Frequency modulation

In telecommunications and signal processing, frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave.

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, music 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.

A signal may be carried by an AM or FM radio wave.
GE FM radio antistatic demonstration 1940
FM has better noise (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 arc as a source of interference behind it, the AM receiver produced only a roar of static, while the FM receiver clearly reproduced a music program from Armstrong's experimental FM transmitter W2XMN in New Jersey.


If the information to be transmitted (i.e., the baseband signal) is 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:

where , being the sensitivity of the frequency modulator and being the amplitude of the modulating signal or baseband 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.

While most of the energy of the signal is contained within fc ± fΔ, 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 fm. This method is also named as single-tone modulation. The integral of such a signal is:

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

where the amplitude of the modulating sinusoid is represented by the peak deviation (see frequency deviation).

The harmonic distribution of a sine wave carrier modulated by such a sinusoidal signal can be represented with Bessel functions; 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:

where is the highest frequency component present in the modulating signal xm(t), and is the peak frequency-deviation—i.e. the maximum deviation of the 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.

If , the modulation is called narrowband FM (NFM), and its bandwidth is approximately . Sometimes modulation index  is considered as NFM, otherwise 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:

where is the symbol period, and 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 is never transmitted. Rather, one of two frequencies is transmitted, either or , depending on the binary state 0 or 1 of the modulation signal.

If , the modulation is called wideband FM and its bandwidth is approximately . While wideband FM uses more bandwidth, it can improve the signal-to-noise ratio significantly; for example, doubling the value of , while keeping constant, results in an eight-fold improvement in the signal-to-noise ratio.[5] (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 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.

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 > 1) than the signal frequency.[6] 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 kHz above and below the center frequency with speech signals of no more than 3.5 kHz bandwidth. Wideband FM is used for FM broadcasting, in which music and speech are transmitted with up to 75 kHz deviation from the center frequency and carry audio with up to a 20 kHz bandwidth and subcarriers up to 92 kHz.

Bessel functions

Waterfall FM
Frequency spectrum and waterfall plot of a 146.52 MHz carrier, frequency modulated by a 1,000 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 functions 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.[4]

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 kHz deviation modulated by a 2.2 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 kHz) or a 13.2 kHz required bandwidth.

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
2.41 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
5.53 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
8.65 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

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 of:

where , as defined above, is the peak deviation of the instantaneous frequency from the center carrier frequency , is the Modulation index which is the ratio of frequency deviation to highest frequency in the modulating signal and is the highest frequency in the modulating signal. Condition for application of Carson's rule is only sinusoidal signals.

where W is the highest frequency in the modulating signal but non-sinusoidal in nature and D is the Deviation ratio which 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 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 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.[7][8]



FM signals can be generated using either direct or indirect frequency modulation:


FM Modulation - en
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 detection for FM broadcasts.


Magnetic tape storage

FM is also used at intermediate frequencies by analog VCR systems (including VHS) to record the 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 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 equalizers to work with due to electronic noise below −60 dB. FM also keeps the tape at saturation level, acting as a form of noise reduction; a 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 analysis, the first sidebands are on 9.5 and 2.5 MHz and the second sidebands are on 13 MHz and −1 MHz. The result is a reversed-phase sideband on +1 MHz; on demodulation, this results in unwanted output at 6 – 1 = 5 MHz. The system must be designed so that this unwanted output is reduced to an acceptable level.[10]


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


FM Broadcast Transmitter High Power
An American FM radio transmitter in Buffalo, NY at WEDG

Edwin Howard Armstrong (1890–1954) was an American electrical engineer who invented wideband frequency modulation (FM) radio.[11] He patented the regenerative circuit in 1914, the superheterodyne receiver in 1918 and the super-regenerative circuit in 1922.[12] 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.[13]

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 and 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—the FM broadcast band). FM receivers employ a special detector for FM signals and exhibit a phenomenon known as the capture effect, in which the 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). However, frequency drift or a lack of selectivity may cause one station to be overtaken by another on an adjacent channel. Frequency drift was a problem in early (or inexpensive) receivers; inadequate selectivity may affect any tuner.

An FM signal can also be used to carry a 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. 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 methods requiring linear amplifiers, such as AM and QAM.

