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Published in:
Introduction to Underwater Acoustic Signal Processing Read chapter Read first chapter

2019 | OriginalPaper | Chapter

5. Mathematical Statistics

Author : Douglas A. Abraham

Published in: Underwater Acoustic Signal Processing

Publisher: Springer International Publishing

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Abstract

Many of the underwater acoustic signal processing applications discussed in this text have their roots in detection and estimation, both of which require a statistical characterization of the data prior to development. This section covers some basic statistical concepts enabling the derivation of algorithms in statistical signal processing. The topics covered include probability, random variables, and random processes. The construction, definitions, and use of complex random variables and complex random processes, which arise when bandpass signals are basebanded, are described. Finally, the properties and characteristics of numerous discrete- and continuous-valued random variables are presented.

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Footnotes
1
Describing probability as belief in the potential occurrence of an event comes from the classical interpretation rather than the relative-frequency interpretation. The classical interpretation enumerates all the elements of the probability space before the experiment occurs and counts those in \(\mathcal {A}\) to assign a belief (the proportion of elements in \(\mathcal {A}\) to the total number) that \({\mathcal {A}}\) will occur.
 
2
The β quantile of the random variable Z is the value z β such that the CDF https://static-content.springer.com/image/chp%3A10.1007%2F978-3-319-92983-5_5/334738_1_En_5_IEq70_HTML.gif .
 
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Metadata
Title
Mathematical Statistics
Author
Douglas A. Abraham
Copyright Year
2019
Book
Underwater Acoustic Signal Processing

Print ISBN: 978-3-319-92981-1

Electronic ISBN: 978-3-319-92983-5

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-92983-5_5