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

By Antonio F. Gualtierotti

The booklet offers the required mathematical foundation to procure and conscientiously use likelihoods for detection issues of Gaussian noise. To facilitate comprehension the textual content is split into 3 vast components – reproducing kernel Hilbert areas, Cramér-Hida representations and stochastic calculus – for which a just a little diverse technique used to be used than of their traditional stand-alone context.

One major acceptable results of the ebook consists of arriving at a common strategy to the canonical detection challenge for energetic sonar in a reverberation-limited setting. still, the overall difficulties handled within the textual content additionally supply an invaluable framework for discussing different present learn components, similar to wavelet decompositions, neural networks, and better order spectral analysis.

The constitution of the ebook, with the exposition featuring as many info as important, was once selected to serve either these readers who're mainly attracted to the implications and those that are looking to study the cloth from scratch. accordingly, the textual content should be precious for graduate scholars and researchers alike within the fields of engineering, arithmetic and statistics.

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Additional resources for Detection of Random Signals in Dependent Gaussian Noise

Example text

2 Atoms and Reduced Measures. . . . . . . . . .. . . . . . . . . 3 Dependence of the Lebesgue Decomposition on Some Related Reproducing Kernel Hilbert Spaces . . . . . . . . . . . 1 Background . . . . . . . . . . . . . . .. . . . . . . . . 2 Lebesgue Decomposition and “Sizes” of Reproducing Kernel Hilbert Spaces Intersections . . 4 Domination of Probabilities on Sub-manifolds .. . . . . . . . . 1 The General Case .

1 Canonical Representations . . . . . . .. . . . . . . . . 2 Proper Canonical Representations . . .. . . . . . . . . 433 433 433 436 438 445 445 456 459 465 467 473 Cramér-Hida Representations via Direct Integrals .. . . . . . . . . 1 Direct Integrals . . . . . . . . . . . . . . . . . .. . . . . . . . . 1 Measurable Fields of Hilbert Spaces . . . . . . . . . . 2 The Direct Integral: Existence . . . . .. . .

1 Some Terminology, Notation, and Attending Facts. . . . . . . . 2 Sets of Measure Zero.. . . . . . . . . . . . . . . . . . . . . . . 1 Adjunction of Sets to -Algebras .. . .. . . . . . . . . 2 Enlargement with All the Sets of Measure Zero and, Possibly, Their Subsets. . . . . . . . . . . . 3 Restriction to a Subset of the Base Set . . . . . . . . . 3 Stopping and Change of Times . . . . . . . . .

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