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

Answer 1

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

Answer 2

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

Answer 3

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