Layers from Sinusoidal Modelling
Sometimes it can be helpful to approach a sound as a combination of some obviously tonal parts, plus other things, like transients and more noisy material. To do this, we can try and isolate the tonal parts using a sinusoidal model, which looks at the signal in the frequency domain and tries to estimate which parts behave as if they were the partials of some sound, which could be either harmonic (like a cello) or inharmonic (like a bell). These parts can then be isolated from the original signal, giving us two layers: one composed of sine waves, and one with the remainder.
This approach to decomposing a signal has a long history in audio analysis, both in musical and engineering settings. One of its attractions is that it feels quite intuitive to think of sounds terms of being made up of sine waves and other kinds of archetypes, like transients and noises. Furthermore, it also produces a representation that we can make sense of in the familiar terms of oscillators with frequencies and amplitudes.
When this model is working well for our material, the sinusoidal layer can be very 'clean' indeed, and therefore amenable to further sound design or analysis. For example, applying wave-shaping or reverb to a well-estimated sinusoidal layer can produce quite different results in comparison to processing the whole sound, which gives us extra possibilities for controlling the density and / or clutter of our designs.
In practice, it can be challenging to make such a decomposition work well on complex sounds. Whilst the intuitive model can work well on dry, isolated sounds with a very clear tonal structure, once a sound becomes more complex (e.g denser or polyphonic), then the modelling assumptions start to struggle, and we can end up with lots of artefacts. However, these can often be tamed somewhat with some tuning, especially of the parameters that control how quickly the algorithm makes up its mind about what counts as a sinusoid or not. For some sounds, it may help to do another type of decomposition first, in order to make the job of the sinusoidal modelling easier. For instance, we could extract transients, or estimate a 'harmonic layer'.