Math blog Math ∩ Programming veers into the world of audio processing with an intro to FFT and some Python code. Most of us will probably skip past the heavy math part to get to the application part!

Probably not many of us want to make DIY audio code … but, lots of hardware, software (DAW plugs and software like CSound and Supercollider) use FFT, so it’s good to know what it’s good for. PLUS the author promises more: “Next up in this series we’ll investigate more techniques on sound processing and other one-dimensional signals.”

Bonus link (another cool application of heavy math): SOS article on convolution. Convolution (among other DSP tricks) lets you map the recorded reverb of any space onto your sounds!  The really cool part is that you can borrow that reverb from an existing recording! There are (or at least, used to be) stand-alone apps to let you do that … or you may find a plug.
(See also followup SOS article on generating reverb spaces from scratch.)