No, real wave maths is continuous wavelets and those are not as useful in processing. (DFT is a kind of wavelet transform, just limited.)
And then you have the advanced tensor wave math which is used in physics but rarely in sound processing. I bet you didn't have evaluating Schrodinger's and symmetric solutions was what you had in mind.
You'll get much more mileage out of statistics and discrete mathematics, plus control theory and optimization theory.
There are many different types of Fourier transforms (i.e. generalisations and specifications(?)) useful for signal analysis, not just the (classical full spectrum) FT. E.g. the fractional FT (useful for signal separation), laplace transform (used all over the place in control for linear(ised) systems and analysis).
> Schrödinger
Well momentum is the FT of position so...
Also note the OP's question is "Whats wave math?" not "why don't use the (D|F)FT?" which I'm still surprised was suggested: Its a tool, use it when appropriate, use something else when its not.
Well I did most of my signals analysis with an oscilloscope circuitry and a function (read: waveform) generator. You could very easily get computer versions of those and substitute the function generator for some music. But I'd consult the elders of the internet for better ideas.
