The Scientist & Engineer's Guide to Digital Signal Processing is a pretty decent book as a crash course. It covers the high level concepts in the first half and the hard core math at the very end.
In the middle there’s a chunk of stuff that’s very practical if you don’t have the time to learn all the math behind it. This is the stuff that I found most useful. It covered the various filters, why you would use one over the other, and basic implementations.
If you really want to learn DSP, a course might be useful but it all depends on what you want from it.
I think this book does a decent job of explaining DSP as a mix of different fields.
That links to an Amazon listing here which says it was published in 1997. Has there really been so little advancement in DSP's over the past nearly 23 years that the information in the book isn't out dated? I understand embedded is a very slow moving field, but oof.
Any engineering job is going to have a significant amount of domain knowledge that is specific to that company's products, services, or research. Getting an engineering degree is just the beginning. Once you get a job at a company, you will need to learn a shit load of new terms, IP, history, and procedures that are specific to that company. It's the next level of your education, and will take years to fully assimilate. School doesn't teach you anywhere near enough to walk into most engineering jobs and be independently productive. You are there to learn as much as do. The senior engineers are your teachers and gaining their knowledge and experience is the key to building a successful career. You need to look at them as a valuable resource that you should be taking every opportunity to learn from. If you don't understand what they are saying, then ask, take notes, and do independent research to fill in your knowledge gaps. Don't just dismiss what they say as techo-babble.
!!!!!! TAKE THIS TO HEART !!!!! - The single biggest challenge you will have in your engineering career is learning how to work well with your peers, seniors, and managers. Interpersonal skills are ABSOLUTELY critical. Engineering is easy: Math, science, physics, chemistry, software, electronics.... all of that is a logical, and learnable, and a piece of cake compared to dealing with the numerous and often quirky personalities of the other engineers and managers. Your success will be determined by your creativity, productivity, initiative, and intelligence. Your failure will be determined by everyone else around you. If they don't like you, no amount of cleverness or effort on your part will get you ahead. Piss off your peers or managers, and you will be stepped on, marginalized, criticized, and sabotaged. It's the hard truth about the work world that they don't teach you in school. You aren't going anywhere without the support of the people around you. You are much more likely to be successful as a moron that everyone loves, than a genius that everyone hates. It sucks, but that's the truth.
You are the new guy, you have lots to learn, and that is normal and expected. It's going to be hard and frustrating for a while, but you will get the hang of it and find your footing. Learn as much as you can, and be appreciative for any help or information that you can get.
As for digitizing a signal, it is correct that you should stick with powers of 2 for a number of technical reasons. At the heart of the FFT algorithm, the signal processing is done in binary. This is part of the "Fast" in Fast Fourier Transforms. By sticking with binary and powers of 2, you can simply shift bits or drop bits to multiply or divide by 2, which is lightning fast for hardware. If you use non powers of 2 integers or fractional sampling rates, then the algorithm would need to do extensive floating point math, which can be much slower for DSPs, embedded CPUs, and FPGAs with fixed-point ALUs. It's about the efficiency of the calculations in a given platform, not what is theoretically possible. Power of 2 sample rates are much more efficient to calculate with integer math for almost all digital signal processing.
I highly recommend reading the book "The Scientist and Engineer's Guide to Digital Signal Processing" by Steven W. Smith. It is by far the best hand-holding, clearly-explained, straight-to-the-point, introductory book for learning the basics of digital signal processing, including the FFT.
You can buy the book from Amazon here. If you can afford it, the physical book is great for flipping though and learning tons about different signal processing techniques.
Or you can download the entire book in PDF form legally for free here. The author is actually giving the book away for free in electronic form ( chapter by chapter ).
I came in here to recommend the JE Gordon books. They are amazing.
FFTs are a math concept so you can hardly not have any math, but this book is heavy on conceptual understanding and I think it doesn't have any calculus.
Edit: PriceZombie reminded me to mention that you can read it online for free.