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I am about to start a new engineering job in the fields of signal processing and machine learning. I have a bachelor's degree in electrical engineering, but for the last two years I have been doing a master's in theoretical physics, so I have been away from the field of signal processing for a while.

In by bachelor's I learned continuous and discrete time signal processing from Lathi's text, and stochastic signal processing from a less known Swedish book.

Now that I am getting back to the field I am looking for something that is more compact and preferably to a higher mathematical standard than Lathi, but that still covers all the essentials. For example, I would now be comfortable with discussing the delta function as a distribution, proper discussion of convergence notions, and would prefer such an approach over the informal approach in Lathi.

My goals are twofold: to get back up to speed with the subject, and to get a deeper understanding.

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    $\begingroup$ theo physics will at least have well-equipped you with the analysis that helps understand both the fields of signal processing and machine learning. Nice! $\endgroup$ Aug 25, 2022 at 13:38
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    $\begingroup$ Do you know which "branch" of signal processing? Higher mathematical standards are usually going to be found in specialized books, hence my question. $\endgroup$
    – Jdip
    Aug 25, 2022 at 15:18
  • $\begingroup$ @Jdip More specifically I will be working with digital signal processing, statistical machine learning (with some emphasis on online learning, and gaussian process regression), sensor fusion. However, as mentioned in the original question, here I am specifically looking for something that covers the essentials of signal processing, but preferably tersely and with some rigour. Though I suppose an emphasis on digital, discrete-time, signal processing might be okay. $\endgroup$
    – ummg
    Aug 25, 2022 at 16:08
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    $\begingroup$ Signal Analysis from Mertins is a compact reminder on modern vector space based signal processing. Multiresolution Signal Decomposition from Akansu will also help being more classical. Furthermore, Statistical Digital Signal Processing from Hayes is a must have imho... $\endgroup$
    – Fat32
    Aug 25, 2022 at 21:54
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    $\begingroup$ @Fat32 might want to flesh that out with links to the books and make it an answer. $\endgroup$
    – Peter K.
    Aug 26, 2022 at 0:25

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For a fast review of modern mathematics applied to signal processing, you can check out the following books:

These are graduate level and relatively modern & compact books, some experience with Linear System Theory will be helpful, though the review in Monson Hayes' book is by itself self sufficient.

For Machine Learning, you will have to also look for many other more modern textbooks, or at least some introductory books from Haykin...

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  • $\begingroup$ These look like promising books, though possibly a bit more specialized than what I had in mind. I will take a closer look at them, and I will wait a bit with accepting, in case someone else wants to chime in. $\endgroup$
    – ummg
    Aug 26, 2022 at 23:55
  • $\begingroup$ Especially Mertins' book seems to be in line with what I had in mind, though it lacks exercises, and seems a bit light on proofs. $\endgroup$
    – ummg
    Aug 27, 2022 at 0:17
  • $\begingroup$ @ummg sure... hope they will be helpful or you will find better suiting books.. Btw, I've deliberately ignored the DTSP classics from Oppenheim or Proakis, as they are not using vector space formalism due to being undergraduate books... $\endgroup$
    – Fat32
    Aug 27, 2022 at 0:59
  • $\begingroup$ I just came across a book called The Mathematics of Signal Processing, by Damelin and Miller, which seems to be written more from the mathematicians perspective, but with an eye on applications. Seems like it could be a good complement to more applied texts like Lathi's. Do you have any experience with it? $\endgroup$
    – ummg
    Aug 27, 2022 at 1:16
  • $\begingroup$ I don't have an experience with that book but I've seen it, and it looks like too much unnecessarily formal in its development, therefore I would not remommend it for engineers, but it's well written for mathematicians otherwise... $\endgroup$
    – Fat32
    Aug 27, 2022 at 1:55

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