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TSM and S+N+T

Time Scale Modification (TSM), and/or frequency scaling, are relatively easy to implement in a sines+noise+transient (S+N+T) model (§10.4.4). Figure 10.17 illustrates schematically how it works. For TSM, the envelopes of the sinusoidal and noise models are simply stretched or squeezed versus time as desired, while the time-intervals containing transients are only translated forward or backward in time--not time-scaled. As a result, transients are not ``smeared out'' when time-expanding, or otherwise distorted by TSM. If a ``transientness'' measure $ {\cal T}$ is defined, it can be used to control how ``rubbery'' a given time-segment is; that is, for $ {\cal T}=1$ , the interval is rigid and can only translate in time, while for $ {\cal T}=0$ it is allowed stretch and squeeze along with the adjacent S+N model. In between 0 and 1, the time-interval scales less than the S+N model. See [149] for more details regarding TSM in an S+N+T framework.

Figure 10.17: Time Scaling for S+N+T Models (from [149]).

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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