If a carrier ($f_c$) is FM modulated by a single sine wave ($f_m$), its spectrum is composed of frequencies at $f_c + kf_m$ ($k \in \mathbb{Z}$) whose amplitudes are weighted by $J_n(\beta)$, the $k$-order Bessel function of modulation index $\beta$. We could get such spectra :
Now, what would be the spectrum of the carrier if it was modulated by a more complex signal like speech or music ?
Short term Fourier transform of the modulating signal would be :
- Harmonic (e.g. : vowel in speech, or a violin note)
- Non harmonic (e.g. : some consonants in speech, some percussive instrument)
In both case, modulating signal will have a more richer frequency content than a single sinusoid.
Will these rich spectra just repeat regularly around $f_c$ as in the case of a single tone modulating signal ? Why ? What would happen in the simple example of a 2 tones modulating signal ?
If a carrier is AM modulated by complex signal like speech, we find the spectrum of modulating signal shifted around the carrier (as seen in the spectrogram below) : what would happen with FM modulation for such rich signals ?