The method known as phase distortion synthesis is similar to FM.
Waveshaping synthesis changes an original waveform by responding to its amplitude in a non-linear fashion. It can generate a bandwidth-limited spectrum, and can be continuously controlled with an index.
The clipping caused by overdriving an audio amplifier is a simple example of this method, changing a sine wave into a square-like wave. (Note that direct digital implementations suffer from aliasing of the clipped signal's infinite number of harmonics, however.)
Discrete summation formulas
DSF synthesis refers to algorithmic synthesis methods which use mathematical formulas to sum, or add together, many numbers to achieve a desired wave shape. This powerful method allows, for example, synthesizing a 3-formant voice in a manner similar to FM voice synthesis. DSF allows the synthesis of harmonic and inharmonic, band-limited or unlimited spectra, and can be controlled by an index. As Roads points out, by reducing digital synthesis of complex spectra to a few parameters, DSF can be much more economical.
Jean-Claude Risset was one notable pioneer in the adoption of distortion methods.
- Nb. Some authors refer to these techniques as 'modulation synthesis'; e.g. Chapter 6 of Roads, Curtis (1996). The computer music tutorial. MIT Press.
- Dodge 1997, pp.115-138
- Roads, Curtis (June 1979). "A Tutorial on Non-Linear Distortion or Waveshaping Synthesis". Computer Music Journal. MIT Press. 3 (2): 29–34. doi:10.2307/3680281. JSTOR 3680281.
- Dodge 1997, pp.139-157
- Dodge 1997, pp.158-168
- J. Chowning (1973). "The Synthesis of Complex Audio Spectra by Means of Frequency Modulation". Journal of the Audio Engineering Society. 21 (7).
- Arfib, D. 1979. "Digital synthesis of complex spectra by means of multiplication of non-linear distorted sine waves." Journal of the Audio Engineering Society 27: 10.
- Marc Le Brun. "Digital Waveshaping Synthesis" in Journal of the Audio Engineering Society, 27(4), 1979, p250-266.
- Moorer, J. A. (November 1976). "The Synthesis of Complex Audio Spectra by Means of Discrete Summation Formulae". Journal of the Audio Engineering Society, 27(4), pp.717-727.
- T Stilson; J Smith (1996). "Alias-free digital synthesis of classic analog waveforms". Proc. Int. Comp. Music Conf. (ICMC'96 Hong Kong): 332–335. CiteSeerX 10.1.1.60.4437.
- C. Roads 1996, p.260-61.
- Dodge, Charles; Thomas A. Jerse (1997). "5. Synthesis Using Distortion Techniques". Computer Music. New York: Schirmer Books. pp. 115–168. ISBN 0-02-864682-7.
- Chowning, John; Bristow, David (1986). FM Theory & Applications - By Musicians For Musicians. Tokyo: Yamaha. ISBN 4-636-17482-8.