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Sines + Noise + Transients Models

As we have seen, sinusoids efficiently model spectral peaks over time, and filtered noise efficiently models the spectral residual left over after pulling out everything we want to call a ``tonal component'' characterized by a spectral peak the evolves over time. However, neither is good for abrupt transients in a waveform. At transients, one may retain the original waveform or some compressed version of it (e.g., MPEG-2 AAC with short window [149]). Alternatively, one may switch to a transient model during transients. Transient models have included wavelet expansion [6] and frequency-domain LPC (time-domain amplitude envelope) [290].

In either case, a reliable transient detector is needed. This can raise deep questions regarding what a transient really is; for example, not everyone will notice every transient as a transient, and so perceptual modeling gets involved. Missing a transient, e.g., in a ride-cymbal analysis, can create highly audible artifacts when processing heavily based on transient decisions. For greater robustness, hybrid schemes can be devised in which a continuous measure of ``transientness'' $ {\cal T}$ can be defined between 0 and 1, say.

Also in either case, the sinusoidal model needs phase matching when switching to or from a transient frame over time (or cross-fading can be used, or both). Given sufficiently many sinusoids, phase-matching at the switching time should be sufficient without cross-fading.

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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