[ska]

> All of the math behind information theory and sampling signals assumes waves are sinusoids

This isn't really true. The point about the sinusiods is mostly that the form a very convenient complete basis of a useful space of functions, hence the fourier expansion. This doesn't amount to an assumption about how the signals are generated, rather how they are represented. You could pick a different basis and you'd get a different representation, but as functions they are identical. By definition this applies equally to any signal in the class, however you generate it.

Where the shape of the underlying basis vectors does show up is in errors and estimation, e.g. the similar estimation error in fourier vs. Haar will show up as sinusoids or steps.