Mathematical Engineering

Topological Signal Processing

Authors: Robinson, Michael

  • 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
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  • ISBN 978-3-642-36104-3
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  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-642-36103-6
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  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
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  • ISBN 978-3-662-52284-4
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  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
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About this book

Signal processing is the discipline of extracting information from collections of measurements. To be effective, the measurements must be organized and then filtered, detected, or transformed to expose the desired information. Distortions caused by uncertainty, noise, and clutter degrade the performance of practical signal processing systems.

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)

Table of contents (6 chapters)

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-642-36104-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-642-36103-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-3-662-52284-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Topological Signal Processing
Authors
Series Title
Mathematical Engineering
Copyright
2014
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-36104-3
DOI
10.1007/978-3-642-36104-3
Hardcover ISBN
978-3-642-36103-6
Softcover ISBN
978-3-662-52284-4
Series ISSN
2192-4732
Edition Number
1
Number of Pages
XVI, 208
Number of Illustrations and Tables
134 b/w illustrations
Topics