Mathematics behind Signal and Systems

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Discussion Overview

The discussion centers around the search for a mathematically rigorous signal processing textbook that incorporates real, complex, and functional analysis with measure theory. Participants explore various resources and recommendations, focusing on the need for foundational mathematical analysis before delving into signal processing topics.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses a need for a signal processing textbook that is mathematically rigorous and reviews topics from mathematical analysis, mentioning "A Mathematical introduction to signal and systems" by A. D. Lewis as a preferred reference.
  • Another participant suggests the “Digital Signal Processing” ebook from the CERN Accelerator School as a potential resource.
  • A third participant advises to focus on mastering the Fourier Transform as a foundational skill in signal processing.
  • One participant proposes a link to a book that may not meet the rigor expected by the original poster, acknowledging this after reviewing the initial request.
  • A later reply mentions finding the second volume of Lewis's notes and recommends "Fourier Analysis and its applications" by Gasquet and Witomski, noting it may not be advanced enough for the original poster's needs.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a single textbook recommendation, with multiple competing suggestions and varying opinions on the rigor and suitability of the proposed resources.

Contextual Notes

Some participants express uncertainty about the level of rigor required and the appropriateness of the suggested texts, indicating a reliance on personal preferences and experiences with the materials.

Who May Find This Useful

Readers interested in advanced signal processing, mathematical analysis, and those seeking rigorous academic resources in these fields may find this discussion beneficial.

amg63
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I am looking for a signal processing textbook that uses real, complex, and functional analysis with measure theory. In other words, mathematically rigorous signal processing. Specifically, I prefer the kind that takes time to review all the topics from mathematical analysis before jumping into the fire (due to a potential experience deficit in some analysis topics), but will gladly consider any rigorous signal processing. A Mathematical introduction to signal and systems by A. D. Lewis is pretty much what I am looking for, however, only first volume is available, so I need an equivalent. Please inform me of any textbooks that you know of that fit my search criteria, and I shall be grateful in return. Thank you for your time.
 
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Google the Fourier Transform and become an expert at that.
 
I think this is the book you are looking for: http://www.fourierandwavelets.org/FSP_v1.1_2014.pdf

EDIT: After looking at the text you posted perhaps my suggestion is not rigorous enough.

Note to moderators this version of the book is posted for free distribution on the author's website.
 
I wasn't familiar with the notes by Lewis, but was intrigued so googled. I found the second volume on the author's web site.
http://www.mast.queensu.ca/~andrew/
Follow the link to course notes, then math 334.

One book I really like is "Fourier Analysis and its applications" by Gasquet and Witomski. It is probably not advanced enough for you; it is certainly less advanced (and shorter!) than the notes by Lewis, but is more polished. I especially like the treatment of Fourier analysis and distribution theory.

Jason
 

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