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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

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  • $\begingroup$ What are some examples of things missing in, say, Oppenheim that you'd like to see? Are the proofs incomplete? $\endgroup$ – AnonSubmitter85 Jul 23 '13 at 1:30
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The Mathematics of Signal Processing by Damelin and Miller that came out recently covers some of the topics you mentioned.

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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/

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

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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

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