Standard Pipeline for EE w/Focus on Signals Analysis

[hygume]

Summary: Took some introductory courses in my BS, but was not an EE major. What's the standard pipeline for EE with a focus in signals analysis?

Mods, my apologies if this is the wrong board for this post. Please feel free to delete or move if that's the case.

My undergraduate degree was a BS in Cyber Operations, which is basically CS with instructors from the NSA. I had the standard courses in Intro to EE, Signals Analysis, Microsystem Controllers, and math up to Calc 3 (I now regret not pushing for Diff Eq or Linear Algebra). My research pulled almost entirely from self study and focused on collecting emanations from PS2 and USB keyboards for translation. I've continued with the theme of self study over the past few years, but have mostly focused on the programming side of the house and now need to get back to the applied sciences theme.

Someone must have a sense of humor, because I've been submitted by the Navy as a candidate for a PhD EE, without a proper background, and I've got roughly a year to get up to speed. What is the standard pipeline that y'all went through when you were working on your BS' and MS'? Do y'all have recommendations on how to proceed? I'm very familiar with the offerings through OCW, EdX, and Coursera and have started some work on Power Electronics, but I'm quickly realizing how behind the ball I am.

I appreciate y'all's help and look forward to annoying y'all with questions in the future.

 

[jasonRF]

I think that the "standard" EE background would be sufficient to be prepared for a PhD program in signal processing. The classes I am thinking of are
1. signals and systems, covering both continuous and discrete time.
2. linear algebra. A good sophomore-level course is sufficient
3. probability theory - preferably taught by the EE department but any solid probability course will do.
4. differential equations

It would also be nice to have taken courses on DSP and control systems, but is not as essential. Ideally you would know the material in those 4 classes (especially the first 3) forwards and backwards prior to a PhD program, but it is common for graduate students with a BS in a different field to take a couple of basic undergrad courses to fill-in the holes in their background. If you know where you will be doing your PhD you may be able to find out how feasible it would be to simply take courses to fill in your gaps.

By the way, I am an EE PhD (grad work was in plasma physics, though) who knew several of the signal processing students during grad school and currently work with many EE PhDs that specialized in signal processing. Most (if not all) of them took upper-level math courses during grad school: real analysis is by far the most common, but some also took courses in abstract algebra and second-courses in linear algebra. Graduate EE signal processing classes can also be highly mathematical, so you really do need a strong background in math.

So what do I think should you do?

1. Reviewing your signals and systems is very important - your grad courses will assume you are fluent in that material. Work problems to help review - if you need problems to do look online or grab a Schaum's outline. Since you have already taken this course you probably will not be able to take it again in grad school so re-learning this subject is probably all on your shoulders.

2. For linear algebra I think it would be best if you could actually take a class at the beginning of your grad program (as opposed to self-study) as it will force you to really learn the material; a lot of signal processing is essentially applied linear algebra and it is hard to overstate how important the subject is. If it is not feasible to take a class, at least work through the OCW class; do all of the readings, all of the assigned homework problems, etc.

3. For probability I think my advice is the same as for linear algebra. I would expect that you would be able to take this at the beginning of grad school.

4. Ordinary differential equations: I think this is "easier" to self-study than linear algebra and probability, simply because most differential equations courses are not deep, and subsequent courses do not seem to build on the theory (although if you end up in control systems my statements here may be wrong). At least having an understanding of linear differential equations and systems of linear, constant-coefficient differential equations would be good.

5. Finally, if your calculus is rusty you may want to brush-up on it some.

Just my 2-cents.

Jason