Editing Frequency modulation

{{Short description|Electronic method of transmitting information with a carrier wave}}
{{For|the application of frequency modulation to radio broadcasting|FM broadcasting}}
{{Redirect|NFM}}
{{Modulation techniques}}

[[File:Amfm3-en-de.gif|thumb|right|250px|A signal may be carried by an [[Amplitude modulation|AM]] or FM radio wave.|alt=Animation of audio, AM and FM signals]]
[[File:GE FM radio antistatic demonstration 1940.jpg|thumb|upright=1.5|FM has better noise ([[Radio Frequency Interference|RFI]]) rejection than AM, as shown in this dramatic New York publicity demonstration by [[General Electric]] in 1940. The radio has both AM and FM receivers. With a million-volt [[electric arc]] as a source of interference behind it, the AM receiver produced only a roar of [[Radio noise|static]], while the FM receiver clearly reproduced a music program from Armstrong's experimental FM transmitter [[W2XMN]] in New Jersey.]]

'''Frequency modulation''' ('''FM''') is a  [[signal modulation]] technique used in electronic communication, originally for transmitting messages with a [[radio wave]]. In frequency modulation a [[carrier wave]] is varied in its [[instantaneous frequency]] in proportion to a property, primarily the instantaneous amplitude, of a message signal, such as an [[audio signal]].<ref>{{Cite book|page=85|title=Machines and Inventions|first=Robert H.|last=Smith|publisher=Time Life|year=1993|location=Alexandria, VA|isbn=0-8094-9704-2}}</ref> The technology is used in [[telecommunications]], [[radio broadcasting]], [[signal processing]], and [[Run-length limited#FM: .280.2C1.29 RLL|computing]].

In [[Analog signal|analog]] frequency modulation, such as radio broadcasting of voice and music, the instantaneous [[frequency deviation]], i.e. the difference between the frequency of the carrier and its center frequency, has a functional relation to the modulating signal amplitude.

[[Digital data]] can be encoded and transmitted with a type of frequency modulation known as [[frequency-shift keying]] (FSK), in which the instantaneous frequency of the carrier is shifted among a set of frequencies. The frequencies may represent digits, such as ''0'' and ''1''. FSK is widely used in computer [[modem]]s such as [[fax modem]]s, telephone [[caller ID]] systems, garage door openers, and other low-frequency transmissions.<ref>{{cite book |last=Gibilisco |first=Stan |title=Teach yourself electricity and electronics |url=https://archive.org/details/teachyourselfele00gibi |url-access=registration |quote=morse-code frequency-shift-keying sent-using-fsk. |publisher=McGraw-Hill Professional |year=2002 |page=[https://archive.org/details/teachyourselfele00gibi/page/477 477] |isbn=978-0-07-137730-0}}</ref> [[Radioteletype]] also uses FSK.<ref>{{cite book |last=Rutledge |first=David B. |title=The Electronics of Radio |url=https://books.google.com/books?id=ZvJYLhk4N64C&q=radio-teletype+fsk&pg=RA2-PA310 |publisher=Cambridge University Press |year=1999 |page=310 |isbn=978-0-521-64645-1}}</ref>

Frequency modulation is widely used for [[FM broadcasting|FM radio]] [[broadcasting]]. It is also used in [[telemetry]], [[radar]], seismic prospecting, and monitoring [[newborn]]s for seizures via [[EEG]],<ref>B. Boashash, editor, ''Time-Frequency Signal Analysis and Processing – A Comprehensive Reference'', Elsevier Science, Oxford, 2003; {{ISBN|0-08-044335-4}}</ref> [[two-way radio]] systems, [[Frequency modulation synthesis|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 [[AM broadcasting|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.

