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I'm trying to understand how American FM multiplexing works. As I understand it, your average FM signal can be made out of:

  • The mono "sum" channel from 30 Hz to 15 kHz, made out of left + right
  • The stereo pilot tone at 19 kHz, indicating the FM station is in stereo
  • The stereo difference channel, made out of left - right, a DSB-SC AM signal centered around 38 kHz
  • Radio Data System, displaying text on radio screens, at 57 kHz
  • Optionally SCA, additional audio tracks at 67 kHz and 92 kHz

All of this is sent as one signal to the frequency modulator, which produces an FM modulated signal. That, to my understanding, sweeps a single carrier wave back and forth across the frequency spectrum, plotting out the amplitude of the signal. All well and good.

So why is a multiplexed station transmitting silence so... spiky?

An SDR recording of an FM radio station, displayed in SDRSharp

This is a short recording of some silence plus a bit of music I accidentally grabbed. It keeps looping, which is why the pattern keeps repeating.

Anyway, there are 7 major spikes (3 pairs + a center spike) in this image when the station is broadcasting silence. My first guess is that the distance between each spike in a pair = the amplitude of the corresponding wave in the demodulated signal, and the height of each spike = the frequency of the corresponding wave in the demodulated signal.

This is wrong. Each spike in the modulated signal is exactly at a subcarrier frequency! From the middle spike to the right, they're at 19 kHz, 38 kHz, and 57 kHz! That makes sense if this was the demodulated signal, but this is happening in the modulated signal, too!

Why are the modulated subcarriers at the exact same places as they are when they're demodulated?

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Why are the modulated subcarriers at the exact same places as they are when they're demodulated?

This is a combination of how FM works, and design intent.

Frequency modulation is nonlinear. If you have a carrier, and you frequency modulate it with a sine wave, then in general the result has a tone at the carrier frequency, and tones at the carrier frequency plus and minus every possible harmonic of the modulating sine wave.

Note that the strength of the various tones differs depending on how strongly the carrier is modulated -- there's a whole body of work on this, I suggest you search on "frequency modulation spectrum" for more information.

At any rate, if you transmit a carrier that is frequency modulated by just a 19kHz sine wave, then you would expect to see spikes at the carrier, $\pm$ 19kHz, $\pm$ 38kHz, etc.

You're seeing something a bit above 57kHz -- I assume that particular station is transmitting some text when you captured that.

All the above is "just how FM works". The design intent part is that FM transmission, and to a far greater extent FM reception, isn't perfect. So when an FM signal is transmitted with a 19kHz subcarrier, the (imperfect) receiver is going to demodulate a signal with tones at 19kHz, 38kHz, 57kHz, etc. So it makes sense to design your transmit signal so that the receiver can ignore what's going on at the harmonics of 19kHz in it's demodulated signal -- and that's exactly what the designers of FM stereo broadcast did.

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  • $\begingroup$ Harmonics makes a lot of sense. The stuff above 57 kHz is weird - demodulating it doesn't actually produce anything, so I'm not sure what it is. Just one more question - when you say the receiver ignores the harmonics, do you mean pre-demodulation? $\endgroup$ Dec 17, 2022 at 2:33

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