Frequency modulation synthesis - AbsoluteAstronomy.com

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

Decibel

The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...

In audio

Sound recording and reproduction

Sound recording and reproduction is an electrical or mechanical inscription and re-creation of sound waves, such as spoken voice, singing, instrumental music, or sound effects. The two main classes of sound recording technology are analog recording and digital recording...

and music

Music

Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...

frequency modulation synthesis (or FM synthesis) is a form of audio synthesis where the timbre

Timbre

In music, timbre is the quality of a musical note or sound or tone that distinguishes different types of sound production, such as voices and musical instruments, such as string instruments, wind instruments, and percussion instruments. The physical characteristics of sound that determine the...

of a simple waveform is changed by frequency modulating

Frequency modulation

In telecommunications and signal processing, frequency modulation conveys information over a carrier wave by varying its instantaneous frequency. This contrasts with amplitude modulation, in which the amplitude of the carrier is varied while its frequency remains constant...

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

Distortion synthesis

Distortion synthesis is a group of sound synthesis techniques which modify existing sounds to produce more complex sounds , usually by using non-linear circuits or mathematics....

, "in accordance with the amplitude

Amplitude

Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...

of a modulating signal." (Dodge and Jerse 1997, p.115)

For synthesizing harmonic sounds, the modulating signal must have a harmonic

Harmonic

A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental...

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.

History

The technique, which was discovered by John Chowning

John Chowning

John M. Chowning is an American composer, musician, inventor, and professor best known for his work at Stanford University and his invention of FM synthesis while there.-Contribution:...

(Chowning 1973, cited in Dodge and Jerse, p.115) at Stanford University

Stanford University

The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...

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

Phase modulation

Phase modulation is a form of modulation that represents information as variations in the instantaneous phase of a carrier wave.Unlike its more popular counterpart, frequency modulation , PM is not very widely used for radio transmissions...

.

FM synthesis is very good at creating both harmonic and inharmonic

Inharmonicity

In music, inharmonicity is the degree to which the frequencies of overtones depart from whole multiples of the fundamental frequency....

("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 synthesizer

Digital synthesizer

A digital synthesizer is a synthesizer that uses digital signal processing techniques to make musical sounds.Electronic keyboards make music through sound waves.-History:...

s from Yamaha, with Yamaha's flagship DX7

Yamaha DX7

The Yamaha DX7 is an FM Digital Synthesizer manufactured by the Yamaha Corporation from 1983 to 1986. It was the first commercially successful digital synthesizer. Its distinctive sound can be heard on many recordings, especially Pop music from the 1980s...

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

Casio

is a multinational electronic devices manufacturing company founded in 1946, with its headquarters in Shibuya, Tokyo, Japan. Casio is best known for its electronic products, such as calculators, audio equipment, PDAs, cameras, musical instruments, and watches...

developed a related form of synthesis called phase distortion synthesis

Phase distortion synthesis

NOTE: any readers who are struggling to understand this text, here are links to the missing Figures A and B:NOTE: any readers who are struggling to understand this text, here are links to the missing Figures A and B:...

, used in its CZ series of synthesizers. It had a similar (but slightly differently derived) sound quality as the DX series.

Don Buchla

Don Buchla

Don Buchla is a pioneer in the field of sound synthesizers, releasing his first units months after Robert Moog's first synthesizers...

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, FM synthesis is now part of the synthesis repertoire of most modern synthesizers, usually in conjunction with additive

Additive synthesis

Additive synthesis is a technique of sound synthesis that creates musical timbre by explicitly adding sinusoidal overtones together.The timbre of an instrument is composed of multiple harmonic or inharmonic partials , of different frequencies and amplitudes, that change over time...

, subtractive

Subtractive synthesis

Subtractive synthesis is a method of sound synthesis in which partials of an audio signal are attenuated by a filter to alter the timbre of the sound...

and sometimes sampling

Sampler (musical instrument)

A sampler is an electronic musical instrument similar in some respects to a synthesizer but, instead of generating sounds, it uses recordings of sounds that are loaded or recorded into it by the user and then played back by means of a keyboard, sequencer or other triggering device to perform or...

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".

Stanford University

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.

Functioning

The harmonic distribution of a simple sine wave signal modulated by another sine wave signal can be represented with Bessel function

Bessel function

In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y of Bessel's differential equation:...

s – 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 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 stronger (higher in amplitude) 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 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 F_c, and a lower sideband appears below F_c. 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 / 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.

External links

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History

Functioning

See also

External links