==Theory==
{{more citations needed|section|date=November 2017}}
If the information to be transmitted (i.e., the [[baseband signal]]) is <math>x_m(t)</math> and the [[sinusoidal]] carrier is <math>x_c(t) = A_c \cos (2 \pi f_c t)\,</math>, where ''f<sub>c</sub>'' is the carrier's base frequency, and ''A<sub>c</sub>'' is the carrier's amplitude, the modulator combines the carrier with the baseband data signal to get the transmitted signal:<ref>{{Cite book |last=Faruque |first=Saleh |url=https://nvhrbiblio.nl/biblio/boek/Faruque%20-%20Radio%20Frequency%20Modulation%20made%20easy.pdf |title=Radio Frequency Modulation Made Easy |publisher=Springer Cham |year=2017 |isbn=978-3-319-41200-9 |pages=33–37 |language=en}}</ref> {{citation needed|date=April 2017}}

:<math>\begin{align} 
  y(t) &= A_c \cos\left(2\pi \int_0^t f(\tau) d\tau\right) \\
       &= A_c \cos\left(2\pi \int_0^t \left[f_c + f_\Delta x_m(\tau)\right] d\tau\right) \\ 
       &= A_c \cos\left(2\pi f_c t + 2\pi f_\Delta \int_0^t x_m(\tau) d\tau\right) \\ 
\end{align}</math>

where <math>f_\Delta = K_f A_m</math>, <math>K_f</math> being the sensitivity of the frequency modulator and <math>A_m</math> being the amplitude of the modulating signal or baseband signal.

In this equation, <math>f(\tau)\,</math> is the ''[[instantaneous phase#Instantaneous frequency|instantaneous frequency]]'' of the oscillator and <math>f_\Delta\,</math> is the ''[[frequency deviation]]'', which represents the maximum shift away from ''f<sub>c</sub>'' in one direction, assuming ''x''<sub>''m''</sub>(''t'') is limited to the range ±1.

This process of integrating the instantaneous frequency to create an instantaneous phase is different from adding the modulating signal to the carrier frequency
:<math>\begin{align} 
  y(t) &= A_c \cos\left(2\pi \left[f_c + f_\Delta x_m(t)\right] t \right) 
\end{align}</math>
which would result in a modulated signal that has spurious local minima and maxima that do not correspond to those of the carrier.

While most of the energy of the signal is contained within ''f<sub>c</sub>'' ± ''f''<sub>Δ</sub>, 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.<ref name=TGTSCS05/>

===Sinusoidal baseband signal===
Mathematically, a baseband modulating signal may be approximated by a [[Sine wave|sinusoid]]al [[continuous wave]] signal with a frequency ''f<sub>m</sub>''. This method is also named as single-tone modulation. The integral of such a signal <math>x_m(t) = cos(2\pi f_m t)</math> is:

:<math>\int_0^t x_m(\tau)d\tau = \frac{\sin\left(2\pi f_m t\right)}{2\pi f_m}\,</math>

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

:<math>y(t) = A_c \cos\left(2\pi f_c t + \frac{f_\Delta}{f_m} \sin\left(2\pi f_m t\right)\right)\,</math>

where the amplitude <math>A_m\,</math> of the modulating [[sine wave|sinusoid]] is represented in the peak deviation <math>f_\Delta = K_f A_m</math> (see [[frequency deviation]]).

The [[harmonic]] distribution of a [[sine wave]] carrier modulated by such a [[sinusoidal]] signal can be represented with [[Bessel function]]s; this provides the basis for a mathematical understanding of frequency modulation in the frequency domain.

===Modulation index===
As in other modulation systems, the modulation index indicates by how much the modulated variable varies around its unmodulated level. It relates to variations in the [[carrier frequency]]:

:<math>h = \frac{\Delta{}f}{f_m} = \frac{f_\Delta \left|x_m(t)\right|}{f_m}</math>

where <math>f_m\,</math> is the highest frequency component present in the modulating signal ''x''<sub>''m''</sub>(''t''), and <math>\Delta{}f\,</math> is the peak frequency-deviation{{snd}}i.e. the maximum deviation of the ''[[instantaneous phase#Instantaneous frequency|instantaneous frequency]]'' from the carrier frequency. For a sine wave modulation, the modulation index is seen to be the ratio of the peak frequency deviation of the carrier wave to the frequency of the modulating sine wave.

