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The harmonic distribution of a simple sine wave signal modulated by another sine wave signal can be represented with Bessel functions - this provides a basis for a mathematical understanding of frequency modulation in the frequency domain.
A rule of thumb, Carson's rule states that nearly all the power of a frequency modulated signal lies within a bandwidth of
where Δf is the peak instantaneous deviation of the carrier from the centre frequency and fm is the highest modulating frequency.
Note that frequency modulation can be regarded as a special case of phase modulation where the carrier phase modulation is the time integral of the FM modulating signal.
Frequency shift keying refers to the simple case of frequency modulation by a simple signal with only two states, such as in Morse code or radio-teletype applications.
Manchester coding may be regarded as a simple version of frequency shift keying, where the high and low frequencies are respectively double and the same as the bit rate, and the bit transitions are synchronous with carrier transitions.
When used in supervisory signaling in telephony, the term frequency-change signaling has been used to describe frequency modulation.
The phrase frequency-modulated, an adjective, should have a hyphen.
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