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 modeling synthesizers.
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,
y(m,n)=y+(m-n)+y-(m+n)
where
y+
y-
y
m
n
Digital waveguide models therefore comprise digital delay lines to represent the geometry of the waveguide which are closed by recursion, digital filters to represent the frequency-dependent losses and mild dispersion in the medium, and often 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.
Waveguides such as acoustic tubes are three-dimensional, but 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 modeled using two-dimensional waveguide meshes, and reverberation in three-dimensional spaces may be modeled using three-dimensional meshes. Vibraphone bars, bells, singing bowls and other sounding solids (also called idiophones) can be modeled by a related method called banded waveguides where multiple band-limited digital waveguide elements are used to model the strongly dispersive behavior of waves in solids.
The term "digital waveguide synthesis" was coined by Julius O. Smith III who helped develop it and eventually filed the patent. It represents an extension of the Karplus–Strong algorithm. Stanford University owned the patent rights for digital waveguide synthesis and signed an agreement in 1989 to develop the technology with Yamaha, however, many of the early patents have now expired.
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.
Prototype waveguide software implementations were done by students of Smith in the Synthesis Toolkit (STK).[1] [2]
The first musical use of digital waveguide synthesis was in the composition May All Your Children Be Acrobats (1981) by David A. Jaffe, followed by his Silicon Valley Breakdown (1982).
.[[VxD]] drivers, not .WDM). No longer made, presumably due to conflict with AC-97 and AC-99 sound card standards (which specify 'wavetables' (sample tables) based on Roland’s XG-competing GS sound system, which Sondius-XG [the means of integrating VL instruments and commands into an XG-compliant MIDI stream along with wavetable XG instruments and commands] cannot integrate with). The MIDI portion of such sound chips, when the VL was enabled, was functionally equivalent to an MU50 Level 1 XG tone module (minus certain digital effects) with greater polyphony (up to 64 simultaneous notes, compared to 32 for Level 1 XG) plus a VL70m (the VL adds an additional note of polyphony, or, rather, a VL solo note backed up by the up-to-64 notes of polyphony of the XG wavetable portion). The 724 only supported stereo out, while the others supported various four and more speaker setups. Yamaha’s own card using these was the WaveForce-128, but a number of licensees made very inexpensive YMF-724 sound cards that retailed for as low as $12 at the peak of the technology’s popularity. The MIDI synth portion (both XG and VL) of the YMF chips was actually just hardware assist to a mostly software synth that resided in the device driver (the XG wavetable samples, for instance, were in system RAM with the driver [and could be replaced or added to easily], not in ROM on the sound card). As such, the MIDI synth, especially with VL in active use, took considerably more CPU power than a truly hardware synth would use, but not as much as a pure software synth. Towards the end of their market period, YMF-724 cards could be had for as little as $12 USD brand new, making them by far the least expensive means of obtaining Sondius-XG CL digital waveguide technology. The DS-XG series also included the YMF-740, but it lacked the Sondius-XG VL waveguide synthesis module, yet was otherwise identical to the YMF-744.