Mathematically inclined books on Signal Processing Theory

Question

First off, i know this may seem off topic but i could not find help in signal processing communities so i was hoping there would be people here who both love mathematics and have interest in signal processing.

I'm an electronics engineering student with high inclination to analysis and pure mathematics ( abstract algebra/linear algebra ... ).

I was just wondering if there was any book ( or any resource ) that treats signal and systems and signal processing with a lot of mathematics rigour ( actually doing proper complex analysis, using functional analysis and linear algebra rigorously to explain convolution, fourier, laplace,haar, hilbert, z transforms for example ).

I'm very disapointed with the books i've read ( Oppenhein, Lathi and related ) on Signal Processing Theory because they actually throw most of the beauty of analysis and algebra away, focusing on the computational side, treating ( undeservedly ) mathematics as a mere tool.

Thanks a lot

What are some examples of things missing in, say, Oppenheim that you'd like to see? Are the proofs incomplete? — AnonSubmitter85, Jul 23 '13 at 01:30

score 5 · Answer 1 · edited Dec 27 '23 at 11:37

5

My favorite is Foundations of Signal Processing by Martin Vetterli, Jelena Kovačević and Vivek Goyal. If you like linear algebra, then this is it.

I was a student at EPFL, in the early days when Martin Vetterli was still teaching a course on advanced signal processing, the material of which eventually formed into this great book; true to the word in the title 'foundations'.

edited Dec 27 '23 at 11:37

Rodrigo de Azevedo

23,788

answered May 17 '18 at 22:55

Rethna Pulikkoonattu

439

1

Do you agree with my edits? – Rodrigo de Azevedo Dec 27 '23 at 11:38

score 3 · Answer 2 · answered Oct 26 '13 at 18:57

3

The Mathematics of Signal Processing by Damelin and Miller that came out recently covers some of the topics you mentioned.

answered Oct 26 '13 at 18:57

hatmatrix

263

score 2 · Answer 3 · answered Jul 27 '17 at 20:18

You can try my book, "Intuitive Guide to Fourier Analysis and Spectral Estimation." I explain the quandary of time and frequency domain, negative frequency and all the other weighty matters related to signal processing and DSP.

Charan Langton

score 1 · Answer 4 · answered Jul 28 '17 at 01:15

1

The closest thing I've seen is Stephane Mallat's A Wavelet Tour of Signal Processing.

answered Jul 28 '17 at 01:15

Mathematically inclined books on Signal Processing Theory

4 Answers4