Hi Jason, thanks for the reply
I was considering the same problem when posting, seeing a whole pile of subfields of signal processing. I think for self study I would probably just focus on the mathematical side of things.
I am currently studying a degree involving laser physics and electrical engineering, which will eventually lead to optical fibre communications. The courses I've taken have cover some basic ( < 3 orders) filters and things like convolution, FFT, Z transform, Laplace transform.
The analogue signal processing I was thinking is mainly about the theoretical aspects and mathematical models of circuit components for continuous signals.
If I have to pick a few subfields to study on, filtering and modulation are what I am already familiar with and probably something I would use the most.