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It can't.

 

FM (like broadcast AM) has two *sidebands*, one at a higher frequency than the transmitter's carrier, one at a lower frequency.

 

The modulating signal (voice, music, etc) of any trasnmitter creates one or more pairs of side frequencies within the two sidebands.

 

A broadcast AM signal can only produce two side frequencies, so an AM transmitter at 1.5 MHz, with a 1 kHz modulating tone (fm), would put out its carrier (fc) at 1.5 MHz, a lower side frequncy at (1.5 - 0.001) = 1.499 MHz, then its carrier at 1.5 MHz, and then the upper side frequency at (1.5 + 0.001) = 1.501 MHz.

 

The AM signal can never be wider than twice the highest modulating frequency (fm), spanning from (fc - fm) to (fc + fm), a span of 2 x fm. Be aware that special-purpose AM systems can generate just *one* sideband - we won't go into that amount of detail apart from noting it.

 

FM signals can be wider than twice the highest modulating frequency. The complete analysis needs the mathematical Fourier Transform, but we can think of it this way.

 

Stronger frequency modulation shows up as a larger change in the transmitted signal frequency. An FM signal at 100 MHz, modulated by a 1 KHz tone, *can* put out a lower side frequency at (100 - 0.001) = 99.999 MHz and an upper side frequency at (100 + 0.001) = 100.001 MHz.

 

You could receive this just fine, but it would sound "weak" compared to normal broadcasts.

 

It's possible to increase the frequency shift to (say) five times. Now, the sidebands must extend from (100 - 5x0.001) = 99.995 MHz to (100 + 5x0.001) = 100.005 MHz. How do we account for the original 1 KHz tone creating a bandwidth of 2x5 kHz?

 

The answer is that we actually have *five* lower side frequencies, at -5, -4, -3, -2, -1 kHz below the carrier, and *five* upper side frequencies at +1, +2, +3 +4 and +5 kHz above the carrier. Notice that they are multiples of the original 1 kHz modulating frequency. These can, in fact, be shown on the instrument called a spectrum analyser.

 

Your question?

 

As with broadcast AM, an FM signal has only two sidebands. In FM, the strength of modulation (the modulation index) controls the number of individual side frequencies, and thus the total bandwidth of the signal.

 

Can an FM signal have *infinite* numbers of side frequencies?

 

Not really. It can have a *very large* number of side frequencies with very great modulation strength. In practice, this would take up *a lot* of the FM radio band, so broadcast FM commonly uses a maximum modulation index of 5.0. This means that a fully-modulating 15 kHz signal would give a bandwidth of -(15 x 5) to +(15 x 5) kHz, which is +/- 75 kHz.

 

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