What Is the Fourier Transform?

If you like Fourier, you're going to love Laplace (or its discrete counterpart, the z transform).

This took me down a very fascinating and intricate rabbit hole years ago, and is still one of my favorite hobbies. Application of Fourier, Laplace, and z transforms is (famously) useful in an incredibly wide variety of fields. I mostly use it for signal processing and analog electronics.

The so-called "Z transform" for discrete sequences is really just a misnomer for the actual method of generating functions (and formal power-series/Laurent-series). You just write a discrete sequence as a power series in z^(-1).