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

Krunok

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Yes, and it's working perfectly as intended. The point of an audio playback system is to accurately and faithfully reproduce the "distortion" of your guitar without adding its own.

Very true. But as bass gutiar is not a sine wave generator but rather an instrument I wouldn't call it's specific harmonics "distortion". :)
 

andreasmaaan

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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 depends. On the one hand, you have “gear shoot-outs” and try-at-home ABX tests, many of which are not scientifically rigorous or contain enough data points.

On the other hand, though, psychoacoustics is a reasonably well-developed field. We have fairly extensive and convergent data on things like masking thresholds, equal loudness contours, etc etc. We have a detailed model of the functioning of the auditory system. There really aren’t that many mysteries left.
 
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GrimSurfer

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It depends. On the one hand, you have “gear shoot-outs” and try-at-home ABX tests, many of which are not scientifically rigorous or contain enough data points.

On the other hand, though, psychoacoustics is a reasonably well-developed field. We have fairly extensive and convergent data on things like masking thresholds, equal loudness contours, etc etc. We have a detailed model of the functioning of the auditory system. There really aren’t that many mysteries left.

Psychoacoustics is reasonably developed in scientific circles, with medical science and acoustics being well developed fields in their own right. Corruption from outside the field (audiophiles, certain companies) is a big issue though. As a result, there are many doctors and acousticians who approach psychoacoustic with a great deal of skepticism.
 

andreasmaaan

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Psychoacoustics is reasonably developed in scientific circles, with medical science and acoustics being well developed fields in their own right. Corruption from outside the field (audiophiles, certain companies) is a big issue though. As a result, there are many doctors and acousticians who approach psychoacoustic with a great deal of skepticism.

What specific aspects of psychoacoustics are approached with sceptisism? Why?
 

DonH56

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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...).


For a given nonlinearity both harmonic and intermodulation distortion can be readily calculated using basic algebra and trig identities. I am not sure if I have presented the math in an article here on ASR but have done it (likely along with most every other EE on the planet).

For two tones with peak amplitude the same as a single tone (which means the two tones are each 1/2 the amplitude of the single tone) IMD2 = HD2 + 6.021 dB and IMD3 = HD3 + 9.542 dB. That means that, for the same nonlinearity, two tones combined having the same amplitude as a single tone will have intermodulation distortion about 6 dB higher for second-order products and 9.5 dB higher for third-order products. That is, the second-order IMD is about twice the amplitude of second-order HD, and third-order IMD is about 3x the amplitude of third-order HD. Higher third-order products are particularly vexing because they appear very near the fundamental signals, but are not harmonically related, so stand out more than harmonics.

Given two frequencies f1 and f2 the resultant distortion terms for harmonic (HD) and intermodulation (IM) distortion are:
  • HD2 = 2*f1, 2*f2 -- twice the original frequencies as expected
  • IMD2 = f1+f2, and |f1-f2| -- roughly twice the the signal frequencies and near DC (low frequency) for closely-spaced tones
  • HD3 = 3*f1, 3*f2 -- three times the original frequencies
  • IMD3 = f1+2f2, 2f1+f2, |f1-2f2|, and |2f1-f2| -- roughly three times the signal frequencies plus spurs very near the original signals
Second-order nonlinearity also adds a DC term (0 Hz). You can take the math on up for higher-order harmonics but this gives you the idea. The math is straight-forward but messy.

To get the total quantity you would RSS the terms (same as for THD).

HTH - Don
 
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GrimSurfer

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What specific aspects of psychoacoustics are approached with sceptisism? Why?

The ability of humans to hear or perceive sound well into the ultrasonic range for one. Human testing and cadaver research over the past 50 years or so show this to be highly unlikely/unreliable.

Then there is the psychoacoustic mumbo jumbo that serves as the basis for hires music, which is touted by some music providers but pretty much debunked by science.
 

andreasmaaan

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The ability of humans to hear or perceive sound well into the ultrasonic range for one. Human testing and cadaver research over the past 50 years or so show this to be highly unlikely/unreliable.

Then there is the psychoacoustic mumbo jumbo that serves as the basis for hires music, which is touted by some music providers but pretty much debunked by science.

That's not psychoacoustics, it's marketing and quackery :cool:
 

svart-hvitt

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Yes, and it's working perfectly as intended. The point of an audio playback system is to accurately and faithfully reproduce the "distortion" of your guitar without adding its own.

What if Ray’s guitar SHOULD have 25% distortion? Then a distorted amp or dac may be just what the doctor ordered?

;)
 

RayDunzl

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The ability of humans to hear or perceive sound well into the ultrasonic range for one.

My "ultrasonic" range starts at such a low frequency that I am constantly inundated with them, and to my perception, apparently not perceiving them.

Sample Perception Test:
Somebody: You hear that?
Me: Hear what?
Somebody: Damn!
 

tmtomh

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I wasn't aware psychoacoustic science made such claim.

Psychoacoustic science in general doesn't claim that humans can hear ultrasonic frequencies. But @GrimSurfer is correct that some folks do make this claim, and they cite a few well-worn sources for it. It turns out that every single one of those sources is based on a single study, the Oohashi study, which claimed to find that ultrasonics create some kind of neurological or psychoacoustic effect that influences how people hear music, and which causes them to perceive the music as sounding better when the ultrasonics are part of the signal.

