Applications of analysis in signal processing/machine learning?

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Dowland
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Hello everyone,

My question for this thread concerns the application of (mainly) mathematical analysis to fields such as signal processing and machine learning. More specifically, I was wondering if you happen to know of some interesting application of things like measure theory or functional analysis in these fields, that might have the potential to be made into a research questions?

My reason for asking is that I'm an electrical engineering student who is looking around for possible research questions for my Master's thesis, and I’m currently suffering from a lack of inspiration. I have a slightly more theoretical interest than most engineering students and I have also taken more math courses than most engineering students, so I thought it would be fun if I could apply the things I have learned in mathematics to something that is also relevant for "information processing" of some kind (e.g. signal processing, machine learning, and the like, which is related to my actual major/specialisation). My mathematical background is not great, but I have taken a basic course in analysis (on the level of Baby Rudin) and also a more advanced course in analysis, treating measure theory and functional analysis (on the level of "Foundations of Modern Analysis" by Avner Friedman). I have also taken courses in abstract algebra, probability and a rigorous course in complex analysis if that's interesting.

Sorry for a vague and very open-ended question. As I hinted at, I am more or less just looking for inspiration.
 
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I will suggest a vague and open-ended book to you. It is pop science (but very good pop-sci ) in my opinion. Might provide inspiration. I learned stuff.
The manipulation of information is certainly becoming more and more important more and more fields.
 
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Some references:

https://towardsdatascience.com/machine-learning-and-signal-processing-103281d27c4b

and more generally these two books:

- Hands On Machine Learning with ScikitLearn and Tensorflow by Geron
- the 100 page Machine Learning book by Burkov

http://themlbook.com/

some applications:
- gunshot detection and device activation ie close and lock a door
- transcribe music ie sound to notes
- smart hearing aid where certain frequencies are boosted under some specific condition like wind or motor noise...

and other applications are mentioned here:

https://en.wikipedia.org/wiki/Digital_signal_processing?wprov=sfti1

you might find something interesting in this presentation:

https://signalprocessingsociety.org/uploads/Publications/SPM/IDSP_SC_act_slides.pdf