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THD, Noise, THD+N. Isn't It All Just Noise?

GrimSurfer

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A recent discussion on the Benchmark's AHB2 discussed the consequences of an amp with measuring THD of -100 vs one with -120 dB. Although unstated, I perceived that the real issue was the audibility spurious sound energy. This got me thinking about how sound levels work across the audio chain...

The decibel is a standard measure of sound pressure. It can be measured as a number of weighted or unweighted values. Setting aside weighting, the two key issues are that:

(1) two or more proximate sound sources of exactly equal value are louder than one source on its own. A loud source and a softer source add up to an incrementally higher spl. Said another way, sound adds up. It doesn't "average out"; and

(2) incremental increases of spl are more significant than simple numbers suggest. Increases of 0.5 dB are audible. Increases of 1 dB are noticeable. Sound intensity appears to double in intensity every 3 dB and doubles in volume every 10 dB. (Hopefully I got that the right way around!)

THD and Noise are caused by different things that don't necessarily factor into the scope of this post. This doesn't mean that these causes are insignificant. Nor does it mean that one isn't necessarily more audible than the other. It is just a way of keeping things simple by looking at the way that the product of both can be heard (or not).

The human auditory system can be fooled that THD is naturally occurring resonance, particularly when the artifacts are even-order (doubling, quadrupling of the primary frequency, etc). Sometimes the ear cannot be fooled, such as happens when encountering audible uneven order harmonics (tripling, quintupling etc.) to which the ear can be quite sensitive.

Regardless of whether the auditory system is fooled or not, sensitive or not, THD is sound extraneous to the intended signal.

Noise is random sound that doesn't necessarily correspond to a fundamental frequency. It too is extraneous to the intended signal but, as is often the case, is spread across a broader frequency range.

Setting aside root causes and the ear's ability to be fooled, THD and Noise is, well, just "noise" to the listener. We may not hear it as such. To some noise is fatiguing. To others it adds certain characteristics to sound, which is sometimes referred to as colour. There are likely more imaginative terms out there to describe the effect Noise has on sound. As an objectivist, many of these fly in one ear and out the other :)

So what are the implications of THD, Noise, or THD+N on the audio chain? The first thing is that the source of the "noise" doesn't matter. A source player, DAC, pre-amp, or amp can (and do) introduce noise at each step of the audio chain. This noise adds up, resulting in a level that is both significant and audible.

Let's look at a practical example of a source player, DAC, pre-amp, and amp -- each of which have THD+N ratings of -100 dB. Together, they have the potential to produce a noise floor of -94 dB. When played at reference levels, they'd theoretically be audible against a human hearing range of 118 dB but probably masked or inaudible except when dynamic peaks rise above reference level.

That same combo with ratings of -120 dB have the potential to produce -114 dB. When played at reference level, they'd theoretically be audible. The levels would be so low, however, that they'd be mostly masked.

I base my probability statements on the Fletcher Munson curves which show that human hearing acuity varies with frequency, with ear being most sensitive to the middle frequencies.

If the components all had noise characteristics in the -124 dB range, then the combined noise of all four devices (-118 dB) would be impossible for the human ear to detect at reference levels. This isn't a matter of opinion. It is based on math and human performance data.

If just one of those components had a spec of -100 dB, the THD+N of the entire audio chain would rise by 18 dB to -99.5 dB.

But what if you could offset that one pedestrian (or to the Aussie vernacular, ordinary) component measuring -100 dB with a really exceptional one measuring -140 dB? Would it average out?

It might not do as much good as you would think. If the other three components were -124 dB, -124 dB, and -140 dB (!) you'd still be looking at a combined THD+N of -99.96 dB. Such is the logarithmic nature of sound pressure levels.

In other words, the overall distortion and noise of an otherwise superb system can be significantly (read: audibly) increased by the introduction of one pedestrian component. This is not a matter of opinion, but an issue of math.

The big take-away is that ALL of the noise, from all of the components in the audio chain, matters.

When playback is much lower than reference levels (say 70-75 dB "easy listening), a certain amount of noise can indeed be inaudible. But anyone seeking exceptional audio performance would likely take greater comfort in knowing that system noise is "inaudible" up to the point of amplifier clipping than having to exercise extreme caution in component matching or volume settings.

I make no claim to having anything but ordinary gear. This doesn't blind me to science. Rather, it sharpens my appreciation of the rarity of exceptional sound and makes me skeptical when people make bold claims against that which math and human physiology says otherwise.

Thoughts?
 

SIY

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A few comments:

Fletcher Munson curves are valid for a single sine wave, not a signal in the presence of another.

Noise sources add as root-square sums since they will generally not be correlated.

Normal rooms have enormously more noise than engineered sources and amplification.

