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I am not sure if this question fits better in physics.stackexchange or ham.stackexchange, feel free to correct me. I am new to studying RF and SDR in general, I was looking up how modulation works and FM by definition encodes information to carrier frequency by modifying the frequency of wave. Considering this, it doesnt make sense how you can tune into an fm frequency, say 101, 101 being the carrier frequency makes sense but once information/music is encoded to this shouldn't the frequency change to something else?

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    $\begingroup$ Welcome, and good question! Since you like math, you might find it interesting to play with formulas that graph out what it looks like to modulate a 1 Mhz carrier by a 440 Hz baseband signal, for both AM and the more complicated FM case. That would be in the "time domain" just for fun. To get a sense of what that looks like in the "frequency domain" check out waterfall graphs like the examples at sigidwiki.com/wiki/Category:Analogue to see how the "sidebands" caused by messing with (modulating) the carrier, different ways, ends up using more bandwidth around the center frequency. $\endgroup$ – natevw - AF7TB Mar 24 at 18:05
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"Tuning" an FM receiver sets the center frequency of the receiver, but its internal circuitry is designed to pass enough of the Bessel sidebands produced by frequency modulation of that waveform to be demodulated with low noise and distortion.

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    $\begingroup$ Thank you for the quick response. Is this safe to look at it this way that FM radio stations all have a frequency band instead of just one frequency then and they give the center frequency to their listeners to tune into? Secondly, on average whats the width of these bands? There has to be an upper and lower boundary, correct? $\endgroup$ – mathemagician Mar 24 at 8:09
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    $\begingroup$ Yes, FM broadcast stations identify themselves by their assigned carrier frequency, which has a 100% value only with zero modulation. "Percentage of Modulation" of a frequency-modulated carrier is arbitrary, but in the U.S. the FCC has defined that to be ±75 kHz deviation of the carrier. The Bessel sidebands produced by modulation are allotted an r-f spectrum of ±100 kHz, centered on the carrier frequency, which the carrier spacing of 200 kHz enables. The FCC does not assign FM stations to use closely-spaced frequencies in any given market. $\endgroup$ – Richard Fry Mar 24 at 9:11
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    $\begingroup$ @mathemagician every radio signal that carries information occupies some range of frequencies to either side of its center frequency. The only signal that occupies "just one frequency" is a pure unvarying sine wave. $\endgroup$ – hobbs - KC2G Mar 24 at 16:53
  • $\begingroup$ @mathemagician "On average what's the width of these bands?" is a good question and might be worth making another Q&A for since I don't actually see one exactly for that yet. (For a sneak peak this answer ham.stackexchange.com/a/5040/1362 on a different question is pretty closely related.) $\endgroup$ – natevw - AF7TB Mar 24 at 17:49
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    $\begingroup$ Having a cheap SDR dongle is a great way to see what radio broadcasts look like in the frequency domain. And, indeed, one sees the upper and lower side bands quite nicely on FM. $\endgroup$ – Jon Custer Mar 24 at 18:41
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There are two ways to look at this: center frequency and bandwidth.

In FM, the frequency varies as the amplitude of the audio varies. If the audio was a sinusoidal tone, the frequency would vary symmetrically around a center frequency, which is constant. More complex audio is generally still symmetrical. The FM receiver actually locks on to that center frequency using the symmetry, so even if your tuning is a bit off (but still within the radio's pass band), it will lock on to the signal. This is a fundamental defining feature of FM.

All transmissions containing information are assigned not just a frequency, but a bandwidth. (Without bandwidth, it can't contain any information.) The bandwidth of the FM transmission is tied with a fixed ratio (frequency modulation index) to the maximum amplitude range of the audio. If the audio has a dynamic range large enough to cause the FM to exceed its assigned bandwidth, it will be clipped before being modulated into FM. The maximum range of amplitude variation of the audio is sometimes called "envelope".

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  • $\begingroup$ Hey, thanks for the explanation. One thing, you said that the bandwidth is tied to amplitude. Shouldn't it be tied to frequency and not amplitude? Since FM by definition modifies frequency of carried. Secondly another thread mentioned by natevw speaks of dependency on information signal's frequency (ham.stackexchange.com/questions/5024/…) $\endgroup$ – mathemagician Mar 25 at 10:41
  • $\begingroup$ Bandwidth is not tied to amplitude. It's tied to the maximum range of the amplitude (negative to positive) of the audio. The radio frequency is tied to the audio amplitude. I'll look through my answer and make sure I wasn't sloppy about that. The bandwidth vs. frequency is by convention only, it's not set in stone. But the higher the frequency, the more space available and the convention is based on this. $\endgroup$ – user10489 Mar 25 at 11:59

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