{{anchor|narrowband_FM_anchor}}If <math>h \ll 1</math>, the modulation is called '''narrowband FM''' (NFM), and its bandwidth is approximately <math>2f_m\,</math>. Sometimes modulation index <math>h < 0.3</math>&nbsp;is considered NFM and other modulation indices are considered wideband FM (WFM or FM).

For digital modulation systems, for example, binary frequency shift keying (BFSK), where a binary signal modulates the carrier, the modulation index is given by:

:<math>h = \frac{\Delta{}f}{f_m} = \frac{\Delta{}f}{\frac{1}{2T_s}} = 2\Delta{}fT_s \ </math>

where <math>T_s\,</math> is the symbol period, and <math>f_m = \frac{1}{2T_s}\,</math> is used as the highest frequency of the modulating binary waveform by convention, even though it would be more accurate to say it is the highest ''fundamental'' of the modulating binary waveform. In the case of digital modulation, the carrier <math>f_c\,</math> is never transmitted. Rather, one of two frequencies is transmitted, either <math>f_c + \Delta f</math> or <math>f_c - \Delta f</math>, depending on the binary state 0 or 1 of the modulation signal.

If <math>h \gg 1</math>, the modulation is called ''wideband FM'' and its bandwidth is approximately <math>2f_\Delta\,</math>. While wideband FM uses more bandwidth, it can improve the [[signal-to-noise ratio]] significantly; for example, doubling the value of <math>\Delta{}f\,</math>, while keeping <math>f_m</math> constant, results in an eight-fold improvement in the signal-to-noise ratio.<ref>{{cite web |last=Der |first=Lawrence |title=Frequency Modulation (FM) Tutorial |url=http://www.silabs.com/Marcom%20Documents/Resources/FMTutorial.pdf |archive-url=https://web.archive.org/web/20141021093250/http://www.silabs.com/Marcom%20Documents/Resources/FMTutorial.pdf |archive-date=2014-10-21 |website=Silicon Laboratories |s2cid=48672999 |access-date=17 October 2019}}</ref> (Compare this with [[chirp spread spectrum]], which uses extremely wide frequency deviations to achieve processing gains comparable to traditional, better-known spread-spectrum modes).

With a tone-modulated FM&nbsp;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 remains 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.

{{anchor|narrowband FM}}
Frequency modulation can be classified as narrowband if the change in the carrier frequency is about the same as the signal frequency, or as wideband if the change in the carrier frequency is much higher (modulation index&nbsp;>&nbsp;1) than the signal frequency.<ref>Lathi, B. P. (1968). ''Communication Systems'', pp.&nbsp;214–17. New York: John Wiley and Sons, {{ISBN|0-471-51832-8}}.</ref> For example, narrowband FM (NFM) is used for [[two-way radio]] systems such as [[Family Radio Service]], in which the carrier is allowed to deviate only 2.5&nbsp;kHz above and below the center frequency with speech signals of no more than 3.5&nbsp;kHz bandwidth. Wideband FM is used for [[FM broadcasting]], in which music and speech are transmitted with up to 75&nbsp;kHz deviation from the center frequency and carry audio with up to a 20&nbsp;kHz bandwidth and subcarriers up to 92&nbsp;kHz.

===Bessel functions===
[[File:Waterfall FM.jpg|thumb|Frequency spectrum and [[waterfall plot]] of a 146.52{{nbsp}}MHz carrier, frequency modulated by a 1,000{{nbsp}}Hz sinusoid.  The modulation index has been adjusted to around 2.4, so the carrier frequency has small amplitude. Several strong sidebands are apparent; in principle an infinite number are produced in FM but the higher-order sidebands are of negligible magnitude.]]

