Applications of analysis in signal processing/machine learning?

In summary: Machine learning algorithms are based on complex optimization problems and linear algebra. In summary, the conversation discusses the application of mathematical analysis, specifically measure theory and functional analysis, in fields such as signal processing and machine learning. The speaker, an electrical engineering student, is seeking inspiration for research questions and suggests reading about topics such as Fourier analysis, neural networks, and cryptography. Various applications of these concepts are also mentioned, including gunshot detection and music transcription. The conversation also touches on Laplace transforms and linear algebra in relation to signal processing and machine learning algorithms.
  • #1
Dowland
51
0
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.
 
Mathematics news on Phys.org
  • #2
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.
 
  • Like
Likes Paul Colby and berkeman
  • #3
The mathematical keywords are Fourier analysis, neural networks, and if you are interested in safety issues, the entire cryptography. I suggest to read about those topics to get a narrower approach of what you are actually interested in.
 
  • Like
Likes berkeman
  • #4
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
 
  • #5
Dowland said:
My question for this thread concerns the application of (mainly) mathematical analysis to fields such as signal processing and machine learning.

If that includes problems in image recognition, look at wavelets and steerable filters.
 
  • #6
Signal processing and control algorithms rely heavily on Laplace transforms.
 

Related to Applications of analysis in signal processing/machine learning?

1. What is signal processing and how is it used in machine learning?

Signal processing is the manipulation and analysis of signals, which can be any type of data that varies over time. In machine learning, signal processing is used to extract meaningful features from signals and convert them into a format that can be used by algorithms to make predictions.

2. What are some common applications of signal processing in machine learning?

Some common applications of signal processing in machine learning include speech recognition, image and video processing, natural language processing, and sensor data analysis.

3. How does analysis play a role in signal processing for machine learning?

Analysis is an essential part of signal processing in machine learning as it involves techniques such as Fourier analysis, wavelet analysis, and spectral analysis to extract features and patterns from signals. These features are then used as inputs for machine learning algorithms.

4. What are the benefits of using signal processing in machine learning?

Signal processing allows for the extraction of meaningful information from complex data, which can then be used to train machine learning models. This can lead to more accurate predictions and better performance of the models.

5. Are there any challenges associated with using signal processing in machine learning?

Yes, there are some challenges associated with using signal processing in machine learning, such as dealing with noisy data, selecting the right features, and choosing appropriate techniques for different types of signals. It also requires a good understanding of both signal processing and machine learning concepts.

Similar threads

Replies
14
Views
1K
Replies
3
Views
839
  • Science and Math Textbooks
Replies
2
Views
1K
  • STEM Academic Advising
Replies
5
Views
936
  • Science and Math Textbooks
Replies
13
Views
2K
  • Topology and Analysis
Replies
11
Views
409
  • STEM Academic Advising
Replies
8
Views
1K
  • Astronomy and Astrophysics
Replies
3
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Replies
1
Views
780
Back
Top