PDEs for EEs: Signal Processing R&D

[kdinser]

This is kind of an off shoot of another thread, but figured it would be better to start my own rather then hijack someone else's :).

What does PDE cover and would it be useful to an EE looking to get into signal processing research and development? If so, could someone recommend a good book on the subject that is aimed more at the engineer then the math major? I don't mind rigorous mathematics when it's called for, but I get annoyed when it overlaps to much with common sense,
Thanks

 

[leright]

Well, if you want to get into signal processing you can never have enough math. Hell, you can never have enough math, period.

PDE is an essential subject to be well versed in no matter what you go into. Right now I am studying tensor analysis on my own (dual major in EE and physics) so I can be prepared to study GR properly, but the next subject I plan to cover on my own is PDE.

 

[piercas]

for starting this thread! It's a great question and one that many engineers may have when considering signal processing research and development.

PDE (Partial Differential Equations) covers a wide range of mathematical techniques used in engineering and science to model and solve complex problems involving multiple variables. In the context of signal processing, PDEs are often used to model the behavior of signals in time and space, and to develop algorithms for processing and analyzing these signals.

For an EE looking to get into signal processing R&D, having a strong understanding of PDEs can be very useful. Many advanced signal processing techniques, such as wavelet transforms and Fourier analysis, rely heavily on PDEs for their theoretical foundation. Additionally, PDEs are used in the development of signal processing algorithms for applications such as image and speech processing, data compression, and filtering.

As for recommended books on the subject, I would suggest "Partial Differential Equations for Scientists and Engineers" by Stanley J. Farlow. This book is aimed at engineers and scientists and provides a good balance between rigorous mathematics and practical applications. Another good resource is "Partial Differential Equations with Fourier Series and Boundary Value Problems" by Nakhle H. Asmar, which also includes numerous examples and exercises for further practice.

In conclusion, having a strong understanding of PDEs can greatly benefit an EE looking to get into signal processing R&D. It is a fundamental tool for understanding and developing advanced signal processing techniques and algorithms. I would highly recommend delving into this subject to further enhance your skills and knowledge in the field of signal processing.