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I have noticed that modern FM radio stations broadcast simple text information about them. While this does not affect the analog sound, it can be decoded by most modern FM receivers, including my mobile phone.
I wonder how is this information encoded. I believe that if I knew a name of the process I would be able to find a very specific documentation.

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up vote 7 down vote accepted

It's called the Radio Data System. It transmits data over a 1187.5 baud QPSK channel at a 57 kHz carrier frequency in the broadcast FM baseband.

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The "name of the process", as you put it, is called a subcarrier. You can think of this as an audio tone on the signal, but it's so high in frequency that you can't hear it, and the normal FM audio part of your receiver doesn't pick it up. Additional circuitry can detect this signal and any information that has been coded onto it.

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