. One issue that often comes up is that measurements are more practical to communicate with shared meaning than are verbal descriptions of subjective perceptions.
 
However, based on your experience, "higher linearity" in our audio devices implies "better sound", where I mean quality like fidelity and realism? Or is this relationship purely subjective?
For me it is, because I believe in reproducing without adding anything or taking away anything. My friend with the 8W single ended EL84 amp will swear that his amp is the most realistic and HiFi.
Definition of personal and subjective.

Jan
 
The relationship between measurements of distortion and noise (i.e. 'figures of merit), and subjective perceptions of fidelity and realism is that two types of information are only partially correlated. More could be said about that of course. One issue that often comes up is that measurements are more practical to communicate with shared meaning than are verbal descriptions of subjective perception
Well it's a bit philosophical isn't it? What's the ultimate measure of 'truth'? One person's subjective experience or another person's measurement?

A recent example that comes to mind: I was looking at distortion simulations, and trying to gauge which would sound better. Then I remembered those old Fletcher Munson equal loudness contours, and how the 'average' ear was far more sensitive to some frequencies (like 1k-4kHz) than others (like <100Hz).
To do it properly (note to self ;) ) I could collect some test results of individual harmonics, adjust the values in a spreadsheet according to a look-up table based on the F-M curves, and re-calculate a superior "weighted-THD".

Nonetheless, if you see something like:
H1 (1kHz) = 1V
H2 = 1mV
H3 = 150uV
H4+ = 100uV
and say that you've calculated for the given system that the threshold for 0dB would be 8uV, it's easy to see that all of the harmonics up to 20 are at risk of being audible. And H3-H4 is potentially >10 times more significant on a linear scale than all of H10-H20 combined.
However, when I checked, THD is calculated in a strange way, and I'm not even sure which formula should be regarded as correct.

One issue, apart from lack of weight
--Some versions seem to calculate the correct power, adjusting for phase shifts so that some harmonics may subtract from the total.
--Other versions, ignore phase and simply add up the absolute values of the harmonics.

Intuitively, I think our ears do a lot of both. The eardrum is sensitive to power levels and offsets and so on. But the cochlea measures amplitudes of frequency bands. I've seen many graphs of waveforms of additive music synths, where by changing the relative phases of individual harmonics, the shape of the wave can be significantly altered, from tall spikes at one extreme to random-like squiggles.
And I'm not certain at all that we are 'deaf' to phase. In fact, it seems quite obvious to me that those keyboard "phasor" effects that rely on subtle frequency shifts could do with some more investigation.
A detuned harmonic is a static property. But what I hear (I only speak for myself) seems to change dynamically, suggesting that the shape of the wave form in the time domain is also significant.
 
Non linear distortion is a broad concept.

But adding audible amounts of harmonic distortion to a musical signal ( like some tube equipment, vinyl and tape is doing) is perfectly understood by the science dudes.

In fact it's the nr 2 tool in the box for any audio engineer (nr1 tool is linear distortion)


So what happens:
When there's audible harmonic distortion added to a signal, we perceive it as louder without is actualy becoming much louder in level. This is because more interaural frequency bands are stimulated. Simple test is to sweep saw wave with a lowpass filter, level doesn't change, but the perceived loudness does.
If you add these harmonics more as level increases, as is the case with vinyl, tape and some tube equipment, the perceived difference is more impact with percussive sounds.

The other thing that happens is that low level signals, that were just below the perception threshold, can become audible.
This can be perceived as more low level detail.

Iow: More impact for percussive sounds and more low level detail.

All up to a point of cause.
 
Well it's a bit philosophical isn't it? What's the ultimate measure of 'truth'? One person's subjective experience or another person's measurement?
Its a complex and not uncontroversial subject. People have been arguing about some of it for decades. There is some (incomplete) science, and lot more in way of opinion and belief. Welcome to the fray.
 

Pinox67

Member
2017-01-20 8:25 pm
Roma
For me it is, because I believe in reproducing without adding anything or taking away anything. My friend with the 8W single ended EL84 amp will swear that his amp is the most realistic and HiFi.
Definition of personal and subjective.

Jan

Greater linearity implies greater fidelity also for me and consequently it should also imply greater listening pleasure. But for many audiophiles (who do not know much about technique, only interested in good listening) this last implication is not always true. They prefer components somewhere in the playback chain (usually tubes in the preamps) which instead distort the signal. For those who have read carefully the links of my initial post, I am trying to study this aspect.

