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.

When I think of Laplace Transforms I always think of control theory - poles, zeros etc.

My control theory professor (who was also my physics advisor -- it was a small college) explained it like this: Physicists like Fourier transforms because they go from minus to plus infinity, like the universe. Control engineers like Laplace transforms because they start at zero, and a control system also has a starting point.