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
Best Answer
My favorite is "Foundations of Signal Processing" by Martin Vetterli, Jelena Kovacevic 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'. Check this out: http://fourierandwavelets.org/