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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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