THD vs. S/N+D


These things get confused so I'd like to offer two tips to help you understand the difference.

The first thing to understand is that they are defined not just by what we'd like to know, but the limitations of measurements.

Signal to Noise plus Distortion is an attempt to understand how much of the output is intended, vs. not. It's calculated by subtracting the output (perhaps with some reduction in level) versus the input. Any remaining signal there is "unintended."

Another way to write this may be:  Signal / (noise + distortion)

N+D is in parenthesis because we can't tell by this measurement what is the result of noise, and what is non-linear amplification of the intended signal.  It is often misread as:  ( Signal/Noise ) + Distortion.

Total Harmonic Distortion is measured differently. Here we attempt to know about the amount of harmonics of the signal, which are multiples of the input frequency.  These are usually (but not always) unintended by-products of amplification, and by amplification this includes gain less than or equal to 1.  This is often measured using a notch filter (very narrow, deep) of the fundamental which leaves the harmonics, but I defer to the Wikipedia article here for the math:


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


While these are standard and important measurements, I want to point out that they have been around since the 1960's if not earlier, and that despite computer and DSP processing progressing greatly these measurements have not, so we should not get to complacent in believing that this is all that can or should be measured.

I look forward to hardware makers and EE readers to expand and correct me in constructive manners below.

Best,

E
erik_squires
The various harmonics are perceived by the ear in different ways. So THD doesn't tell the whole story, and often amps with low THD might not sound as good as an amp with higher THD. Here's some of why:

The ear does two things with harmonics. One is that it assigns a tonality to all forms of distortion, including harmonics. the lower orders (2nd-4th) cause 'warmth', 'bloom', 'body' and the like and the ear is considerably less sensitive to them. The higher orders (5th and above) are used by the ear to sense sound pressure and so the ear is **keenly** sensitive to them!

For this reason I've felt for a long time that a weighting system should be used on the harmonics, perhaps a '1' assigned to the 2nd and a '1000' assigned to the 7th, that sort of thing. In this way we might be able to tell how an amp might sound simply by looking at the spec sheet.


The second thing the ear does with harmonics I already mentioned- the higher orders are used to gauge sound pressure. As a result of these two things, a system with small amounts of higher ordered harmonic content (but more than the signal has) will sound louder, brighter and harsher than it should.

If these harmonics are kept to a minimum, the system will sound smoother, more relaxed and you may not be able to tell how loud its playing. So that old saw about a small amount of distortion being 'inaudible' is rubbish, if we are talking about the higher ordered harmonics!  The ear has to be able to sense sound pressure over a 130dB range or so, so it **has** to be keenly sensitive to tiny amounts of higher ordered harmonics. Add to this the Fletcher-Munson curve, and now its easy to see how brightness due to distortion is so easily heard.






Post removed 
The various harmonics are perceived by the ear in different ways. So THD doesn't tell the whole story, and often amps with low THD might not sound as good as an amp with higher THD.


Which is kind of my point.  Measurements are good, but translating them into the scale of human value/quality is difficult.  I'm sure Pass too feels he has a handle on this, so does Bose. There will always be a gap between what an oscilloscope can measure and what consumers will pay money for.
I will be up all night thinking about this.


Oh, how thoughtless of me to post something that requires intellectual curiosity.  I hope this does not deter you, @ebm from constantly being constructive and bringing interesting observations and topics to the forum as you have so far.

Erik