To summarize, sines+noise modeling is carried out by a procedure such as the following:

- Compute a
*sinusoidal model*by tracking peaks across STFT frames, producing a set of amplitude envelopes and frequency envelopes , where is the frame number and is the spectral-peak number. - Also record
*phase*for frames containing a transient. - Subtract modeled peaks from each STFT spectrum to form a
*residual spectrum*. - Fit a smooth
*spectral envelope*to each residual spectrum. - Convert envelopes to reduced form,
*e.g.*, piecewise linear segments with nonuniformly distributed breakpoints (optimized to be maximally sparse without introducing audible distortion). - Resynthesize audio (along with any desired transformations) from
the amplitude, frequency, and noise-floor-filter envelopes.
- Alter frequency trajectories slightly to hit the desired phase
for transient frames (as described below equation
Eq.
(10.19)).

Because the signal model consists entirely of *envelopes*
(neglecting the phase data for transient frames), the signal model is
easily *time scaled*, as discussed further in §10.5 below.

For more information on sines+noise signal modeling, see, *e.g.*,
[146,10,223,248,246,149,271,248,271]. A discussion from an historical
perspective appears in §G.11.4.

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