| A 220 Hz carrier tone fm modulated by a 440 Hz modulating tone fc, 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). |
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In audio and music 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. The frequency of an oscillator is altered or distorted, "in accordance with the amplitude of a modulating signal." (Dodge and Jerse 1997, p.115)
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.
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The technique of the digital implementation of frequency modulation, which was developed by John Chowning (Chowning 1973, cited in Dodge and Jerse, p.115) at Stanford University in 1967-68, was patented in 1975 and later licensed to Yamaha.
The implementation commercialized by Yamaha (US Patent 4018121 Apr 1977 or U.S. Patent 4,018,121) 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.
Don Buchla implemented FM on his instruments in the mid-1960s, prior to Yamaha's patent. His 158, 258 and 259 dual oscillator modules had a specific FM control voltage input, and the model 208 (Music Easel) had a modulation oscillator hard-wired to allow FM as well as AM of the primary oscillator. These early applications used analog oscillators.
With the expiration of the Stanford University FM patent in 1995, digital FM synthesis is now part of the synthesis repertoire of most modern digital synthesizers, usually in conjunction with additive, subtractive and sometimes sampling techniques. The FM synthesis patent brought Stanford $20 million dollars before it expired, making it (in 1994) "the second most lucrative licensing agreement in Stanford's history".[1]
Stanford University are currently working on a new FMHD synthesis protocol with improved sound generation properties, and a real-time property modelling editor, that allows the user to encapsulate Karplus-Strong and other physical modelling aspects with relative ease.
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.
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 Fc. An audio-frequency modulating waveform, with a frequency Fm, 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 Fc . Otherwise, the amplitude of the modulating signal causes the frequency of the carrier oscillator to swing above and below Fc . This frequency swing is known as "deviation".
In simple terms, the stronger (higher in amplitude) the modulating signal is, the more the carrier frequency changes. For illustration, suppose Fc 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 sideband signals to appear at frequencies above and below the carrier frequency. Therefore for each frequency component in the modulating signal, an upper sideband appears above Fc, and a lower sideband appears below Fc. A complex modulating waveform (containing more partials than a simple sinewave) will create sidebands corresponding to each of its sinewave components.
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 / Fm ) 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.
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