sines + noise + transients

SNT

DCT

Discrete Cosine Transform

Transformations

Transformations

Synthesis

Synthesis

signals can are composed of slowly-varying sinusoids and quasi-stationary broad-

band noises. This view is quite schematic, as it neglects the most interesting part

of sound events: transients. Sound modifications would be much more easily

achieved if transients could be taken apart and treated separately. For instance,

in most musical instruments extending the duration of a note does not have any

effect on the quality of the attack, which should be maintained unaltered in a

time-stretching task.

tion comes from the observation that, as sinusoidal signals in the time domain

are mapped to well-localized spikes in the frequency domain, by duality short

pulses in the time domain would correspond to sine-like curves in the frequency

domain. Therefore, the sinusoidal model can be applied in the frequency domain

to represent these sinusoidal components. The scheme of the SNT decomposition

is represented in figure 4.

Modelling

Modelling

cluster of impulses becomes a superposition of cosines. Therefore, in the trans-

formed domain it makes sense to use the sinusoidal model and to extract a

second residue that is given by transient components.