Coherence : in signal processing and machine learning / David Ramírez, Ignacio Santamaría, Louis Scharf.
Ramirez, David, author.; Santamaría, Ignacio, author.; Scharf, Louis L., author.
2022
TK5102.9 .R36 2022
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Title Coherence : in signal processing and machine learning / David Ramírez, Ignacio Santamaría, Louis Scharf.
Author Ramirez, David, author.
ISBN 9783031133312 electronic book
3031133315 electronic book
9783031133305
3031133307
DOI https://doi.org/10.1007/978-3-031-13331-2
Published Cham, Switzerland : Springer, 2022.
Language English
Description 1 online resource (1 volume) : illustrations (black and white, and colour).
Item Number 10.1007/978-3-031-13331-2 doi
Call Number TK5102.9 .R36 2022
Dewey Decimal Classification 621.382/2
Summary This book organizes principles and methods of signal processing and machine learning into the framework of coherence. The book contains a wealth of classical and modern methods of inference, some reported here for the first time. General results are applied to problems in communications, cognitive radio, passive and active radar and sonar, multi-sensor array processing, spectrum analysis, hyperspectral imaging, subspace clustering, and related. The reader will find new results for model fitting; for dimension reduction in models and ambient spaces; for detection, estimation, and space-time series analysis; for subspace averaging; and for uncertainty quantification. Throughout, the transformation invariances of statistics are clarified, geometries are illuminated, and null distributions are given where tractable. Stochastic representations are emphasized, as these are central to Monte Carlo simulations. The appendices contain a comprehensive account of matrix theory, the SVD, the multivariate normal distribution, and many of the important distributions for coherence statistics. The book begins with a review of classical results in the physical and engineering sciences where coherence plays a fundamental role. Then least squares theory and the theory of minimum mean-squared error estimation are developed, with special attention paid to statistics that may be interpreted as coherence statistics. A chapter on classical hypothesis tests for covariance structure introduces the next three chapters on matched and adaptive subspace detectors. These detectors are derived from likelihood reasoning, but it is their geometries and invariances that qualify them as coherence statistics. A chapter on independence testing in space-time data sets leads to a definition of broadband coherence, and contains novel applications to cognitive radio and the analysis of cyclostationarity. The chapter on subspace averaging reviews basic results and derives an order-fitting rule for determining the dimension of an average subspace. These results are used to enumerate sources of acoustic and electromagnetic radiation and to cluster subspaces into similarity classes. The chapter on performance bounds and uncertainty quantification emphasizes the geometry of the Cramer-Rao bound and its related information geometry.
Bibliography, etc. Note Includes bibliographical references (pages 467-482) and index.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Added Author Santamaría, Ignacio, author.
Scharf, Louis L., author.
Available in Other Form Coherence.
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Record Appears in Online Resources > Ebooks
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Introduction
Historical perspective, motivating problems, and preview of what is to come
Least Squares and related
Classical correlations and coherence
Coherence in the multivariate normal (MVN) model
Classical tests for correlation
One-channel matched subspace detectors
Adaptive subspace detectors
Two channel matched subspace detectors
Detection of spatially-correlated time series
Coherence and the detection of cyclostationarity
Partial coherence for testing causality
Subspace averaging
Coherence and performance bounds
Variations on coherence
Conclusion.

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