Q.An FM signal with single tone modulation has a frequency deviation of 12 kHz and a bandwidth of 50 kHz. Find the frequency of the modulating signal.

Unlike AM, an FM wave modulated by a single tone contains infinitely many sidebands, spaced from each other by the modulating frequency $f_m$ and distributed symmetrically about the carrier. Their amplitudes — and the carrier's — are given by Bessel functions of the first kind of the modulation index, $J_0(m_f), J_1(m_f), J_2(m_f), \dots$, read from a standard Bessel table. Sidebands equidistant from the carrier have equal amplitudes.

In practice most of these sidebands are negligibly small. A significant sideband is one whose amplitude is at least 1% of the carrier amplitude; the number of significant sidebands, $n$, is fixed by the modulation index. The theoretical FM bandwidth is infinite, but the practical bandwidth spans only the significant sidebands:

A convenient shortcut is Carson's rule, which estimates the bandwidth as twice the sum of the maximum frequency deviation and the highest modulating frequency: …