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Transient Models

Another improvement to sines+noise modeling in the late 1990s was explicit transient modeling [6,149,147,144,148,290,282]. These methods address the principal remaining deficiency in sines+noise modeling, preserving crisp ``attacks'', ``clicks'', and the like, without having to use hundreds or thousands of sinusoids to accurately resynthesize the transient.G.13

The transient segment is generally ``spliced'' to the steady-state sinusoidal (or sines+noise) segment by using phase-matched sinusoids at the transition point. This is usually the only time phase is needed for the sinusoidal components.

To summarize sines+noise+transient modeling of sound, we can recap as follows:

So, although sinusoids are sufficiently general thanks to Fourier's theorem the combination of sines, filtered-noise, and transient segments can provide a much more compact basis for audio signals. Such compact building-blocks for sound are useful for audio coding and manipulation.

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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University