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Published in:
Introduction and Informal Discussion Read chapter Read first chapter

2014 | OriginalPaper | Chapter

4. Detection

Author : Michael Robinson

Published in: Topological Signal Processing

Publisher: Springer Berlin Heidelberg

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Abstract

Detectors are tools which extract and emphasize important features of a signal. In order to be useful, a detector should be functorial, in that it preserves the features of the signal. In most practical settings, it is desirable for detectors to be lossy. Specifically, one usually wants to transform a signal into a representation that removes noise and irrelevant signals. Merely requiring that certain qualitative features of a signal be preserved will motivate our definition of detectors as certain kinds of forgetful functors. These ideas are showcased in a crucial way in two contexts; that of sampling theory and mapping a radio network.

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previous chapter Signals
next chapter Transforms
Footnotes
1
The proof of the Jordan curve theorem (for instance see (Hatcher (2002), Sect. 2.B)) usually relies on singular homology, which does not depend on the sheaf cohomology theory we are developing here.
 
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Metadata
Title
Detection
Author
Michael Robinson
Copyright Year
2014
Publisher
Springer Berlin Heidelberg
Book
Topological Signal Processing

Print ISBN: 978-3-642-36103-6

Electronic ISBN: 978-3-642-36104-3

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-642-36104-3_4