Overview
- Presents a systematic treatment of the common research threads on the interface between topology and signal processing
- Includes relevant background materials as well as case studies of topological signal processing applied to actual data
- Written by an expert in the field
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathematical Engineering (MATHENGIN)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
Keywords
About this book
In aggressively uncertain situations, the full truth about an underlying signal cannot be known. This book develops the theory and practice of signal processing systems for these situations that extract useful, qualitative information using the mathematics of topology -- the study of spaces under continuous transformations. Since the collection of continuous transformations is large and varied, tools which are topologically-motivated are automatically insensitive to substantial distortion. The target audience comprises practitioners as well as researchers, but the book may also be beneficial for graduate students.
Reviews
From the book reviews:
“This text provides a nice exposition of the topological ideas used to extract information from signals and the practical details of signal processing. … Robinson’s intended audience is first year graduate students in both engineering and mathematics, and advanced undergraduates. … Throughout the text there are numerous examples and diagrams. Each chapter also ends with some open questions. These features make the book quite readable.” (Michele Intermont, MAA Reviews, February, 2015)
“Three major goals for this book: firstly to show that topological invariants provide qualitative information about signals that is both relevant and practical, second to show that the signal processing concepts of filtering, detection, and noise correspond respectively to the concepts of sheaves, functoriality and sequences, and third to advocate for the use of sheaf theory in signal processing. … The target audience is practitioners so that the theoretical notions are covered with the practitioner in mind with motivations emphasized.” (Jonathan Hodgson, zbMATH, Vol. 1294, 2014)Authors and Affiliations
Bibliographic Information
Book Title: Topological Signal Processing
Authors: Michael Robinson
Series Title: Mathematical Engineering
DOI: https://doi.org/10.1007/978-3-642-36104-3
Publisher: Springer Berlin, Heidelberg
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2014
Hardcover ISBN: 978-3-642-36103-6Published: 20 January 2014
Softcover ISBN: 978-3-662-52284-4Published: 23 August 2016
eBook ISBN: 978-3-642-36104-3Published: 07 January 2014
Series ISSN: 2192-4732
Series E-ISSN: 2192-4740
Edition Number: 1
Number of Pages: XVI, 208
Number of Illustrations: 134 b/w illustrations
Topics: Signal, Image and Speech Processing, Topology, Communications Engineering, Networks, Computational Science and Engineering, Information and Communication, Circuits