I have been told by a professor that natural processes are a superposition of harmonics (e.g. piano). I am wondering if this is an overgeneralization - I have been searching around and am unable to find such a claim being written about. I am aware that some natural processes can be written as such, but I am wondering about the more general statement regarding all (or most) natural processes.
I am looking for some sources that talk about the intuition behind processes being the sum of sinusoids to write about as the introduction to a paper I am writing on spectral analysis. Any help to point me in the right direction would be helpful, thank you!
As I'm sure you know, Fourier proved that any function can be represented as the sum of a possibly infinite number of basis functions, so long as the basis set had certain properties (as, for instance, sines and cosines do). Many harmonic processes such as a piano are naturally represented this way because harmonic functions are eigenfunctions of the Hamiltonian (or energy function for the system) and it makes sense to say that a complex tone is such a superposition. But many random processes, like the diffusion of a particle, Brownian motion, etc., are not naturally represented this way.
Further detail: Any continuous function can be represented by a possibly infinite number of basis functions, but that does not mean that it is a natural or appropriate representation. The Fourier description of the exact three-dimensional position of a molecule diffusing through a gas would not provide insight and it would be a stretch to in any way imply that the particle's motion was due to an infinite sum of other "basis" motions. The question poser is seeking "intuition" about the use of bases such as sines and cosines for physical processes. For a piano string, the link is natural and extremely helpful. For particle diffusion (and many other related processes) it is unnatural and unhelpful.