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Dec 28, 2019 at 12:35 vote accept Chris_F
Dec 28, 2019 at 12:34 comment added Chris_F @MattL. Then I think that is more or less what I suggested in my question. At a small enough time scale the carrier frequency is present, but at longer time scales it cancels out.
Dec 27, 2019 at 22:51 comment added hotpaw2 BTW, if one chops up your 10 kHz carrier into enough small sections, the fragments could be reassembled to look like 5 kHz or 0.5 kHz (etc.) also.
Dec 27, 2019 at 22:44 comment added hotpaw2 A small window contains that frequency. But the sum of an infinite sequences of small windows of exact opposite polarity cancels out to zero.
Dec 27, 2019 at 19:07 history edited Matt L. CC BY-SA 4.0
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Dec 27, 2019 at 18:56 comment added Matt L. @Chris_F: I've updated my answer to address your example of a square wave modulating a carrier.
Dec 27, 2019 at 18:55 history edited Matt L. CC BY-SA 4.0
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Dec 27, 2019 at 16:57 comment added Chris_F I updated my question.
Dec 27, 2019 at 16:08 comment added TimWescott Edit your question with the above comment, and the answers can address the gap in your intuition. It may seem counter-intuitive, but in the ideal case there really is no energy at the carrier frequency. Which means that your spectrum analyzer is working right. Yes, chopping the signal up into fine enough segments will regenerate the carrier - but to do that so that the carrier energy reappears means that your "chopping-up" signal would have to be synchronous with your modulating signal, which makes it a special case.
Dec 27, 2019 at 13:46 comment added Chris_F I already know the trigonometric identity. It's probably the first thing you see on Wikipedia. That doesn't answer my question. It doesn't seem to intuitively follow that that should be the case. As I said in my question, if you look at the waveform the 10KHz carrier wave is still clearly visible, it simply periodically inverts its phase 180 degrees. So how do you explain that? If I took a tiny enough chunk of audio data, small enough that the phase does not have time to invert, then my intuition tells me that a 10KHz signal would be there.
Dec 27, 2019 at 12:05 history answered Matt L. CC BY-SA 4.0