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FM Harmonic Amplitudes (Bessel Functions)

FM bandwidth expands as the modulation-amplitude $ A_m$ is increased in (G.2) above. The $ k$ th harmonic amplitude is proportional to the $ k$ th-order Bessel function of the first kind $ J_k$ , evaluated at the FM modulation index $ \beta=A_m$ . Figure G.7 illustrates the behavior of $ J_k(\beta)$ : As $ \beta $ is increased, more power appears in the sidebands, at the expense of the fundamental. Thus, increasing the FM index brightens the tone.

Figure: Bessel functions of the first kind for a range of orders (harmonic numbers) $ k$ and argument (FM index) $ \beta $ (from [264]).
\includegraphics[width=\twidth]{eps/bessel}

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