In telecommunications, frequency modulation (FM) conveys information over a carrier wave by varying its frequency (contrast this with amplitude modulation, in which the amplitude of the carrier is varied while its frequency remains constant). In analog applications, the instantaneous frequency of the carrier is directly proportional to the instantaneous value of the input signal. Digital data can be sent by shifting the carrier's frequency among a set of discrete values, a technique known as frequency-shift keying.
Suppose the baseband data signal (the message) to be transmitted is
and is restricted in amplitude to be
and the sinusoidal carrier is
where fc is the carrier's base frequency and Ac is the carrier's amplitude. The modulator combines the carrier with the baseband data signal to get the transmitted signal,
In this equation, is the instantaneous frequency of the oscillator and is the frequency deviation, which represents the maximum shift away from fc in one direction, assuming xm(t) is limited to the range ±1.
Although it may seem that this limits the frequencies in use to fc ± fΔ, this neglects the distinction between instantaneous frequency and spectral frequency. The frequency spectrum of an actual FM signal has components extending out to infinite frequency, although they become negligibly small beyond a point.
The harmonic distribution of a sine wave carrier modulated by a sine wave signal can be represented with Bessel functions - this provides a basis for a mathematical understanding of frequency modulation in the frequency domain.
where is the highest modulating frequency of xm(t). If , the modulation is called narrowband FM, and its bandwidth is approximately . If , the modulation is called wideband FM and its bandwidth is approximately . While wideband FM uses more bandwidth, it can improve signal-to-noise ratio significantly.
With a tone-modulated FM wave, if the modulation frequency is held constant and the modulation index is increased, the (non-negligible) bandwidth of the FM signal increases, but the spacing between spectra stays the same; some spectral components decrease in strength as others increase. If the frequency deviation is held constant and the modulation frequency increased, the spacing between spectra increases.
where is the peak deviation of the instantaneous frequency from the center carrier frequency (assuming is in the range ).
A common method for recovering the information signal is through a Foster-Seeley discriminator.
Edwin Armstrong presented his paper: "A Method of Reducing Disturbances in Radio Signaling by a System of Frequency Modulation", which first described FM radio, before the New York section of the Institute of Radio Engineers on November 6, 1935. The paper was published in 1936.
As the name implies, wideband FM (W-FM) requires a wider signal bandwidth than amplitude modulation by an equivalent modulating signal, but this also makes the signal more robust against noise and interference. Frequency modulation is also more robust against simple signal amplitude fading phenomena. As a result, FM was chosen as the modulation standard for high frequency, high fidelity radio transmission: hence the term "FM radio" (although for many years the BBC called it "VHF radio", because commercial FM broadcasting uses a well-known part of the VHF band; in certain countries, expressions referencing the more familiar wavelength notion are still used in place of the more abstract modulation technique name).
FM receivers employ a special detector for FM signals and exhibit a phenomenon called capture effect, where the tuner is able to clearly receive the stronger of two stations being broadcast on the same frequency. Problematically however, frequency drift or lack of selectivity may cause one station or signal to be suddenly overtaken by another on an adjacent channel. Frequency drift typically constituted a problem on very old or inexpensive receivers, while inadequate selectivity may plague any tuner.
An FM signal can also be used to carry a stereo signal: see FM stereo. However, this is done by using multiplexing and demultiplexing before and after the FM process, and is not part of FM proper. The rest of this article ignores the stereo multiplexing and demultiplexing process used in "stereo FM", and concentrates on the FM modulation and demodulation process, which is identical in stereo and mono processes.
A high-efficiency radio-frequency switching amplifier can be used to transmit FM signals (and other constant-amplitude signals). For a given signal strength (measured at the receiver antenna), switching amplifiers use less battery power and typically cost less than a linear amplifier. This gives FM another advantage over other modulation schemes that require linear amplifiers, such as AM and QAM.
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 is the frequency modulation using only a discrete number of frequencies. Morse code transmission has been implemented this way, as were most early telephone-line modems and radioteletype applications.
By the phenomenon of slope detection whereby FM is converted to AM in a frequency-selective circuit tuned slightly away from the nominal signal frequency, AM receivers may detect some FM transmissions, though this does not provide an efficient method of detection for FM broadcasts.
FM modulation is also used in telemetry applications.
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