- The amplitudes of the spectral components produced by FM can be analytically determined from the trigonometric identity:

where*J*_{k}(*x*) is a Bessel function of the first kind and order*k*given by

- The time-varying output of a simple FM algorithm is

where is referred to the ``modulation index''. - Note the difference between the phase argument of Eq. (2) and the previously mentioned equation for the instantaneous carrier frequency, Eq. (1), as
.
- If
, then the instantaneous frequency is given by

Since this expression must equal that of Eq. (1), we have

- Each spectral component amplitude is proportional to
*J*_{k}(*I*), values of which are plotted in Fig. 11 below. - Lower frequency sidebands will wrap around 0 Hz and interfere with the other components (either constructively or destructively).
- For any given modulation index, individual components of the spectrum (including the carrier frequency) may be missing.

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