For the case of a carrier modulated by a single sine wave, the resulting frequency spectrum can be calculated using [[Bessel function]]s of the first kind, as a function of the [[sideband]] number and the modulation index. The carrier and sideband amplitudes are illustrated for different modulation indices of FM signals. For particular values of the modulation index, the carrier amplitude becomes zero and all the signal power is in the sidebands.<ref name=TGTSCS05>T.G. Thomas, S. C. Sekhar  ''Communication Theory'', Tata-McGraw Hill 2005, {{ISBN|0-07-059091-5}}  p. 136</ref>

Since the sidebands are on both sides of the carrier, their count is doubled, and then multiplied by the modulating frequency to find the bandwidth. For example, 3&nbsp;kHz deviation modulated by a 2.2&nbsp;kHz audio tone produces a modulation index of 1.36. Suppose that we limit ourselves to only those sidebands that have a relative amplitude of at least 0.01. Then, examining the chart shows this modulation index will produce three sidebands. These three sidebands, when doubled, gives us (6 × 2.2&nbsp;kHz) or a 13.2&nbsp;kHz required bandwidth.
{| class="wikitable" style="text-align:right;"
|-
! rowspan=2  | Modulation<br />index
! colspan=17 | Sideband amplitude
|-
! 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
|
|
|
|
|
|
|
|
|
|
|
|
|-
! 2.40483
| 0.00
| 0.52
| 0.43
| 0.20
| 0.06
| 0.02
|
|
|
|
|
|
|
|
|
|
|
|-
!  2.5 
| −0.05
|  0.50
|  0.45
|  0.22
|  0.07
|  0.02
|  0.01
|
|
|
|
|
|
|
|
|
|
|-
!  3.0 
| −0.26
|  0.34
|  0.49
|  0.31
|  0.13
|  0.04
|  0.01
|
|
|
|
|
|
|
|
|
|
|-
!  4.0 
| −0.40
| −0.07
|  0.36
|  0.43
|  0.28
|  0.13
|  0.05
|  0.02
|
|
|
|
|
|
|
|
|
|-
!  5.0 
| −0.18
| −0.33
|  0.05
|  0.36
|  0.39
|  0.26
|  0.13
|  0.05
|  0.02
|
|
|
|
|
|
|
|
|-
!  5.52008
|  0.00   
| −0.34
| −0.13
|  0.25
|  0.40
|  0.32
|  0.19
|  0.09
|  0.03
|  0.01
|
|
|
|
|
|
|
|-
!  6.0 
|  0.15
| −0.28
| −0.24
|  0.11
|  0.36
|  0.36
|  0.25
|  0.13
|  0.06
|  0.02
|
|
|
|
|
|
|
|-
!  7.0 
|  0.30
|  0.00
| −0.30
| −0.17
|  0.16
|  0.35
|  0.34
|  0.23
|  0.13
|  0.06
|  0.02
|
|
|
|
|
|
|-
!  8.0 
|  0.17
|  0.23
| −0.11
| −0.29
| −0.10
|  0.19
|  0.34
|  0.32
|  0.22
|  0.13
|  0.06
|  0.03
|
|
|
|
|
|-
!  8.65373
|  0.00   
|  0.27
|  0.06
| −0.24
| −0.23
|  0.03
|  0.26
|  0.34
|  0.28
|  0.18
|  0.10
|  0.05
|  0.02
|
|
|
|
|-
!  9.0 
| −0.09
|  0.25
|  0.14
| −0.18
| −0.27
| −0.06
|  0.20
|  0.33
|  0.31
|  0.21
|  0.12
|  0.06
|  0.03
|  0.01
|
|
|
|-
!  10.0 
| −0.25
|  0.04
|  0.25
|  0.06
| −0.22
| −0.23
| −0.01
|  0.22
|  0.32
|  0.29
|  0.21
|  0.12
|  0.06
|  0.03
|  0.01
|
|
|-
!  12.0 
|  0.05
| −0.22
| −0.08
|  0.20
|  0.18
| −0.07
| −0.24
| −0.17
|  0.05
|  0.23
|  0.30
|  0.27
|  0.20
|  0.12
|  0.07
|  0.03
|  0.01
|}

