I have no knowledge/experience with signal processing. At my job we have a signal processing algorithm that... processes a signal. Its very important to us, but nobody knows how it works. We hired someone a long time ago to design it for us. It was designed, and now the person no longer works here. The algorithm is very slow and I've been asked if I can optimize it. I'm afraid to touch it without totally understanding what it's doing. It's generally accepted here that nobody can really hope to understand the algorithm and trying to tweak it is a fool's errand. The sad part is that it doesn't even work that well! But it's the best we've got...

Anyways, I want to understand it. I see lots of mysterious terms like "filters", "serial correlation", "convolution", "discrete fourier transform", "FIR filters", "kernels", "blackman windows", and many more. I have no clue what any of these things are.

What kind of mathematical background do I need? I have a degree in computer science, so I took Calc I, II and Linear Algebra. What books should I start reading? Am I even at a good starting point to start learning this stuff or do I have the completely wrong degree? Some google searching implied this is mostly stuff electrical engineers do, and I am definitely not an electrical engineer.

Thanks for any advice!