DBTs are necessary if one claims that engineered components, run within their limits, sound different. That's the final test of audibility claims, not "math."
 

andreasmaaan

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While all you say is broadly true, IMO you've left out the most important component: the loudspeaker, whose THD will tend to be in the range of -60B to +X dB (depending on SPL and frequency); in other words, significantly higher than the worst electronic component in the chain.

Further, it's worth noting that due to auditory masking, a single THD figure is near-meaningless.

Assume a test signal of band-limited noise centred at 1kHz played at an SPL of 80dB at the listening position: a 7kHz tone at -65dB is likely to be audible; a 2kHz tone at -40dB is almost certain not to be:

1561156595935.png


In other words, the overall distortion and noise of an otherwise superb system can be significantly (read: audibly) increased by the introduction of one pedestrian component. This is not a matter of opinion, but an issue of math.

The big take-away is that ALL of the noise, from all of the components in the audio chain, matters.

This is the part I take issue with, especially the words "audibly". Your post seems to imply that an electronic component producing THD+N of -100dB is "ordinary". For the reasons mentioned above, it is incredibly unlikely that nonlinear distortion produced by such a component will be audible.

Final note: the addition of distortion products is dependent on their phase. Your sums add up (I think) if the starting assumption is that all distortion products of all audio components are in phase with each other.
 

DonH56

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In my world distortion from nonlinearity is not treated the same as random noise. Distortion is much more obnoxious and easier to hear IME. And note harmonic distortion means intermodulation distortion as well and to me that is the worst offender.

YMMV - Don
 

Blumlein 88

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One correction. -124 db, -124 db and -140 db will become -117.3 db.
 
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GrimSurfer

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It should read: -100 dB + -124 dB + -124 dB + -140 dB = -99.96 dB.

I agree with Don that distortion, particularly of the uneven harmonic variety, can be most apparent to the listener.

Good point on Fletcher Munson, SIY. Oversimplification on my part as I work near the limits of my knowledge/understanding... It must get awfully complicated with complex sounds.

Great point on speakers. If one focuses on speakers, then it's easy to become very lax elsewhere. Then the issue is that nothing matters... even THD and N in the -70ish range.

Equally good point on rooms. Unfortunately, no two rooms are exactly alike. Also, one ends up getting into the same mess as with speakers...

Another great point on phase. Yes, that was my assumption, Andreas. But it's not one that is absolute. Nor is it one that all amps can easily overcome (large phase shifts, high spl, low freqs etc.).

I have a mixed view on DBTs, SIY...

DBTs only go as far as the test audience. To achieve statistical significance, the audience size needs to be quite large to count to a statistician. To have any hope of statistical significance, the test would have to be a population sized studies, using multivariate statistical methods to account for the variables of age, hearing acuity, formal and informal training, etc. IME, this is the issue preventing DBTs from getting past almost hopeless levels of ambiguity.

I do, however, believe it is an excellent practice when individuals audition gear for purchase. The ambiguity between the test subject and the purchaser is zero. So the results are significant on an individual level and are not easily transferable to somebody else due to potential (and very real) differences in hearing acuity, musical training/appreciation, etc.

The aim of my post wasn't to present an overarching theory but to show that one average component's distortion and noise can drag the cumulative performance an entire system down. This is contrary to some, but it does have an objective rationality. The degree to which it holds true depends on many, many things... some of which can be controlled and others which can not be controlled.
 

SIY

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It should read: -100 dB + -124 dB + -124 dB + -140 dB = -99.96 dB.

DBTs only go as far as the test audience. To achieve statistical significance, the audience size needs to be quite large to count to a statistician. To have any hope of statistical significance, the test would have to be a population sized studies, using multivariate statistical methods to account for the variables of age, hearing acuity, formal and informal training, etc. IME, this is the issue preventing DBTs from getting past almost hopeless levels of ambiguity.

That is not generally true- it VERY much depends on what question is being asked. Here's three related examples:

1. Can Grim hear the effect of a particular box of gain inserted into the signal path?
2. What percentage of people can hear the effect of that box of gain inserted into the signal path?
3. Can anyone hear the effect of that box of gain inserted into the signal path?

These require different experiments, different statistical analyses, and have very different degrees of difficulty. This is why it's important to state the question in advance and not try to use one experimental design to cover every possibility (the Procrustean Fallacy).
 
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GrimSurfer

GrimSurfer

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Absolutely, SIY!

The first one is easy. Then things get harder and MUCH harder.

I see a lot of people equating the results from a limited DBT to that of a population survey. Some of the test methodology or data could apply, but I have yet to see ANY DBT report present data in statistical terms beyond the elementary school level.

It's not that I'm a statistician but I've designed and executed enough surveys and crunched Chi Squared enough times to tell the difference between a proper approach and one undertaken by a few audio buff and engineers.
 

restorer-john

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1. Can Grim hear the effect of a particular box of gain inserted into the signal path?
2. What percentage of people can hear the effect of that box of gain inserted into the signal path?
3. Can anyone hear the effect of that box of gain inserted into the signal path?