===Carson's rule===
{{Main|Carson bandwidth rule}}

A [[rule of thumb]], ''Carson's rule'' states that nearly all (≈98 percent) of the power of a frequency-modulated signal lies within a [[bandwidth (signal processing)|bandwidth]] <math> B_T\, </math> of:

:<math>B_T = 2\left(\Delta f + f_m\right) = 2f_m(h + 1)</math>

where <math>\Delta f\,</math>, as defined above, is the peak deviation of the instantaneous frequency <math>f(t)\,</math> from the center carrier frequency <math>f_c</math>, <math>h</math> is the modulation index which is the ratio of frequency deviation to highest frequency in the modulating signal, and <math>f_m\,</math>is the highest frequency in the modulating signal.
Carson's rule can only be applied to sinusoidal signals. For non-sinusoidal signals:

:<math>B_T = 2(\Delta f + W) = 2W(D + 1)</math>

where W  is the highest frequency in the modulating signal but non-sinusoidal in nature and D is the Deviation ratio which is the ratio of frequency deviation to highest frequency of modulating non-sinusoidal signal.

==Noise reduction==
FM provides improved [[signal-to-noise ratio]] (SNR), as compared for example with [[amplitude modulation|AM]]. Compared with an optimum AM scheme, FM typically has poorer SNR below a certain signal level called the noise threshold, but above a higher level – the full improvement or full quieting threshold – the SNR is much improved over AM. The improvement depends on modulation level and deviation. For typical voice communications channels, improvements are typically 5–15&nbsp;dB. FM broadcasting using wider deviation can achieve even greater improvements. Additional techniques, such as pre-emphasis of higher audio frequencies with corresponding de-emphasis in the receiver, are generally used to improve overall SNR in FM circuits. Since FM signals have constant amplitude, FM receivers normally have limiters that remove AM noise, further improving SNR.<ref>{{cite book |title=Reference Data for Radio Engineers |edition=Fifth |pages=21–11 |year=1970 |publisher=Howard W. Sams & Co. |editor=H. P. Westman}}</ref><ref>{{cite book |title=The ARRL Handbook for Radio Communications |publisher=American Radio Relay League |year=2010 |editor=H. Ward Silver |editor2=Mark J. Wilson|author=Alan Bloom |chapter=Chapter 8. Modulation |page=8.7 |isbn=978-0-87259-146-2}}</ref>

=={{anchor|Practical Implementation}}Implementation==

===Modulation===
FM signals can be generated using either direct or indirect frequency modulation:
* Direct FM modulation can be achieved by directly feeding the message into the input of a [[voltage-controlled oscillator]].
* For indirect FM modulation, the message signal is integrated to generate a [[phase modulation|phase-modulated signal]]. This is used to modulate a [[crystal oscillator|crystal-controlled oscillator]], and the result is passed through a [[frequency multiplier]] to produce an FM signal. In this modulation, narrowband FM is generated leading to wideband FM later and hence the modulation is known as indirect FM modulation.<ref>Haykin, Simon [Ed]. (2001). ''Communication Systems'', 4th&nbsp;ed.</ref>

===Demodulation===
{{see also|Detector (radio)#Frequency and phase modulation detectors}}
[[File:FM Modulation - en.png|thumb|FM modulation]]
Many FM detector circuits exist. A common method for recovering the information signal is through a [[Foster–Seeley discriminator]] or [[ratio detector]]. A [[phase-locked loop]] can be used as an FM demodulator. ''Slope detection'' demodulates an FM signal by using a tuned circuit which has its resonant frequency slightly offset from the carrier. As the frequency rises and falls the tuned circuit provides a changing amplitude of response, converting FM to AM. AM receivers may detect some FM transmissions by this means, although it does not provide an efficient means of [[detector (radio)|detection]] for FM broadcasts.

