Signal processing is a pretty huge branch of what I would (maybe wrongly) call electrical engineering. I have heard here and there whispers of interesting connections between signal processing - in particular sampling theory - and algebraic geometry.
I am not interested in "local" applications to solve specific problems. Instead, I'm looking for something like a general approach to signal processing and sampling theory which intrinsically uses notions of algebraic geometry. Kind of like the approach to number theory via algebraic geometry.
I am very interested to read how these two fields relate to each other and would be grateful for references.