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

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.[14]

See also


  1. ^ Stan Gibilisco (2002). Teach yourself electricity and electronics. McGraw-Hill Professional. p. 477. ISBN 978-0-07-137730-0.
  2. ^ David B. Rutledge (1999). The Electronics of Radio. Cambridge University Press. p. 310. ISBN 978-0-521-64645-1.
  3. ^ B. Boashash, editor, "Time-Frequency Signal Analysis and Processing – A Comprehensive Reference", Elsevier Science, Oxford, 2003; ISBN 0-08-044335-4
  4. ^ a b T.G. Thomas, S. C. Sekhar Communication Theory, Tata-McGraw Hill 2005, ISBN 0-07-059091-5 page 136
  5. ^ Der, Lawrence, Ph.D., Frequency Modulation (FM) Tutorial,, Silicon Laboratories, Inc., accessed 2013 February 24, p. 5
  6. ^ Lathi, B. P. (1968). Communication Systems, p. 214–217. New York: John Wiley and Sons, ISBN 0-471-51832-8.
  7. ^ H. P. Westman, ed. (1970). Reference Data for Radio Engineers (Fifth ed.). Howard W. Sams & Co. p. 21-11.
  8. ^ Alan Bloom (2010). "Chapter 8. Modulation". In H. Ward Silver and Mark J. Wilson (Eds). The ARRL Handbook for Radio Communications. American Radio Relay League. p. 8.7. ISBN 978-0-87259-146-2.CS1 maint: Extra text: editors list (link)
  9. ^ Haykin, Simon [Ed]. (2001). Communication Systems, 4th ed.
  10. ^ : "FM Systems Of Exceptional Bandwidth" Proc. IEEE vol 112, no. 9, p. 1664, September 1965
  11. ^ A. Michael Noll (2001). Principles of modern communications technology. Artech House. p. 104. ISBN 978-1-58053-284-6.
  12. ^ ‹See Tfd›US 1342885
  13. ^ Armstrong, E. H. (May 1936). "A Method of Reducing Disturbances in Radio Signaling by a System of Frequency Modulation". Proceedings of the IRE. IRE. 24 (5): 689–740. doi:10.1109/JRPROC.1936.227383.
  14. ^ Ф. Лбов. Новая система радиофона // «Радиолюбитель». — 1924. — № 6. — С. 86.

Further reading

  • A. Bruce Carlson. Communication Systems, 4th edition. McGraw-Hill Science/Engineering/Math. 2001. ISBN 0-07-011127-8, ISBN 978-0-07-011127-1.
  • Gary L. Frost. Early FM Radio: Incremental Technology in Twentieth-Century America. Baltimore: Johns Hopkins University Press, 2010. ISBN 0-8018-9440-9, ISBN 978-0-8018-9440-4.
  • Ken Seymour, AT&T Wireless (Mobility). Frequency Modulation, The Electronics Handbook, pp 1188–1200, 1st Edition, 1996. 2nd Edition, 2005 CRC Press, Inc., ISBN 0-8493-8345-5 (1st Edition).
Analog transmission

Analog transmission is a transmission method of conveying information using a continuous signal which varies in amplitude, phase, or some other property in proportion to that information. It could be the transfer of an analog source signal, using an analog modulation method such as frequency modulation (FM) or amplitude modulation (AM), or no modulation at all.

Some textbooks also consider passband data transmission using a digital modulation method such as ASK, PSK and QAM, i.e. a sinewave modulated by a digital bit-stream, as analog transmission and as an analog signal. Others define that as digital transmission and as a digital signal. Baseband data transmission using line codes, resulting in a pulse train, are always considered as digital transmission, although the source signal may be a digitized analog signal.

Angle modulation

Angle modulation is a class of carrier modulation that is used in telecommunications transmission systems. The class comprises frequency modulation (FM) and phase modulation (PM), and is based on altering the frequency or the phase, respectively, of a carrier signal to encode the message signal. This contrasts with varying the amplitude of the carrier, practiced in amplitude modulation (AM) transmission, the earliest of the major modulation methods used widely in early radio broadcasting.

Audio Frequency Modulation

Audio Frequency Modulation (AFM) is an audio recording standard used by VHS Hi-Fi stereo, 8mm and Hi8 video systems. AFM is mono on 8mm systems and stereo on Hi8.

Differential Manchester encoding

Differential Manchester Encoding (DM) is a line code in which data and clock signals are combined to form a single 2-level self-synchronizing data stream. In various specific applications, this line code is also called by various other names, including Biphase Mark Code (CC), Frequency Modulation (FM), F2F (frequency/double frequency), Aiken Biphase, and Conditioned diphase.

DM is a differential encoding, using the presence or absence of transitions to indicate logical value. It is not necessary to know the polarity of the sent signal since the information is not represented by the absolute voltage levels but in their changes: in other words it does not matter which of the two voltage levels is received, but only whether it is the same or different from the previous one; this makes synchronization easier.