In [[software-defined radio]] implementations, the demodulation may be carried out by using the [[Hilbert transform]] (implemented as a filter) to recover the instantaneous phase, and thereafter differentiating this phase (using another filter) to recover the instantaneous frequency. Alternatively, a complex mixer followed by a bandpass filter may be used to translate the signal to baseband, and then proceeding as before. For sampled signals, phase detection, and therefore frequency modulation detection, can be approximated by taking the IQ (complex) sample and multiplying it with the complex conjugate of the previous IQ sample, <math>x[n]\cdot \overline{x[n-1]}</math>.<ref>{{Cite book |last=Shima |first=James Michael |url=https://books.google.com/books?id=Aq7uygAACAAJ |title=FM Demodulation Using a Digital Radio and Digital Signal Processing |date=1995 |publisher=University of Florida |language=en}}</ref> If the demodulated signal is sampled at or above Nyquist, this allows for recovery of near-instantaneous phase changes.

==Applications==
=== Doppler effect===
When an echolocating [[bat]] approaches a target, its outgoing sounds return as echoes, which are Doppler-shifted upward in frequency. In certain species of bats, which produce constant frequency (CF) [[Animal echolocation|echolocation]] calls, the bats compensate for the [[Doppler shift]] by lowering their call frequency as they approach a target. This keeps the returning echo in the same frequency range of the normal echolocation call. This dynamic frequency modulation is called the '''Doppler Shift Compensation''' (DSC), and was discovered by [[Hans Schnitzler]] in 1968.

===Magnetic tape storage===
FM is also used at [[Intermediate frequency|intermediate frequencies]] by analog [[Video cassette recorder|VCR]] systems (including [[VHS]]) to record the [[Luminance (video)|luminance]] (black and white) portions of the video signal. Commonly, the [[chrominance]] component is recorded as a conventional AM signal, using the higher-frequency FM signal as [[Tape bias|bias]]. FM is the only feasible method of recording the luminance ("black-and-white") component of video to (and retrieving video from) [[magnetic tape]] without distortion; video signals have a large range of frequency components – from a few [[hertz]] to several [[megahertz]], too wide for [[Equalization (audio)|equalizers]] to work with due to electronic noise below −60&nbsp;[[decibel|dB]]. FM also keeps the tape at saturation level, acting as a form of [[noise reduction]]; a [[audio level compression|limiter]] can mask variations in 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]].

These FM systems are unusual, in that they have a ratio of carrier to maximum modulation frequency of less than two; contrast this with FM audio broadcasting, where the ratio is around 10,000. Consider, for example, a 6-MHz carrier modulated at a 3.5-MHz rate; by [[Bessel function|Bessel]] analysis, the first sidebands are on 9.5 and 2.5&nbsp;MHz and the second sidebands are on 13&nbsp;MHz and −1&nbsp;MHz. The result is a reversed-phase sideband on +1&nbsp;MHz; on demodulation, this results in unwanted output at 6 – 1 = 5&nbsp;MHz. The system must be designed so that this unwanted output is reduced to an acceptable level.<ref>"FM Systems Of Exceptional Bandwidth" Proc. IEEE vol. 112, no. 9, p. 1664, September 1965</ref>

===Sound===
FM is also used at [[audio frequency|audio frequencies]] to synthesize sound. This technique, known as [[frequency modulation synthesis|FM synthesis]], was popularized by early digital [[synthesizer]]s and became a standard feature in several generations of [[personal computer]] [[sound card]]s.

