Detection of Random Signals in Dependent Gaussian Noise
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Beschreibung
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.
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.
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
Autor*in
Antonio F. Gualtierotti
Themen in »Detection of Random Signals in Dependent Gaussian Noise«
Cramér-Hida representations Girsanov‘s theory Goursat processes dependent signals with arbitrary laws prediction processes reproducing kernel Hilbert spaces signal detection uniqueness class of continuous local martingales information and communication, circuits
Stimmen zu »Detection of Random Signals in Dependent Gaussian Noise«
“The book rigorously develops the mathematical foundations to assess the possible likelihoods for detection problems with Gaussian noise. … The text would be very useful for graduate students and researchers alike in the fields of mathematics, engineering and statistics.” (John Schmeelk, zbMATH 1364.60004, 2017)
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