Overview
- Derives a new likelihood function for solving basic problems in the theory of signal detection
- Completes the Cramér-Hida representation theory
- Investigates the scope of the signal-plus-noise model
- Includes the necessary details to make the theory ready for application
- References to statistical communication theory illustrate the power of the mathematics involved
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Table of contents (17 chapters)
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Front Matter
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Reproducing Kernel Hilbert Spaces
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Front Matter
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Likelihoods
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Front Matter
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Keywords
About this book
The book presents the necessary mathematical basis to obtain and rigorously use likelihoods for detection problems with Gaussian noise. To facilitate comprehension the text is divided into three broad areas – reproducing kernel Hilbert spaces, Cramér-Hida representations and stochastic calculus – for which a somewhat different approach was used than in their usual stand-alone context.
One main applicable result of the book involves arriving at a general solution to the canonical detection problem for active sonar in a reverberation-limited environment. Nonetheless, the general problems dealt with in the text also provide a useful framework for discussing other current research areas, such as wavelet decompositions, neural networks, and higher order spectral analysis.
The structure of the book, with the exposition presenting as many details as necessary, was chosen to serve both those readers who are chiefly interested in the results and those who want to learn the material from scratch. Hence, the text will be useful for graduate students and researchers alike in the fields of engineering, mathematics and statistics.
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Authors and Affiliations
Bibliographic Information
Book Title: Detection of Random Signals in Dependent Gaussian Noise
Authors: Antonio F. Gualtierotti
DOI: https://doi.org/10.1007/978-3-319-22315-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-22314-8Published: 09 February 2016
Softcover ISBN: 978-3-319-79392-4Published: 14 November 2020
eBook ISBN: 978-3-319-22315-5Published: 15 December 2015
Edition Number: 1
Number of Pages: XXXIV, 1176
Number of Illustrations: 5 b/w illustrations
Topics: Probability Theory and Stochastic Processes, Functional Analysis, Information and Communication, Circuits