A 220 Hz carrier tone modulated by a 440 Hz modulating tone with various choices of modulation index, β. The time domain signals are illustrated above, and the corresponding spectra are shown below (spectrum amplitudes in dB). An audio demonstration of the four synthesized tone timbres is available here.

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.

For synthesizing harmonic sounds, the modulating signal must have a harmonic relationship to the original carrier signal. As the amount of FM modulation increases, the sound grows progressively more complex. 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.

The technique was invented by John Chowning at Stanford University in the early 1970s, was patented in 1975 and was later licensed to Yamaha.

FM synthesis is very good at creating 'clang', 'twang' or 'bong' noises. Complex FM synthesis using analog oscillators is not generally feasible due to their inherent pitch instability, but FM synthesis 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. Casio, in order to avoid the FM patent, developed a related form of synthesis called phase distortion synthesis, used in its CZ series of synthesizers.

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.

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.

Reference

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

See also:

• Harmonic series
• Subtractive synthesis
• Additive synthesis
• Wavetable synthesis
• Digital waveguide synthesis
• Physical modelling synthesis
• Phase distortion synthesis

External links

• An Introduction To FM (http://ccrma.stanford.edu/software/snd/snd/fm.html), by Bill Schottstaedt
• FM tutorial (http://www.sfu.ca/~truax/fmtut.html)
• Article: FM Synthesis (http://www.sospubs.co.uk/sos/apr00/articles/synthsecrets.htm)
• some Chowning paper citations (http://citeseer.nj.nec.com/context/105473/0)