If the information to be transmitted (i.e., the baseband signal) is ${\displaystyle x_{m}(t)}$ and the sinusoidal carrier is ${\displaystyle x_{c}(t)=A_{c}\cos(2\pi f_{c}t)\,}$, where f_c is the carrier's base frequency, and A_c is the carrier's amplitude, the modulator combines the carrier with the baseband data signal to get the transmitted signal:^{[citation needed]}

In analog frequency modulation, such as FM radio broadcasting of an audio signal representing voice or music, the instantaneous frequency deviation, the difference between the frequency of the carrier and its center frequency, is proportional to the modulating signal.

Digital data can be encoded and transmitted via FM by shifting the carrier's frequency among a predefined set of frequencies representing digits – for example one frequency can represent a binary 1 and a second can represent binary 0. This modulation technique is known as frequency-shift keying (FSK). FSK is widely used in modems such as fax modems, and can also be used to send Morse code.^[1] Radioteletype also uses FSK.^[2]

Frequency modulation is widely used for FM radio broadcasting. It is also used in telemetry, radar, seismic prospecting, and monitoring newborns for seizures via EEG,^[3] two-way radio systems, sound synthesis, magnetic tape-recording systems and some video-transmission systems. In radio transmission, an advantage of frequency modulation is that it has a larger signal-to-noise ratio and therefore rejects radio frequency interference better than an equal power amplitude modulation (AM) signal. For this reason, most music is broadcast over FM radio.

Frequency modulation and phase modulation are the two complementary principal methods of angle modulation; phase modulation is often used as an intermediate step to achieve frequency modulation. These methods contrast with amplitude modulation, in which the amplitude of the carrier wave varies, while the frequency and phase remain constant.

If the information to be transmitted (i.e., the baseband signal) is ${\displaystyle x_{m}(t)}$ and the sinusoidal carrier is ${\displaystyle x_{c}(t)=A_{c}\cos(2\pi f_{c}t)\,}$, where f_c is the carrier's base frequency, and A_c is the carrier's amplitude, the modulator combines the carrier with the baseband data signal to get the transmitted signal:^{[citation needed]}

where ${\displaystyle f_{\Delta }=K_{f}A_{m}}$, ${\displaystyle K_{f}}$ being the sensitivity of the frequency modulator and ${\displaystyle A_{m}}$ being the amplitude of the modulating signal or baseband signal.

In this equation, ${\displaystyle f(\tau )\,}$ is the instantaneous frequency of the oscillator and ${\displaystyle f_{\Delta }\,}$ is the frequency deviation, which represents the maximum shift away from f_c in one direction, assuming x_m(t) is limited to the range ±1.

While most of the energy of the signal is contained within f_c ± f_Δ, it can be shown by Fourier analysis that a wider range of frequencies is required to precisely represent an FM signal. The frequency spectrum of an actual FM signal has components extending infinitely, although their amplitude decreases and higher-order components are often neglected in practical design problems.^[4]

Sinusoidal baseband signal

Mathematically, a baseband modulating signal may be approximated by a sinusoidal continuous wave signal with a frequency f_m. This method is also named as single-tone modulation. The integral of such a signal is:

${\displaystyle \int _{0}^{t}x_{m}(\tau )d\tau ={\frac {\sin \left(2\pi f_{m}t\right)}{2\pi f_{m}}}\,}$

In this case, the expression for y(t) above simplifies to:

${\displaystyle f(\tau )\,}$