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D. Rocchesso: Sound Processing
waveshape preservation
broad-band noise
LPC analysis
sines-plus-noise
decomposition
sound modification
Extraction of the residual
The extraction of a broad-spectrum noise residual could be performed either
in the frequency domain or, as proposed in figure 1, directly by subtraction
in the time domain. This is possible because the STFT analysis preserves the
information on phase, thus allowing a waveshape preservation. The stochastic
component can be itself represented on a frame-by-frame basis, but the corre-
sponding frame can be smaller than the analysis frame so that transients are
captured more accurately.
Residual spectral fitting
The stochastic component is modeled as broad-band noise filtered by a lin-
ear coloring block. Such decomposition corresponds to a subtractive synthesis
model [78], whose parameters may be obtained by LPC analysis (see section 4.2).
However, if the purpose of the sines-plus-noise decomposition is that of sound
modification, it is more convenient to model the stochastic part in the frequency
domain. The magnitude spectrum of the residual can be approximated by means
of a piecewise-linear function, that is described by the coordinates of the joints.
The time-domain resynthesis can be operated in the time domain by inverse
FFT, after having imposed the desired magnitude profile and a random phase
profile.
Sound modifications
The sinusoidal model is interesting because it allows to apply musical transfor-
mations to sounds that are taken from actual recordings. The separation of the
stochastic residual from the sinusoidal part allows a separate treatment of the
two components.
Examples of musical transformations are:
Coloring: The spectral profile can be changed at will;
Emphasizing: The stochastic or the sinusoidal components can be exagger-
ated;
Time Stretching: the temporal extension of the sound can be altered without
pitch modifications and with limited artifacts;
Pitch Shifting: The pitch can be transposed without changing the sound
length and with limited artifacts;
Morphing: for instance,
· The spectral envelope of a sound can be imposed to another sound;
· A residual from a different sound can be used for resynthesis.
Figure 3 shows the framework for performing these musical modifications.