The study was done with a very small subject group, included results that contradict its main claimed finding, has been criticized on multiple grounds, and - unsurprisingly - has not been able to be replicated by anyone.

https://en.wikipedia.org/wiki/Hypersonic_effect

I am not exaggerating when I say that every claim and source citation on behalf of the audibility (or other brain impact) of ultrasonics rests on this single study: Every single comment and article I've ever read that argues we can hear ultrasonics either (a) doesn't cite any sources; (b) cites Oohashi; or (c) cites sources that themselves cite Oohashi, and only Oohashi.
 
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GrimSurfer

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GrimSurfer

GrimSurfer

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What if Ray’s guitar SHOULD have 25% distortion? Then a distorted amp or dac may be just what the doctor ordered?

;)

Ray's guitar has 100% distortion. 25% he can hear. 75% lies in the ultra-ray range :)
 

Blumlein 88

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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..

I do IMD sweeps. Here is one for a March Dac 1. Background goes to gray at - 120 db. I sweep tones spaced 1 khz apart. By juggling FFT size and sweep rate you can also pick a given frequency and get an accurate reading of the distortion levels at any frequency. I've been surprised that most DACs are fairly consistent with usually only modest increased IMD at higher frequencies.
1561236584648.png


I suppose you could do a single twin tone IMD and notch out the two tones getting a reading of whatever is left as Total IMD+N. I don't see anyone doing such a thing. Probably would want 2 khz spacing so the notches would be done better without obscuring results. I've seen a moderately math intense paper suggesting multi-tone IMD with spacing determined mathematically and deriving a weighted total IMD number. I didn't see the advantage over plain twin tone IMD myself, and it apparently never caught on as this was 20 or more years ago.

For comparison here is one from the Marantz 7701 pre/pro showing more HD and a higher level of IMD with more sum and difference tones and some aliasing in the ADC (the line sloping in the opposite direction is aliasing, and this was a different ADC).

1561237119430.png
 

DonH56

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Multitone measurements are popular in the RF world, as are NPR (noise-power ratio) measurements, but I have not seen them performed at audio either.

Most measurements I have seen jump from SNR to THD to SINAD. SINAD includes all non-signal "stuff" be it HD, IMD, power supply spurs, random noise, or what have you. When I was designing and testing my circuits I wrote a MATLAB program to calculate SNR, SINAD, SFDR, THD, and IMD for single- and multi-tone (up to ten IIRC) measurements. Easy enough using something like that, and of course using the IEEE or some other scheme to choose the test frequency(ies) to prevent binning multiple products into a single bin.
 
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Blumlein 88

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Multitone measurements are popular in the RF world, as are NPR (noise-power ratio) measurements, but I have not seen them performed at audio either.

Most measurements I have seen jump from SNR to THD to SINAD. SINAD includes all non-signal "stuff" be it HD, IMD, power supply spurs, random noise, or what have you. When I was designing and testing my circuits I wrote a MATLAB program to calculate SNR, SINAD, THD, and IMD for single- and multi-tone (up to ten IIRC) measurements. Easy enough using something like that, and of course using the IEEE or some other scheme to choose the test frequency(ies) to prevent binning multiple products into a single bin.
I rather liked the idea of SFDR which is subtly different than SINAD.
 

DonH56

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I rather liked the idea of SFDR which is subtly different than SINAD.

Yes, of course! Added it to my post; my MATLAB routine calculated it as well. One of "the" key measurements for RF and data converters. Though I do not consider the difference subtle, at least the way we calculated it.

For those who might not realize:

SNR = signal to noise ratio and ideally does not include distortion terms (a subject of endless debate)
THD = total harmonic distortion = ratio of signal to all harmonic distortion terms (ten harmonics is generally accepted as sufficient)
THD+N = signal to harmonic distortion plus all noise; commonly includes everything but the signal itself in the "noise" part so really is SINAD
SINAD = signal to noise and distortion ratio so signal to "everything" else
SFDR = spurious-free dynamic range and is the ratio (expressed in dB) of the signal amplitude to the highest spurious (distortion or noise) signal

SFDR, when noise limited, depends upon the FFT resolution.

As an example, the ratio of signal to quantization noise for a data converter (ADC or DAC) is about 6N. Take the signal, compare it to all the quantization noise when "added up" (not a simple sum but conveys the idea), and the SNR for say a perfect 16-bit DAC is about 96 dB. However, the SFDR goes as 9N, so for that same perfect 16-bit DAC is about 144 dB. Think of the noise floor in an FFT plot, then SNR is what you get when you compare the peak signal to the total of all the noise, and SFDR is the distance from the peak signal to any one spot along the noise floor. Distortion reduces both accordingly since distortion adds more "noise" and also creates a spur that reduces the SFDR.

See e.g. https://www.audiosciencereview.com/...ital-audio-converters-dacs-fundamentals.1927/
 

scott wurcer

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Human testing and cadaver research over the past 50 years or so show this to be highly unlikely/unreliable.

I would hope cadavers would not shed light on any useful issues.
 

restorer-john

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I would hope cadavers would not shed light on any useful issues.

I'd say the researchers needed completely unbiased participants who were 'acoustically dead' for their testing.
 
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