Digital waveguide synthesis is the synthesis of audio using a digital waveguide. Digital waveguides are efficient computational models for physical media through which acoustic waves propagate. For this reason, digital waveguides constitute a major part of most modern physical modelling synthesizers. The term synthesizer is also used to mean frequency synthesizer, an electronic system found in communications, or video synthesizer. ... Audio can mean: Sound that can be heard. ... A waveguide used for propagating RF or electromagnetic waves. ... Physical modelling synthesis is the synthesis of sound by using a set of equations and algorithms to simulate a physical source of sound. ...

A basic one-dimensional digital waveguide (likely of a string) with a rigid termination on one end (left) and a frequency-dependent attenuating filter at the other (right).

A lossless digital waveguide realizes the discrete form of d'Alembert's solution of the one dimensional wave equation as the superposition of a right-going wave and a left-going wave, Image File history File links DigitalWaveguide. ... Jean le Rond dAlembert, pastel by Maurice Quentin de la Tour Jean Le Rond dAlembert (November 16, 1717 – October 29, 1783) was a French mathematician, mechanician, physicist and philosopher. ... The wave equation is an important partial differential equation which generally describes all kinds of waves, such as sound waves, light waves and water waves. ...

y(m,n) = y ⁺ (m − n) + y ⁻ (m + n)

where y ⁺ is the right-going wave and y ⁻ is the left-going wave. It can be seen from this representation that sampling the function y at a given point m and time n merely involves summing two delayed copies of its travelling waves.

Digital waveguide models are therefore comprised of delay lines to represent the geometry of the waveguide, digital filters to represent the frequency-dependent losses and dispersion in the medium, and often include non-linear elements. Losses incurred throughout the medium are generally consolidated so that they can be calculated once at the termination of a delay line, rather than many times throughout. The term delay line has multiple meanings: In electronics and derivative fields such as telecommunications, a delay line is rigorously defined as a single-input-channel device, in which the output channel state at a given instant, t, is the same as the input channel state at the instant t... An FIR filter In electronics, a digital filter is any electronic filter that works by performing digital math operations on an intermediate form of a signal. ... To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ...

Although waveguides such as a acoustic tubes may be thought of as three-dimensional, because their lengths are often much greater than their cross-sectional area, it is reasonable and computationally efficient to model them as one dimensional waveguides. Membranes, as used in drums, may be modelled using two-dimensional waveguide meshes, and reverberation in three dimensional spaces may be modelled using three-dimensional meshes. For other kinds of drums, see drum (disambiguation). ...

Digital waveguide synthesis was developed by Julius O. Smith III and represents an extension of the Karplus-Strong algorithm. Stanford University owns the patent for digital waveguide synthesis and signed an agreement in 1989 to develop the technology with Yamaha. Karplus-Strong string synthesis is a method of physical modelling synthesis that loops a short waveform through a filtered delay line to simulate the sound of a hammered or plucked string or some types of percussion. ... For other meanings of Stanford, see Stanford (disambiguation). ... 1989 (MCMLXXXIX) is a common year starting on Sunday of the Gregorian calendar. ... The Yamaha Corporation (ヤマハ株式会社) TYO: 7951 is a Japanese company with a large number of product areas. ...

An extension to DWG synthesis of strings made by Smith is commuted synthesis, wherein the excitation to the digital waveguide contains both string excitation and the body response of the instrument. This is possible because the digital waveguide is linear and makes it unnecessary to model the instrument body's resonances after synthesizing the string output, greatly reducing the number of computations required for a convincing resynthesis. The word linear comes from the Latin word linearis, which means created by lines. ...

See also

• Frequency modulation synthesis
• Subtractive synthesis
• Additive synthesis
• Wavetable synthesis
• Physical modelling synthesis
• Granular synthesis
• Dynamic stochastic synthesis

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. ... Subtractive synthesis is a method of sound synthesis characterised by the application of an audio filter to a source signal. ... Additive synthesis is a technique of audio synthesis which creates musical timbre. ... Wavetable synthesis is used in digital musical instruments (synthesizers) to produce natural tone-like sounds. ... Physical modelling synthesis is the synthesis of sound by using a set of equations and algorithms to simulate a physical source of sound. ... Granular synthesis (aka Brassage) is a sound synthesis method for digital musical instruments (synthesizers) that operates on the microsound time scale. ...

External links

• Julius O. Smith III's ``A Basic Introduction to Digital Waveguide Synthesis"
• Waveguide Synthesis home page