These require different experiments, different statistical analyses, and have very different degrees of difficulty. This is why it's important to state the question in advance and not try to use one experimental design to cover every possibility (the Procrustean Fallacy).

"a box of gain" would generally suggest a shifting of the entire gain structure of a system (higher level in one stage and more attenuation someplace else) and that would often (not always) be quite obvious due to an increase or decrease in audible residual noise (hiss).

An example is a 2.0V CD player into a 150mV AUX input and the preamp volume pot at 8 o'clock into an attenuated (level pots) power amp Vs a digitally attenuated CD source (150mV) into the same preamp with its volume pot at full and the same power amp wide open. One will be often very obvious in terms of residual noise, even though the system output level is the same.

If you are just talking about putting a unity gain buffer in line, obviously it's just playing the multi-generational A/D-D/A game isn't it?
 

SIY

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Typically, you pad down the gain either by an internal volume control or an external divider so that in and out of circuit are level matched. It's not too hard for most cases to keep the noise from being obtrusive, unless the box of gain is noisy, and there's your detection.
 

Wombat

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That is not generally true- it VERY much depends on what question is being asked. Here's three related examples:

1. Can Grim hear the effect of a particular box of gain inserted into the signal path?
2. What percentage of people can hear the effect of that box of gain inserted into the signal path?
3. Can anyone hear the effect of that box of gain inserted into the signal path?

These require different experiments, different statistical analyses, and have very different degrees of difficulty. This is why it's important to state the question in advance and not try to use one experimental design to cover every possibility (the Procrustean Fallacy).


What is a box of gain?
 

restorer-john

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What is a box of gain?

Gain comes in various forms and packages, it would seem. Powdered and liquid, bottles (tubes) and boxes.

I believe using too much gain can cause instability and lead to excess foaming. Some machines will shutdown in this situation, or alternatively, flood the entire laundry and trip your breaker panel.

This 2x Ultra Gain, Joyful Expressions could be just the trick for you Wombat. ;)



1561184853782.png
 

RayDunzl

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My bass guitar has 23% THD, after several attempts to find a picking technique that did not yield 100% - where the 2nd harmonic was louder than the fundamental.


1561188557702.png


The real trick might be to hear the minute amounts of electronic THD on top of it.

And 48% noise? What's with that?
 

zalive

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In my world distortion from nonlinearity is not treated the same as random noise. Distortion is much more obnoxious and easier to hear IME. And note harmonic distortion means intermodulation distortion as well and to me that is the worst offender.

YMMV - Don

I agree with your view, in fact I share it.

I've one question regarding IMD.

Since this particular distortion comes from the interaction of any two frequencies, and taking into account that any two frequencies will create many IM byproducts (though f1+f2 and f2-f1 will be main ones for their amplitude)...what does it mean in terms of overal quantity of IMD: total IM distortion?

I ask this because THD seems more limited to me in overall impact, it's each frequency creating harmonics, while with the IMD its each frequency * each other frequency (square relation!) which creates distortion.

Will this cause (in a realistic situation) that actual total IMD (TIMD?) would be much higher than THD? (IMO, taking into account IM measurements available, I don't see any other possibilty...).
 

Krunok

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I agree with your view, in fact I share it.

I've one question regarding IMD.

Since this particular distortion comes from the interaction of any two frequencies, and taking into account that any two frequencies will create many IM byproducts (though f1+f2 and f2-f1 will be main ones for their amplitude)...what does it mean in terms of overal quantity of IMD: total IM distortion?

I ask this because THD seems more limited to me in overall impact, it's each frequency creating harmonics, while with the IMD its each frequency * each other frequency (square relation!) which creates distortion.

Will this cause (in a realistic situation) that actual total IMD (TIMD?) would be much higher than THD? (IMO, taking into account IM measurements available, I don't see any other possibilty...).

You should be aware that in the scenario when 3 or more tones are playing simultaneously IMD components become more and more complex/numerous. For that reason I don't think it is possible to express total IMD. What you typically see as IMD figure is two tone IMD but I don't remember seeing IMD "sweep" measurements over the entire frequency range. Not to mention that distance between 2 tones could be variable as well..
 

pozz

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@GrimSurfer is right that most discussions tend to focus on one component in isolation. Attention to how the measured values stack up across the chain should be a more widespread norm, and would probably lead to better design overall.
 

Krunok

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Attention to how the measured values stack up across the chain should be a more widespread norm, and would probably lead to better design overall.

I agree with this, although one can argue that these days all "electronic" part of the chain is pretty much transparent so the real focus should be on speakers/headphones. Unfortunately loudspeakers are the components where measurements are scarse and lack detail. I believe it was Floyd Toole who once said you are getting more info printed on the car's tyres than in the manual of $10000 loudspeakers. Unfortunately that goes for all loudspeaker manufacturers including Harman.[/QUOTE]
 
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