Frequency Modulation

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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 signal 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.

FM is commonly used at VHF radio frequency for high-fidelity radio broadcasting of music and Speech communication (see FM broadcasting). Normal (analog) TV sound is also broadcast using FM. A narrowband form is used for human voice communications in commercial and amateur radio settings. The type of FM used in broadcast is generally called wide-FM, or W-FM. In two-way radio, narrowband narrow-fm (N-FM) is used to conserve bandwidth. In addition, it is used to send signals into space.

FM is also used at intermediate frequencies by most analog Video cassette recorder systems, including VHS, to record the Luminance (video) (black and white) portion of the video signal. FM is the only feasible method of recording video to and retrieving video from magnetic tape without extreme distortion, as video signals have a very large range of frequency components — from a few hertz to several megahertz, too wide for equalisers to work with due to electronic noise below -60 decibel. FM also keeps the tape at saturation level, and therefore acts as a form of audio noise reduction, and a simple audio level compression can mask variations in the playback output, and the FM capture effect removes print-through and pre-echo. A continuous pilot-tone, if added to the signal — as was done on V2000 and many Hi-band formats — can keep mechanical jitter under control and assist timebase correction.

FM is also used at audio frequency to synthesize sound. This technique, known as frequency modulation synthesis, was popularized by early digital synthesizers and became a standard feature for several generations of personal computer sound cards. Applications in radio 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.

Wideband FM (W-FM) requires a wider bandwidth than amplitude modulation by an equivalent modulating signal, but this also makes the signal more robust against Noise (radio) and interference. Frequency modulation is also more robust against simple signal amplitude fading phenomena. As a result, FM was chosen as the modulation standardization for high frequency, high fidelity radio transmission: hence the term "FM radio" (although for many years the BBC insisted on calling 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 receiver (radio) employ a special Detector (radio) for FM signals and exhibit a phenomenon called capture, where the Tuner (radio) is able to clearly receive the stronger of two stations being broadcast on the same frequency. Problematically however, frequency drift or lack of Electronic selectivity may cause one station or signal to be suddenly overtaken by another on an adjacent channel. Frequency drift (telecommunication) 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 stereophonic sound 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.

Theory

Suppose the signal to be transmitted is

x_m(t)\,

and is restricted in amplitude to be

\left| x_m(t) \right| \le 1, \,

and the sinusoidal carrier is

x_c(t) = A \cos (2 \pi f_c t)\,

where fc is the carrier's base frequency and A is an arbitrary amplitude. Then the carrier will be modulated by the signal as in

x_c(t) = A \cos \left( 2 \pi \int_{0}^{t} f(\tau)\, d \tau \right) = A \cos \left( 2 \pi \int_{0}^{t} \left f_c + f_\Delta x_m(\tau) \right \, d \tau \right)

where f(\tau) = f_c + f_\Delta x_m(\tau). \,

In this equation, f(\tau)\, is the instantaneous phase#Instantaneous frequency of the oscillator and f_{\Delta}\, 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.

Modulation index As with other modulation index, in FM this quantity indicates by how much the modulated variable varies around its unmodulated level. For FM, it relates to the variations in the frequency of the carrier signal:

h = \frac{\Delta{}f}{f_m} = \frac{f_\Delta |x_m(t)|}{f_m} \

If h \ll 1, the modulation is called narrowband FM, and its bandwidth is approximately 2 f_m. If h \gg 1, the modulation is called wideband FM and its bandwidth is approximately 2 f_\Delta. 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. If the frequency deviation is held constant and the modulation index increased, the bandwidth stays roughly the same, but the spacing between spectra decreases.

Carson's rule A rule of thumb, Carson bandwidth rule states that nearly all (~98%) of the power of a frequency-modulated signal lies within a bandwidth B_T of

\ B_T = 2(f_\Delta +f_m)\,

where fΔ is the peak deviation of the instantaneous frequency f(t) from the center carrier frequency fc (assuming xm(t) is in the range ±1) and fm is the highest modulating frequency of xm(t).

Bessel Functions The carrier and sideband amplitudes are illustrated for different modulation indexes of FM signals. Based on the Bessel Functions.{| class="wikitable"|-! Modulation Index! Carrier! 1! 2! 3! 4! 5! 6! 7! 8! 9! 10! 11! 12! 13! 14! 15! 16|-| 0.00| 1.00|||||||||||||||||-| 0.25| 0.98| 0.12||||||||||||||||-| 0.5| 0.94| 0.24| 0.03|||||||||||||||-| 1.0| 0.77| 0.44| 0.11| 0.02||||||||||||||-| 1.5| 0.51| 0.56| 0.23| 0.06| 0.01|||||||||||||-| 2.0| 0.22| 0.58| 0.35| 0.13| 0.03|||||||||||||-| 2.41| 0| 0.52| 0.43| 0.20| 0.06| 0.02||||||||||||-| 2.5| −.05| 0.50| 0.45| 0.22| 0.07| 0.02| 0.01|||||||||||-| 3.0| −.26| 0.34| 0.49| 0.31| 0.13| 0.04| 0.01|||||||||||-| 4.0| −.40| −.07| 0.36| 0.43| 0.28| 0.13| 0.05| 0.02||||||||||-| 5.0| −.18| −.33| 0.05| 0.36| 0.39| 0.26| 0.13| 0.05| 0.02|||||||||-| 5.53| 0| −.34| −.13| 0.25| 0.40| 0.32| 0.19| 0.09| 0.03| 0.01||||||||-| 6.0| 0.15| −.28| −.24| 0.11| 0.36| 0.36| 0.25| 0.13| 0.06| 0.02||||||||-| 7.0| 0.30| 0.00| −.30| −.17| 0.16| 0.35| 0.34| 0.23| 0.13| 0.06| 0.02|||||||-| 8.0| 0.17| 0.23| −.11| −.29| −.10| 0.19| 0.34| 0.32| 0.22| 0.13| 0.06| 0.03||||||-| 8.65| 0| 0.27| 0.06| −.24| −.23| 0.03| 0.26| 0.34| 0.28| 0.18| 0.10| 0.05| 0.02|||||-| 9.0| −.09| 0.25| 0.14| −.18| −.27| −.06| 0.20| 0.33| 0.31| 0.21| 0.12| 0.06| 0.03| 0.01||||-| 10.0| −.25| 0.04| 0.25| 0.06| −.22| −.23| −.01| 0.22| 0.32| 0.29| 0.21| 0.12| 0.06| 0.03| 0.01|||-| 12.0| 0.05| −.22| −.08| 0.20| 0.18| −.07| −.24| −.17| 0.05| 0.23| 0.30| 0.27| 0.20| 0.12| 0.07| 0.03| 0.01|}

Implementation One common method of generating the FM signal is to feed the information signal into the input of a VCO.A common method for recovering the information signal is through a Foster-Seeley discriminator.

Miscellaneous

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 is the simple case of frequency modulation by a signal with only discrete states, such as in Morse code or radioteletype applications.

When used in supervisory signaling in telephony, the term frequency-change signaling has been used to describe frequency modulation.

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 Detector (radio) for FM broadcasts.