Differential Manchester encoding has the following advantages over some other line codes:

A transition is guaranteed at least once every bit, for robust clock recovery.

In a noisy environment, detecting transitions is less error-prone than comparing signal levels against a threshold.

Unlike with Manchester encoding, only the presence of a transition is important, not the polarity. Differential coding schemes will work exactly the same if the signal is inverted (e.g. wires swapped). Other line codes with this property include NRZI, bipolar encoding, coded mark inversion, and MLT-3 encoding.

If the high and low signal levels have the same magnitude with opposite polarity, the average voltage around each unconditional transition is zero. Zero DC bias reduces the necessary transmitting power, minimizes the amount of electromagnetic noise produced by the transmission line, and eases the use of isolating transformers.

These positive features are achieved at the expense of doubling the bandwidth—there are two clock ticks per bit period (marked with full and dotted lines in the figure). At every second clock tick, marked with a dotted line, there is a potential level transition conditional on the data. At the other ticks, the line state changes unconditionally to ease clock recovery. One version of the code makes a transition for 0 and no transition for 1; the other makes a transition for 1 and no transition for 0.

Differential Manchester is specified in the IEEE 802.5 standard for token ring LANs, and is used for many other applications, including magnetic and optical storage. As Biphase Mark Code (BMC), it is used in AES3, S/PDIF, SMPTE time code, and USB PD. Many magnetic stripe cards also use BMC encoding, often called F2F (frequency/double frequency) or Aiken Biphase, according to the ISO/IEC 7811 standard. Differential Manchester is also the original "frequency modulation" (FM) used on "single-density" floppy disks, followed by "double-density" modified frequency modulation (MFM), which gets its name from its relation to FM, or Differential Manchester, encoding.

Edwin Howard Armstrong

Edwin Howard Armstrong (December 18, 1890 – February 1, 1954) was an American electrical engineer and inventor, best known for developing FM (frequency modulation) radio and the superheterodyne receiver system. He held 42 patents and received numerous awards, including the first Medal of Honor awarded by the Institute of Radio Engineers (now IEEE), the French Legion of Honor, the 1941 Franklin Medal and the 1942 Edison Medal. He was inducted into the National Inventors Hall of Fame and included in the International Telecommunication Union's roster of great inventors.

FM broadcasting

FM broadcasting is a method of radio broadcasting using frequency modulation (FM) technology. Invented in 1933 by American engineer Edwin Armstrong, wide-band FM is used worldwide to provide high-fidelity sound over broadcast radio. FM broadcasting is capable of better sound quality than AM broadcasting (under normal listening conditions), the chief competing radio broadcasting technology, so it is used for most music broadcasts. Theoretically wideband AM can offer equally good sound quality, provided the reception conditions are ideal. FM radio stations use the VHF frequencies. The term "FM band" describes the frequency band in a given country which is dedicated to FM broadcasting.

FM broadcasting in Japan

The frequency modulation radio broadcast band in Japan is 76-95 MHz. The 90-108 MHz section was used for television for VHF channels 1, 2 and 3 until the analog shutdown occurred on July 24, 2011. The narrowness of the Japanese band (19 MHz compared to slightly more than 20 MHz for the CCIR band) limits the number of FM stations that can be accommodated on the dial.

In late 2013, the Ministry of Internal Affairs and Communications published a report proposing the expansion of the FM band to 95 MHz. Many stations that had been previously only available on the AM band were issued preliminary licenses to broadcast from 90-95 MHz. The first station to go on air in the expanded band was Nankai Broadcasting, which began test broadcasts on 91.7 FM on November 3, 2014.

Figure of merit

A figure of merit is a quantity used to characterize the performance of a device, system or method, relative to its alternatives.

Frequency modulation synthesis

Frequency modulation synthesis (or FM synthesis) is a form of sound synthesis where the frequency of a waveform, called the carrier, is changed by modulating its frequency with a modulator. The frequency of an oscillator is altered "in accordance with the amplitude of a modulating signal." (Dodge & Jerse 1997, p. 115)

FM synthesis can create both harmonic and inharmonic sounds. For synthesizing harmonic sounds, the modulating signal must have a harmonic relationship to the original carrier signal. As the amount of frequency modulation increases, the sound grows progressively more complex. Through the use of modulators with frequencies that are non-integer multiples of the carrier signal (i.e. inharmonic), inharmonic bell-like and percussive spectra can be created.

