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I hold a master's degree in mechanical engineering. However at my job I am more and more diving into topics of signal processing and data science. I find it great to discover about new topics and to learn on the go as I work on projects. During my study I had some basic courses on which I can build on. But sometimes I wonder if it wouldn't be easier and also more fun to for instance do a 2nd master or something similar on the topics I am trying to learn. I think my employer would support me if I want to and as I liked studying in the past I think that could be a great experience.

So with that the question arises what type of course/study would be a good fit? Ideally it would cover relevant topics* for my work/interest, be able to partake in part-time, be online (or taught block-wise in central europe) and include collaborative elements (I don't want to just learn and work by myself without interactions).

*some topics I recently dealt with that I would like to know more about:

  • Singular Value Decomposition
  • Kalman Filters (especially in the context of inertia measurement units and nonlinear problems)
  • Principal Component Analysis
  • Digital Filter Design
  • Control theory (implementing a control algorithm and tuning it for a problem)
  • Running a control algortihm on a microprocessor
  • Machine Learning for Audio Processing
  • Wavelet Transforms
  • ...
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    $\begingroup$ You have very broad interests, great ! Each of these topics separate and you can go very deep on most (think one full graduate level class). Hence some prioritization might help here. As long as you do stuff on a computer a good foundation in "DSP fundamentals" and especially discrete time and frequency processing could benefit most topics. Take a look at dsp.stackexchange.com/questions/427/… $\endgroup$
    – Hilmar
    Apr 30 at 11:20
  • $\begingroup$ For DSP, defenitly I recommend "Understanding digital signal processing", the author is member of this forum! books.google.fi/books/about/… $\endgroup$
    – MimSaad
    Apr 30 at 19:16
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I've kind of grouped your subjects into larger overall subjects.

Note that there's a lot of overlap here, with the possible exception of actually making it work in a microprocessor (except -- in my opinion the best person to implement something is someone who understands it. So -- overlap).

Specifically, you could claim that it's all applied math. Or all signal processing. You could even stretch this list a bit and wedge it into control theory, but it wouldn't be an easy fit.

  • Applied Math
    • Singular Value Decomposition
    • Principal Component Analysis
    • Machine Learning for Audio Processing
  • Signal Processing
    • Digital Filter Design
    • Kalman Filters (especially in the context of inertia measurement units and nonlinear problems)
    • Wavelet Transforms
  • Control Theory
    • Kalman Filters (especially in the context of inertia measurement units and nonlinear problems)
    • Control theory (implementing a control algorithm and tuning it for a problem)
  • Embedded Software (or systems) Engineering
    • Running a control algorithm on a microprocessor

A weakness of the US tertiary educational system is that all of these subjects will be used in engineering departments, but they're all really applied math. So different universities will group them differently, and it can be hard to find a program that will cover them all. I'm not sure if that applies to where you live. I happened to end up -- by luck more than design -- at an institution that let me get enough of a grounding in the related subjects that I could learn the rest on my own (Worcester Polytechnic Institute -- it's a great place).

I would suggest that you approach this by finding a university program that includes the classes you need to get a grounding in this, and get your second master's. Don't expect to learn all of this within a Master's program -- I can lay claim to about 90% of this list, but about half of it are things that I learned on the job, over the last three decades.

Classes to look for are below. Note that you're not going to have time for them all, so you'll need to pick and choose. If you want to grow into your full list, take as much math as you can and expect to do self-study:

  • Stochastic signals and systems (basically, this is the study of finding the optimal system to process a signal with random components).
    • If you haven't taken it, a 4th-year course on statistics from the math department.
  • Real analysis (AKA "Advanced Calculus", but I think that's an obsolete name). It's an invaluable help when you're sitting at your desk at work wondering if the nifty new thing you're applying is actually mathematically sound.
  • If it's offered, estimation and detection theory. This is basically a follow-on to stochastic signals and systems. It's a deep dive into the math underlying the detection of signals, signals in noise, etc. The one that I took had you derive the basic Kalman filter from first principles in a homework problem -- which gives you an idea of the depth of the subject.
  • Any class on optimal state estimation (i.e., Kalman filtering and all its variations).
  • Signal processing, assuming you haven't taken a class in it.
  • Digital signal processing, ditto.
  • Control theory classes will just be called "control theory", but you may not be able to fit much in. If there's a class offered in state-space systems and you've already got classical (transfer function) control under your belt -- take it.
  • If you want to specialize in control theory, go for nonlinear control or whatever is offered. But if you do that, you probably won't have time for the Detection & Estimation class, so think hard.

I'm not sure what to suggest on the implementation front -- that's basically yet another specialty. I just picked that up on my own, on the way. But, I started out as a kit with a hobby in electronics and a microprocessor board, so I was already doing basic embedded programming when I was 13. Then when I got an EE degree, any class that involved digital circuits was either "oh, yes, I've done this", or "oooh! what a neat formal way to do what I've struggled through intuitively".

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Following undergraduate lectures serve as the basis:

1-) Signals and Systems (Oppenheim's book)

2-) Probability and Random Processes (Kay's book)

3-) Linear feedback systems (Ogata's book)

However, they can fall quite theoretical (without practical focus) and also include much more material than necessary for specialised applications. For example, just to design some digital filters, an almost completely independent approach that summarise the necessary algebra could have been taken; you don't really need those whole books to design basic digital filters, or to learn wavelets.

Similarly eventhough Kalman filters require statistical signal processing and control theory basis, mevertheless, one can still learn how they operate, and how to design and implement basic Kalman stuff without having taken such courses. Some experienced friend can help you understand how to handle them without actually learning the inside of the box.

So you really need someone experienced in those things to give you private lessons.

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