How much calculus would it require in order to get a decent grasp on signal processing? Not to work in the field or become an expert, but to gain an at least somewhat intelligent outsider’s understanding of it?
Learn what's the deal with the Fourier Transform and the Z transform. Then learn how to design some digital FIR filters. Oh and do learn about the Nyquist-Shannon sampling theorem, it's very important. And that's about it...just joking, there's tons more. But that would be a good start.
Don’t work in the field but I believe fast fourier transforms are commonplace so at least enough to have a solid grasp of that?