Topological Signal Processing

  • Michael┬áRobinson

Part of the Mathematical Engineering book series (MATHENGIN)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Michael Robinson
    Pages 1-7
  3. Michael Robinson
    Pages 9-37
  4. Michael Robinson
    Pages 39-83
  5. Michael Robinson
    Pages 85-131
  6. Michael Robinson
    Pages 133-161
  7. Michael Robinson
    Pages 163-193
  8. Back Matter
    Pages 195-208

About this book

Introduction

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.

Keywords

Discrete Approximations to Spaces Indoor Acoustics Niyogi-Smale-Weinberger Theory Persistent Homology Shape Filtering Sheaf Cohomology Signal Space Fingerprinting Signals and Sheaves Stochastic Noise in Signals Topological Noise

Authors and affiliations

  • Michael┬áRobinson
    • 1
  1. 1.Department of Mathematics and StatisticsAmerican UniversityWashingtonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-36104-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2014
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-36103-6
  • Online ISBN 978-3-642-36104-3
  • Series Print ISSN 2192-4732
  • Series Online ISSN 2192-4740
  • About this book