===Radio===

{{Main|FM broadcasting}}
[[File:FM Broadcast Transmitter High Power.jpg|thumb|An American FM radio transmitter at [[WEDG]] in Buffalo, New York]]
[[Edwin Howard Armstrong]] (1890–1954) was an American electrical engineer who invented wideband frequency modulation (FM) radio.<ref>{{Cite book
 |title = Principles of modern communications technology
 |author = A. Michael Noll
 |publisher = Artech House
 |year = 2001
 |isbn = 978-1580532846
 |page = [https://archive.org/details/principlesofmode0000noll/page/104 104]
 |url = https://archive.org/details/principlesofmode0000noll
|url-access = registration
 }}</ref>
He patented the regenerative circuit in 1914, the superheterodyne receiver in 1918 and the super-regenerative circuit in 1922.<ref>{{patent|US|1342885}}</ref> 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.<ref>{{Cite journal
 |first = E. H.
 |last = Armstrong
 |title = A Method of Reducing Disturbances in Radio Signaling by a System of Frequency Modulation
 |journal = Proceedings of the IRE
 |volume = 24
 |issue = 5
 |pages = 689–740
 |publisher = IRE
 |date= May 1936
 |doi = 10.1109/JRPROC.1936.227383
|s2cid = 43628076
 }}</ref>

As the name implies, wideband FM (WFM) requires a wider [[signal bandwidth]] than [[amplitude modulation]] by an equivalent modulating signal; this also makes the signal more robust against [[Noise (radio)|noise]] and [[Interference (communication)|interference]]. Frequency modulation is also more robust against 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 part of the [[VHF]] band{{snd}}the [[FM broadcast band]]). FM [[receiver (radio)|receivers]] employ a special [[Detector (radio)|detector]] for FM signals and exhibit a phenomenon known as the ''[[capture effect]]'', in which the [[Tuner (radio)|tuner]] "captures" the stronger of two stations on the same frequency while rejecting the other (compare this with a similar situation on an AM receiver, where both stations can be heard simultaneously). [[Frequency drift]] or a lack of [[selectivity (radio)|selectivity]] may cause one station to be overtaken by another on an [[adjacent channel]]. Frequency [[drift (telecommunication)|drift]] was a problem in early (or inexpensive) receivers; inadequate selectivity may affect any tuner.

A wideband FM signal can also be used to carry a [[stereophonic sound|stereo]] signal; this is done with [[multiplexing]] and demultiplexing before and after the FM process. The FM modulation and demodulation process is identical in stereo and monaural processes.

FM is commonly used at [[VHF]] [[radio frequencies]] for [[high-fidelity]] [[radio broadcasting|broadcasts]] of music and [[Speech communication|speech]]. In broadcast services, where audio fidelity is important, wideband FM is generally used. Analog TV sound is also broadcast using FM. Narrowband FM is used for voice communications in commercial and [[amateur radio]] settings. In [[two-way radio]], narrowband FM (NBFM) is used to conserve bandwidth for land mobile, marine mobile and other radio services.

A high-efficiency radio-frequency [[switching amplifier]] can be used to transmit FM signals (and other [[constant envelope|constant-amplitude signals]]). For a given signal strength (measured at the receiver antenna), switching amplifiers use [[low-power electronics|less battery power]] and typically cost less than a [[linear amplifier]]. This gives FM another advantage over other modulation methods requiring linear amplifiers, such as AM and [[Quadrature amplitude modulation|QAM]].

There are reports that on October 5, 1924, Professor [[Mikhail A. Bonch-Bruevich]], during a scientific and technical conversation in the [[Nizhny Novgorod Radio Laboratory]], reported about his new method of telephony, based on a change in the period of oscillations. Demonstration of frequency modulation was carried out on the laboratory model.<ref>Ф. Лбов. [https://sergeyhry.narod.ru/rl/rl1924_06_09.htm Новая система радиофона] «Радиолюбитель».{{snd}}1924.{{snd}}№ 6.{{snd}}С. 86.</ref>