FM synthesis using analog oscillators may result in pitch instability. However, FM synthesis can also be implemented digitally, the latter proving to be more stable and is currently seen as standard practice. Digital FM synthesis (implemented as phase modulation) was the basis of several musical instruments beginning as early as 1974. Yamaha built the first prototype digital synthesizer in 1974, based on FM synthesis, before commercially releasing the Yamaha GS-1 in 1980. The Synclavier I, manufactured by New England Digital Corporation beginning in 1978, included a digital FM synthesizer, using an FM synthesis algorithm licensed from Yamaha. Yamaha's groundbreaking DX7, released in 1983, brought FM to the forefront of synthesis in the mid-1980s.

FM synthesis had also become the usual setting for games and software until the mid-nineties. Through sound cards like the AdLib and Sound Blaster, IBM PCs popularized Yamaha chips like OPL2 and OPL3. The related OPN2 was used in the Sega Genesis as one of its sound generator chips.


The Korg OASYS PCI is a DSP-based PCI-card for PC and Mac released in 1999. It offers many synthesizer engines from sampling and substractive to FM and physical modelling.

Because of its high market price and low polyphony production was stopped in 2001.

About 2000 cards were produced.

Modified Frequency Modulation

Modified Frequency Modulation, commonly MFM, is a run-length limited (RLL) coding scheme used to encode the actual data-bits on most floppy disks. It was first introduced in disk drives in 1970 with the IBM 3330 hard disk drive and then in floppy disk drives beginning with the "double density" IBM 53FD in 1976. MFM is a modification to the original digital FM (digital frequency modulation also known as delay coding) scheme for encoding data on single-density floppy disks and some early hard disk drives.

Due to the minimum spacing between flux transitions that is a property of the disk, head and channel design, MFM, which guarantees at most one flux transition per data bit, can be written at higher density than FM, which can require two transitions per data bit. It is used with a data rate of 250–500 kbit/s (500–1000 kbit/s encoded) on industry standard 5¼-inch and 3½-inch ordinary and high density diskettes. MFM was also used in early hard disk designs, before the advent of more efficient types of run-length limited codes. Except for the steadily disappearing 360 KiB/1.2 MiB (5.25-inch) and 720~880 KiB/1.4~1.6 MiB (3.5-inch) floppy disk formats, MFM encoding is obsolete in magnetic recording.


In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a modulating signal that typically contains information to be transmitted. Most radio systems in the 20th century used frequency modulation (FM) or amplitude modulation (AM) for radio broadcast.

A modulator is a device that performs modulation. A demodulator (sometimes detector or demod) is a device that performs demodulation, the inverse of modulation. A modem (from modulator–demodulator) can perform both operations.

The aim of analog modulation is to transfer an analog baseband (or lowpass) signal, for example an audio signal or TV signal, over an analog bandpass channel at a different frequency, for example over a limited radio frequency band or a cable TV network channel. The aim of digital modulation is to transfer a digital bit stream over an analog communication channel, for example over the public switched telephone network (where a bandpass filter limits the frequency range to 300–3400 Hz) or over a limited radio frequency band. Analog and digital modulation facilitate frequency division multiplexing (FDM), where several low pass information signals are transferred simultaneously over the same shared physical medium, using separate passband channels (several different carrier frequencies).

The aim of digital baseband modulation methods, also known as line coding, is to transfer a digital bit stream over a baseband channel, typically a non-filtered copper wire such as a serial bus or a wired local area network.

The aim of pulse modulation methods is to transfer a narrowband analog signal, for example, a phone call over a wideband baseband channel or, in some of the schemes, as a bit stream over another digital transmission system.

In music synthesizers, modulation may be used to synthesize waveforms with an extensive overtone spectrum using a small number of oscillators. In this case, the carrier frequency is typically in the same order or much lower than the modulating waveform (see frequency modulation synthesis or ring modulation synthesis).

Non-contact atomic force microscopy

Non-contact atomic force microscopy (nc-AFM), also known as dynamic force microscopy (DFM), is a mode of atomic force microscopy, which itself is a type of scanning probe microscopy. In nc-AFM a sharp probe is moved close (order of Angstroms) to the surface under study, the probe is then raster scanned across the surface, the image is then constructed from the force interactions during the scan. The probe is connected to a resonator, usually a silicon cantilever or a quartz crystal resonator. During measurements the sensor is driven so that it oscillates. The force interactions are measured either by measuring the change in amplitude of the oscillation at a constant frequency just off resonance (amplitude modulation) or by measuring the change in resonant frequency directly using a feedback circuit (usually a phase-locked loop) to always drive the sensor on resonance (frequency modulation).

