Never trust a THD+N measurement: v2

In the last post, I talked about why a THD+N measurement is useless if you don’t know about the type of distortion that you’re measuring. Let’s now talk about another reason why it’s useless in isolation.

Once again, let’s assume that we’re doing a THD+N measurement the old-fahsioned way where we put a sine wave into a device, and apply a notch filter to the output at the same frequency of the sine wave and find the ratio of the level of the sine wave to the output of the notch filter.

This time, instead of taking a signal and distorting it, I’ll do some additive synthesis. In other words, I’ll build a final signal that contains four components (although they’re not entirely independent…):

  1. a “signal” consisting of a 100 Hz sine wave which we’ll call “the fundamental”
  2. sine tones at frequencies that are multiples of the fundamental frequency (in other words, they are harmonically related to the fundamental).
  3. sine tones at frequencies that are not multiples of the fundamental frequency (in other words, they are not harmonically related to the fundamental).
  4. wide-band noise
Version 1: No artefacts

Let’s start by listening to the original 100 Hz sine wave with a level of -10 dB FS without any other additional components. If you hear any distortion or noise, then this is a problem in your playback system (unless your system is so good that you can hear the quantisation error caused by the fact that I didn’t dither the signal).

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Version 2: Wide-band noise

Now let’s add noise. I’ve added noise with a white spectrum and a level such that a THD+N measurement will tell us that we have 10% THD+N (relative to the level of the 100 Hz sine tone signal). In other words, I have a sine wave with a level of -10 dB FS and I have added white noise with a long-term RMS level of  -30 dB FS.

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 It should be pretty obvious, even with poor playback equipment, that I have added noise to the 100 Hz tone. This should not be surprising, since a 10% THD+N is pretty bad.
Version 3: 2nd harmonic
For this version, I’ll add a 200 Hz sine tone to the 100 Hz tone. The fundamental (100 Hz) has a level of -10 dB FS. The level of its second harmonic (200 Hz) is -30 dB FS. This means that, again, I get a THD+N value of 10%.
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Version 4: 3rd harmonic
For this version, I’ll add a 300 Hz sine tone to the 100 Hz tone. The fundamental (100 Hz) has a level of -10 dB FS. The level of its third harmonic (300 Hz) is -30 dB FS. This means that, again, I get a THD+N value of 10%.
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Version 5: 2nd to 5th harmonics
For this version, I’ll add a four additional sine tones to the 100 Hz tone. The fundamental (100 Hz) has a level of -10 dB FS. I have added tones at 200 Hz, 300 Hz, 400 Hz and 500 Hz (the 2nd through to the 5th harmonics, inclusive) with a spectral pattern where each successive tone is half the amplitude of the previous. In other words, 500 Hz is half the amplitude of 400 Hz which, in turn, is half the amplitude of the 300 Hz tone, which is half the amplitude of the 200 Hz tone.
I have adjusted the overall level of the harmonics so that we get a THD+N value of 10%. In other words, the RMS level of the signal comprised of the 200 Hz to 500 Hz sine tones (inclusive) is -30 dB FS.
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Version 6: 5 kHz
For this version, I’ll add a 5 kHz sine tone to the 100 Hz tone. The fundamental (100 Hz) has a level of -10 dB FS. The level of the 5 kHz tone is -30 dB FS. This means that, again, I get a THD+N value of 10%.
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Version 7: Noise plus five sine tones with random frequencies
For this version, I’ll add a mess to the 100 Hz tone. The fundamental (100 Hz) has a level of -10 dB FS. To this I added a signal that is comprised of wide-band white noise and 5 sine tones at random frequencies between 0 Hz and 20 kHz (no, I don’t know what they are – but it doesn’t matter for the purposes of this discussion). The levels of the noise and 5 sine tones are random.
I have adjusted the overall level of the signal comprised of the noise and 5 random sine tones so that we get a THD+N value of 10%. In other words, the RMS level of the signal comprised of the noise and 5 random sine tone is -30 dB FS.
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The punch line!

Each of the six signals I’ve presented above in Versions 2 through 7 (inclusive) is a “distorted” version of the original 100 Hz sine tone in Version 1. Each of those six signals will have a measurable THD+N of 10%. However, it is quite obvious that they have very different spectral patterns, and therefore they sound quite different.

This isn’t really revolutionary – it’s jut another reminder that a THD value, in the absence of any other information, isn’t terribly useful – or at least, it doesn’t tell you much about how the signal sounds.

  1. Andreas Cygnus says:

    Brother, you have cleared up the bull and saved me much anxiety. When I read your info, I realized I was worried for nothing. I am very new to sound technology; still, I have a natural aptitude toward technology and some physics, that helps me to catch up fast and comprehend simple logic, as you so clearly explained. I was going through the specs of a “Marantz SR7007” av receiver and the power amplifier’s rated output says:
    Front:
    125 W + 125 W (8 ohm, 20 Hz – 20 kHz with 0.08 % T.H.D.)
    195 W + 195 W (6 ohm, 1 kHz with 10 % T.H.D.)
    You see, I would like to mate this receiver with a pair of AT1 speakers from “Atlantic Technology”. The AT1 is a 6 ohm speaker at 200 watt max. So, my kind friend, if you could possibly take a look at the pdf manual/specs of the Marantz SR7007 and then see the spec sheet of the AT1 from Atlantic Technology – I would appreciate your feed back as to weather this would be an amazing or unwise setup.
    Receiver link: SR7007
    http://us.marantz.com/us/products/pages/ProductDetails.aspx?CatId=avreceivers&ProductId=SR7007
    Speaker link: AT1
    http://www.atlantictechnology.com/default.asp?NodeId=159

    Thank you for your smart research and very useful knowledge.

  2. Good day!
    I know this may never be read however, I have a similar question.
    Same sr7007 as above….6ohms 10%thd at 1 K H z which would be 1000hz. Based on your article which was working at 100 Hz I don’t know if there’s any difference or if I even have enough information to determine there’s a difference in the amount of distortional get 195 W Now I do I generally trust marantz, sure. But I do like clean sound- Ion the other hand was planning to drive some PSP’s T2’s

  3. Hi,

    Your guess that you don’t have enough information to make a decision is correct. Basically, what I hope to have shown in the posting above is that a THD+N measurement is basically useless – easy to measure, but fairly devoid of useful information… Of course, it gives you some arbitrary limit to look at, but without giving a detailed description of the exact characteristics of the type of distortion, a number isn’t enough information.

    Cheers
    – geoff

  4. Thank you! Guess I’ll just have to email Marantz~ only to satisfy my curiosity lol. You’d think there would have been more responses in this since this as this AVR has been successful for years….and in stereo it does sound good…..Its either a misprint or a negligible “value” to consumers ears. Either way I’m getting the PSBs. Cheers!

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