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I encode data in audio by energising 5 frequencies between 17.5kHz and 19.5kHz:

I play the WAV on a sports stadium (20k seating, so BIG) PA rig, placing a microphone somewhere in the spectator seating area.

This is the data (I did it at vol=0.6 and vol=1):

enter image description here

As can be seen, there is some kind of 'ringing' occurring. Now the frequency channels are using are all integer multiples of a fundamental frequency (~100Hz), and the ghost frequencies appear at exact harmonics. If I crank up the volume I also get energy midway between harmonics.

There is one further effect: Ghosting at 1/2 f. This is most visible if I analyse a sweep (vol=0.8:

enter image description here

As can be seen, much of the energy at frequency f has been redirected to 1/2 f.

Can anyone explain these unwanted artefacts?

PS Often I observe a perfectly valid SE question attracts several instant down/close-votes before making it back to the surface. It always makes me scratch my head a little. It seems rather feeble to downvote without supplying a comment to summarise the decision logic. e.g. Is it OT / malformed / inarticulate / lazy / etc, and how so?

PPS Someone has now suggested _intermodulation_ in a comment. Now this is valuable information. The question together with this keyword, once catalogued by Google, adds to the effectiveness of the Internet as a resource for Information. Yet the question is teetering on 4 (un--publicly-justified) close-votes. I do not think this is right. :/

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  • $\begingroup$ I doubt a PA system is designed for more than 10kHz. Doing things that are not compatible with a system's purpose will have unintended behavior. $\endgroup$
    – user28715
    Nov 12 '18 at 0:57
  • $\begingroup$ My first step would be to consult the manufacturer. $\endgroup$
    – MBaz
    Nov 12 '18 at 1:38
  • $\begingroup$ The problem doesn't appear to be specific to one particular manufacturer. I can even reproduce the symptoms on my MacBook Air 2011. $\endgroup$
    – P i
    Nov 12 '18 at 1:42
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    $\begingroup$ I’ve observed the 1/2 F phenomenon myself, but never figured out how to explain it. Could you detail your setup a bit more? As well as the MacBook setup? $\endgroup$
    – Dan Szabo
    Nov 12 '18 at 13:21
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    $\begingroup$ I'm not 100% sure that I understood your description of the problem, but it does sound like you may be describing the effect of intermodulation distortion? (en.wikipedia.org/wiki/Intermodulation) $\endgroup$
    – Cal-linux
    Nov 25 '18 at 19:46
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First of all, like Cal-linux mention in their comment, I would strongly suggest intermodulation distortion for the frequencies that are not multiple integers of the fundamental.

Now, regarding the sweep tone artefacts. Since you are talking about high frequencies we are talking about a high-frequency driver. Nowadays, most high-frequency drivers are domes with some kind of compression driver attached to them. It has been proposed by Hubbard that compression drivers generate subharmonics. By visual inspection (as you also state) part of the energy of the sweep seems to be present at the first subharmonic $\frac{1}{2} f$, which could potentially be somehow related to the results Hubbard presented.

Further investigation is needed to be able to say for sure but this is indeed a very interesting observation. I work as a P.A. engineer, so I will try to duplicate the effect and work more on it. I will post back if I manage to reach any conclusions.

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