OLT (mobile network)

OLT (Norwegian for Offentlig Landmobil Telefoni, Public Land Mobile Telephony), was the first land mobile telephone network in Norway. It was established December 1, 1966, and continued until it was obsoleted by NMT in 1990. In 1981, there were 30,000 mobile subscribers, which at the time made this network the largest in the world.

The network operated in the 160 MHz VHF band, using frequency modulation (FM) on 160-162 MHz for the mobile unit, and 168-170 MHz for the base station. Most mobile sets were semi-duplex, but some of the more expensive units were full duplex. Each subscriber was assigned a five digit phone number.

In 1976, the OLT system was extended to include UHF bands, incorporating MTD, and allowing international roaming within Scandinavian countries.

Phase modulation

Phase modulation (PM) is a modulation pattern for conditioning communication signals for transmission. It encodes a message signal as variations in the instantaneous phase of a carrier wave. Phase modulation is one of the two principal forms of angle modulation, together with frequency modulation.

The phase of a carrier signal is modulated to follow the changing signal level (amplitude) of the message signal. The peak amplitude and the frequency of the carrier signal are maintained constant, but as the amplitude of the message signal changes, the phase of the carrier changes correspondingly.

Phase modulation is widely used for transmitting radio waves and is an integral part of many digital transmission coding schemes that underlie a wide range of technologies like Wi-Fi, GSM and satellite television.

PM is used for signal and waveform generation in digital synthesizers, such as the Yamaha DX7 to implement FM synthesis. A related type of sound synthesis called phase distortion is used in the Casio CZ synthesizers.

Pulse-frequency modulation

Pulse-Frequency Modulation (PFM) is a modulation method for representing an analog signal using only two levels (1 and 0). It is analogous to pulse-width modulation (PWM), in which the magnitude of an analog signal is encoded in the duty cycle of a square wave. Unlike PWM, in which the width of square pulses is varied at constant frequency, PFM fixes the width of square pulses while varying the frequency. In other words, the frequency of the pulse train is varied in accordance with the instantaneous amplitude of the modulating signal at sampling intervals. The amplitude and width of the pulses is kept constant.

Quantum noise

In physics, quantum noise refers to the uncertainty of a physical quantity that is due to its quantum origin. In certain situations, quantum noise appears as shot noise; for example, most optical communications use amplitude modulation, and thus, the quantum noise appears as shot noise only. For the case of uncertainty in the electric field in some lasers, the quantum noise is not just shot noise; uncertainties of both amplitude and phase contribute to the quantum noise. This issue becomes important in the case of noise of a quantum amplifier, which preserves the phase. The phase noise becomes important when the energy of the frequency modulation or phase modulation of waves is comparable to the energy of the signal (which is believed to be more robust with respect to additive noise than an amplitude modulation).

Shivaraj Municipality

Shivaraj is a Municipality in Kapilvastu District in the Lumbini Zone of southern Nepal. The former village development committee was transformed into Municipality from 18 May 2014 by merging the existing Birpur, Nepal, Chanai, Bishunpur, Jawabhari and Shivapur village development committees. At the time of the 1991 Nepal census it had a population of 7241 people living in 1067 individual households.To promote local culture Shivapur has one FM radio stations Radio Voice – 104.5 MHz, which is a Community radio Station. For the better help another frequency modulation radio has been running with a name, Shivraj FM. It has been giving information about local activities, news and program. Chandrauta is one of the reputed cities located in Shivraj municipality.

Yamaha DX7

The Yamaha DX7 is a synthesizer manufactured by the Yamaha Corporation from 1983 to 1989. It was the first commercially successful digital synthesizer and became one of the bestselling synthesizers in history, selling over 200,000 units.

In the early 1980s, the synthesizer market was dominated by analog synthesizers. Frequency modulation (FM) synthesis, a means of generating sounds digitally with different results, was developed by John Chowning at Stanford University, California. Yamaha licensed the technology to create the DX7, combining it with very-large-scale integration chips to lower manufacturing costs.

With its digital display, complex menus, and lack of conventional controls, few learned to program the DX7 in depth. However, its preset sounds became staples of 1980s pop music, used by artists including A-ha, Kenny Loggins, Kool & the Gang, Whitney Houston, Chicago, Phil Collins, Luther Vandross, and Billy Ocean. Its piano sound was particularly widely used, especially in power ballads. Producer Brian Eno mastered the programming and it was instrumental to his work in ambient music. In later years the DX7's sounds came to be seen as dated or cliched, and interest in FM synthesis declined.

Color systems
Frequencies & Bands
Network topology
and switching
Subcarrier signals

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