I'm requesting resourses to dive deep and get a good grip on complex signals, Fourier analysis and connections to information theory and information encoded by complex signals.

My background: 3rd year physics undergraduate, in the process of learning quantum mechanics, have some intuitive understanding of Fourier transforms.

My motivation: I am trying to understand and reason about information encoded by wave functions. Specifically, I am trying to draw connections to Nyquist-Shannon sampling theorem.

Here's some problems I encountered:

• a lot of resources related to signal processing spend a lot of time talking about real-valued functions and I need a more general understanding of how things work for complex-valued functions without putting a lot of emphasis on the special case of real functions;
• a lot of resources related to signal processing quickly go from idealized signals to those constrained by the limitations of the real world(noise and stuff) and I need a better understanding of these idealized signals without delving deeper into things a real engineer would need;

Additionally, I'd also love to see some quantum information resources that go into information encoded in continuous systems. A lot of what I've seen is centered on discrete cases like spin because that's what is actually feasible to use in quantum computing.

I'm trying to get the knowledge I need piece by piece, but I thought it doesn't hurt to try and you people about some recommendations :)