Frequency modulation synthesis (or FM synthesis) is a form of audio synthesis where the timbre of a simple waveform is changed by frequency modulating it with a modulating frequency that is also in the audio range, resulting in a more complex waveform and a different-sounding tone. graphs of various frequency modulated sine waves in the time domain for various modulation indices File links The following pages link to this file: Frequency modulation synthesis Categories: GFDL images ... The modulation index (mf) is defined as the ratio of the frequency deviation σ to the modulating signal frequency fi, i. ... For other uses, see Decibel (disambiguation). ... graphs of frequency modulation spectra for various modulation indices File links The following pages link to this file: Frequency modulation synthesis Categories: GFDL images ... The term synthesiser is also used to mean frequency synthesiser, an electronic system found in communications. ... In music, timbre, or sometimes timber, (from Fr. ... In telecommunications, frequency modulation (FM) conveys information over a carrier wave by varying its frequency. ...

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., non harmonic), bell-like dissonant and percussive sounds can easily be created. This article is about the components of sound. ...

History

The technique, which was discovered by John Chowning at Stanford University in 1967-68, was patented in 1975 and later licensed to Yamaha. John M. Chowning (1934 - Present) Contribution Born in Salem New Jersey, John M. Chowning is most famously known for having discovered the frequency modulation (FM) algorithm, in which both the carrier frequency and the modulating frequency are within the audio band. ... Stanford redirects here. ... Year 1975 (MCMLXXV) was a common year starting on Wednesday (link will display full calendar) of the Gregorian calendar. ... The headquarters of Yamaha Corporation Yamaha redirects here. ...

It should be noted that the implementation commercialized by Yamaha (US Patent 4018121 Apr 1977) is actually based on phase modulation.

FM synthesis is very good at creating both harmonic and inharmonic ('clang', 'twang' or 'bong' noises) sounds. Complex (and proper) FM synthesis using analog oscillators is not generally feasible due to their inherent pitch instability, but FM synthesis (using the frequency stable phase modulation variant) is easy to implement digitally. As a result, FM synthesis was the basis of some of the early generations of digital synthesizers from Yamaha, with Yamaha's flagship DX7 synthesizer being ubiquitous throughout the 1980s. Yamaha had patented its hardware implementation of FM, allowing it to nearly monopolize the market for that technology. Casio developed a related form of synthesis called phase distortion synthesis, used in its CZ series of synthesizers. It had a similar (but slightly differently derived) sound quality as the DX series. Oscillation is the periodic variation, typically in time, of some measure as seen, for example, in a swinging pendulum. ... A digital synthesizer is a synthesizer that uses digital signal processing (DSP) techniques to make musical sounds. ... The Yamaha DX7 was a synthesizer manufactured by the Yamaha Corporation from 1983 to 1986, based on FM synthesis developed by John Chowning. ... The 1980s was the decade spanning from 1980 to 1989, also called The Eighties. The decade saw social, economic and general upheaval as wealth, production and western culture migrated to new industrializing economies. ... Casio Computer Co. ... Figure A depicting the saw wave phase distortion transform Phase distortion synthesis is a synthesis method introduced 1984 by Casio in its CZ range of synths, and similar to Frequency modulation synthesis in the sense that they are both build on phase modulation. ...

With the expiration of the Stanford University FM patent in 1995, FM synthesis is now part of the synthesis repertoire of most modern synthesizers, usually in conjunction with additive, subtractive and sometimes sampling techniques. Year 1995 (MCMXCV) was a common year starting on Sunday. ... Additive synthesis is a technique of audio synthesis which creates musical timbre. ... Subtractive synthesis is a method of subtracting harmonic content from a sound via sound synthesis, characterised by the application of an audio filter to an audio signal. ... An AKAI MPC2000 sampler Playing a Yamaha SU10 Sampler A sampler is an electronic music instrument closely related to a synthesizer. ...

Functioning

The harmonic distribution of a simple sine wave signal modulated by another sine wave signal can be represented with Bessel functions - this provides a basis for a simple mathematical understanding of FM synthesis. In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y(x) of Bessels differential equation: x2 for an arbitrary real or complex number α. The most common and important special case is where α is an integer n, then α is referred...

FM synthesis is a form of "distortion synthesis" or "nonlinear synthesis". It begins with an oscillator generating an audio-frequency "carrier" waveform with a frequency of F_c . An audio-frequency modulating waveform, with a frequency F_m, is then applied to change or "modulate" the frequency of the carrier oscillator.

If the amplitude of the modulator is 0, the output frequency of the carrier oscillator is simply F_c . Otherwise, the amplitude of the modulating signal causes the frequency of the carrier oscillator to swing above and below F_c . This frequency swing is known as "deviation".

In simple terms, the "louder" the modulating signal is, the more the carrier frequency changes. For illustration, suppose F_c is 1000 Hz. Modulation amplitude might be applied that causes the carrier to swing between 900 Hz and 1100 Hz, that is, 100 Hz in either direction. This is termed a "deviation" of 100 Hz.

At the same time, the frequency of the modulating signal causes what are termed "sideband" frequencies to appear on either "side" of the carrier frequency. Therefore for each frequency component in the modulating signal, an "upper" sideband appears above F_c, and a "lower" sideband appears below F_c. Clearly a modulating waveform containing many frequencies (e.g. "partials") will create many FM sidebands.

Deviation (d) is partly responsible for the power of each component of the output audio signal. When d=0, all the power is heard at the carrier frequency. The larger the deviation, the more power is shifted to the sidebands.

The ratio of deviation to modulation frequency is called the "index of modulation". ( I = d / F_m ) This ratio controls the spectral richness of the sound. By varying deviation through modulation amplitude, and varying the spectrum of the modulating waveform, the resulting audio can be evolved without further instrument complexity. This is the power of FM synthesis.

References

• J. Chowning (1973). "The Synthesis of Complex Audio Spectra by Means of Frequency Modulation". Journal of the Audio Engineering Society 21 (7). 

• Chowning, John; Bristow, David (1986). FM Theory & Applications - By Musicians For Musicians. Tokyo: Yamaha. ISBN 4-636-17482-8. 

• Dodge, Charles; Jerse, Thomas A. (1997). Computer Music: Synthesis, Composition and Performance. New York: Schirmer Books. ISBN 0-02-864682-7. 

External links

• An Introduction To FM, by Bill Schottstaedt
• FM tutorial
• SOUNDSHOCK, an English language discussion forum dedicated exclusively to FM Synthesis
• Article: FM Synthesis
• Paul Wiffens Synth School: Part 3
• F.M. Synthesis including complex operator analysis