===Hearing assistive technology===
Frequency modulated systems are a widespread and commercially available [[assistive technology]] that make speech more understandable by improving the signal-to-noise ratio in the user's ear. They are also called ''auditory trainers'', a term which refers to any sound amplification system not classified as a [[hearing aid]]. They intensify signal levels from the source by 15 to 20 decibels.<ref>{{cite tech report |author=ASHA Ad Hoc Committee on FM Systems |date=2002 |orig-date=Original March 1994 |edition=Revised |title=Guidelines for Fitting and Monitoring FM Systems |institution=[[American Speech–Language–Hearing Association]] |url=https://www.asha.org/policy/gl2002-00010/ |doi=10.1044/policy.GL2002-00010}}</ref> FM systems are used by hearing-impaired people as well as children whose listening is affected by disorders such as [[auditory processing disorder]] or [[ADHD]].<ref>{{Cite journal |last1=Schafer |first1=Erin C. |last2=Bryant |first2=Danielle |last3=Sanders |first3=Katie |last4=Baldus |first4=Nicole |last5=Algier |first5=Katherine |last6=Lewis |first6=Audrey |last7=Traber |first7=Jordan |last8=Layden |first8=Paige |last9=Amin |first9=Aneeqa |date=June 1, 2014 |title=Fitting and Verification of Frequency Modulation on Children with Normal Hearing |journal=Journal of the American Academy of Audiology |volume=25 |issue=6 |pages=529–540 |doi=10.3766/jaaa.25.6.3 |issn=1050-0545 |pmid=25313543 |id={{EBSCOhost|107832936}} |via=[[EBSCOhost]]}}</ref> For people with [[sensorineural hearing loss]], FM systems result in better speech perception than hearing aids. They can be coupled with behind-the-ear hearing aids to allow the user to alternate the setting.<ref>{{Cite journal |last1=Lewis |first1=M. Samantha |last2=Crandall |first2=Carl C. |last3=Valente |first3=Michael |last4=Enrietto Horn |first4=Jane |date=2004 |title=Speech perception in noise: directional microphones versus frequency modulation (FM) systems |url=https://digitalcommons.wustl.edu/audio_hapubs/5 |journal=Journal of the American Academy of Audiology |volume=15 |issue=6 |pages=426–439 |doi=10.3766/jaaa.15.6.4 |pmid=15341224 |doi-access=free|url-access=subscription }}</ref> FM systems are more convenient and cost-effective than alternatives such as [[cochlear implants]], but many users use FM systems infrequently due to their conspicuousness and need for recharging.<ref>{{Cite journal |last=McArdle |first=Rachel |last2=Abrams |first2=Harvey B. |last3=Hnath Chisholm |first3=Theresa |date=2005 |title=When Hearing Aids Go Bad: An FM Success Story |journal=Journal of the American Academy of Audiology |volume=16 |issue=10 |pages=809–821 |doi=10.3766/jaaa.16.10.5 |id={{EBSCOhost|106441304}} |via=[[EBSCOhost]]}}</ref>

==See also==
{{Commons category|Frequency modulation}}
* [[Continuous-wave frequency-modulated radar]]
* [[Chirp]]
* [[FM stereo]]
* [[FM-UWB]] (FM and Ultra Wideband)
* [[History of radio]]
* [[Modulation]], for a list of other modulation techniques

==References==
{{reflist|25em}}

==Further reading==
* {{cite book |last=Carlson |first=A. Bruce |title=Communication Systems |publisher=McGraw-Hill |edition=4th |year=2001 |series=Science/Engineering/Math |isbn=978-0-07-011127-1}}
* {{cite book |last=Frost |first=Gary L. |title=Early FM Radio: Incremental technology in twentieth-century America |publisher=Johns Hopkins University Press |location=Baltimore, MD |year=2010 |isbn=978-0-8018-9440-4 }} 
* {{cite book |last=Seymour |first=Ken<!-- AT&T Wireless (Mobility) --> |chapter=Frequency Modulation |title=The Electronics Handbook |publisher=CRC Press |edition=2nd |orig-year=1996 |year=2005|pages=1188–1200 |isbn=0-8493-8345-5}}

==External links==
* [https://colab.research.google.com/drive/14Ws9gX1hPzBkE7P1sBepVuoz-uo2f-Be?usp=sharing Analog Modulation online interactive demonstration] using Python in [https://colab.research.google.com Google Colab Platform], by C Foh.

{{Analogue TV transmitter topics}}
{{Telecommunications}}
{{Audio broadcasting}}
{{Authority control}}

[[Category:Radio modulation modes]]