In summary, the hypothesis is that "linearity" and "fidelity" refer to the medium (disc, liquid, etc.) that we listen to on our playback chain. Among the signal collected from the original music sources to this medium are a myriad of processing in the production chain that ultimately inject distortions, whether intentional or not, into the signal we hear.
If these distortions in modest quality systems are not audible (indeed, the purpose of the desired ones is to make listening more enjoyable), in high quality ones, more radiographic, instead they make listening unnatural and tiring: we also hear distortions that have nothing to do with the original sound.
If we accept this hypothesis, it is easy to understand the reason for a large part of subjectivity in the sector, where we prefer (often unconsciously) components that alter the signal in order to mask these distortions. Difficult task, given that there is no precise recipe of how to do it, since the type of intervention depends on many factors, such as:

  • type of processing in production chain
  • type of music
  • listening level
  • reproduction chain

To investigate this hypothesis, I wrote a program that, given an audio file in PCM format in input, of any bit depth or sampling frequency, produces an output file resulting from the application one or more of the following interventions:

  • Upsampling, with different filter types.
  • Downsampling, with different filters types.
  • Dithering and Noise Shaping of different types.
  • White noise injection, possibly with limitation in any band.
  • Injection of static non-linear distortion of any order, possibly with limitation in any band.

In addition to performing listening tests with above modifications, I am working on the implementation of algorithms for the measurement and injection of dynamic non-linear distortion, which best represents our audio devices but is much more complex.

If anyone would like to experience the effect of static distortion injection on their system, I am available: put your reference audio files in a shared directory; on the same I can put new versions of these ones modified with different types of distortion. Of course, the listening test should be blind...

Pino
 
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I had read one of the Olson"s books (difficult to get them in my country) and the Langford Smith's Radiotron, and both concludes that distortion is perceived depending on the listening history and ear education. If you always listening to a Spika, then your ears (brain, etc) will accomodate to this kind of sounds and never will recognize higher quality sound sources.

I personally agree with both authors. Although my ears aren't musically trained (I don't differenciate la440 from la432 nor in error in a note played by a musician) I do recognize when a rig has small amounts of distortion because I always listen to good music and in relatively good sounding equipment.
 
Greater linearity implies greater fidelity also for me and consequently it should also imply greater listening pleasure...
For most people around here, the term 'linearity' seems to imply low measured harmonic distortion. Is that what it means to you?

One reason I ask is because I was browsing Bob Cordell's book on power amplifier design, 2nd Ed., Chapter 16: Other Sources of Distortion. Low and behold, not all of them necessarily show up as easily seen HD spurs on an FFT.

Another reason I ask is that there are some other possibly applicable terms besides linearity that come up in engineering, medicine, and other disciplines: time-invariance and stationarity. I have gotten some flack for using the latter term which has been assigned very specific meaning in statistics, although among other things it has not always been so narrowly defined in practice. Regarding the former term, time-invariance, no one seems to disagree too much that it physically occurs in audio circuits, mostly objections seem to be to the effect that it can be considered negligible. Not everyone necessarily agrees on that, however.

Seems to me if there is going to be meaningful discussion on why people don't agree on what audio technology they prefer, we should at least be sure we agree on a few key terms. Then might be a more appropriate time to bring in to the discussion what I prefer to call, 'errors of listening,' that which some other people might more loosely refer to as 'imagining things that aren't real.'

EDIT: Given the research project effort described by the OP, I would mention I know a guy who is a professional full-time high-end audio designer. He insists that there are some things about even the best digital reproduction available today that makes it inferior to the best of phono and or analog tape reproduction. At first I was very skeptical of his claim, but it turned out he seems to have been onto something. It has to do with accurate, perceptually convincing reproduction of the stereo illusion of soundstage, with width beyond the distance between the speakers and depth into the distance behind them even past the back wall of a room (and for some people it includes a perception of height). Thinking about those things in a technical sense looks to me like it implies accurate reproduction of certain perceptual cues, such as, for example, ratio of direct verses reflected sound implying distance, and HF loss associated with distance. Nobody seems to have figured out how to test human preference for aberrations of reproduction that interfere with the stereo illusion, aside perhaps that part of it attributed to loudspeakers and rooms. There is more to it, again, as it turns out.

My point in mentioning analog reproduction was, if starting out with the premise that various hypothesis can be tested digitally, already some bias is being introduced that may miss the forest for the trees.
 
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He insists that there are some things about even the best digital reproduction available today that makes it inferior to the best of phono and or analog tape reproduction.

Strange that the opinion of a non expert in this field were,re talking about richt now, is taken seriously.
A sound engineer is not a scientist.

Vinyl and tape alway’s adds audible artefacts. The effect of that are fully understood as I’ve mentioned earlyer.