Download Detection of Random Signals in Dependent Gaussian Noise by Antonio F. Gualtierotti PDF

By Antonio F. Gualtierotti

ISBN-10: 3319223143

ISBN-13: 9783319223148

The e-book offers the required mathematical foundation to acquire and conscientiously use likelihoods for detection issues of Gaussian noise. To facilitate comprehension the textual content is split into 3 huge parts – reproducing kernel Hilbert areas, Cramér-Hida representations and stochastic calculus – for which a slightly assorted strategy used to be used than of their traditional stand-alone context.

One major appropriate results of the e-book includes arriving at a normal technique to the canonical detection challenge for lively sonar in a reverberation-limited surroundings. still, the final difficulties handled within the textual content additionally supply an invaluable framework for discussing different present learn components, corresponding to wavelet decompositions, neural networks, and better order spectral analysis.

The constitution of the publication, with the exposition providing as many information as valuable, was once selected to serve either these readers who're mainly drawn to the implications and those that are looking to research the fabric from scratch. for this reason, the textual content could be necessary for graduate scholars and researchers alike within the fields of engineering, arithmetic and statistics.

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Extra resources for Detection of Random Signals in Dependent Gaussian Noise

Sample text

3 The Index of Stationarity of a Gaussian Process .. . . . 4 The Case of Finite Multiplicity . . . . . . . . . . . . . Part III 665 672 697 703 703 706 710 718 736 751 751 756 768 786 Likelihoods 10 Bench and Tools.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Some Terminology, Notation, and Attending Facts. . . . . . . . 2 Sets of Measure Zero.. . . . . . . . . . . . . . . . .

505 505 506 515 518 Some Facts About Multiplicity . . . . . . . . . . . . . . . . . . . . . 1 All Multiplicities May Occur . . . . . . . . . . . . . . . . . . . 2 Invariance of Multiplicity .. . . . . . . . . . . .. . . . . . . . . 1 The Case of Projections . . . . . . . . . . . . . . . . . 2 The Case of Unitary Transformations .. . . . . . . . . 3 Other Linear Transformations Which Preserve Multiplicity .

795 795 797 798 807 808 814 814 829 833 833 835 842 843 846 Contents 11 Calculus for Cramér-Hida Processes . . . . . . . . .. . . . . . . . . 1 Integrators: Cramér-Hida Processes . . . . . . .. . . . . . . . . 1 The -Algebras Generated by a Cramér-Hida Process . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The Reproducing Kernel Hilbert Space of a Cramér-Hida Process . . . .

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