Download Detection of Random Signals in Dependent Gaussian Noise by Antonio F. Gualtierotti PDF
By Antonio F. Gualtierotti
The booklet offers the mandatory mathematical foundation to acquire and conscientiously use likelihoods for detection issues of Gaussian noise. To facilitate comprehension the textual content is split into 3 wide parts – reproducing kernel Hilbert areas, Cramér-Hida representations and stochastic calculus – for which a slightly diverse process was once used than of their ordinary stand-alone context.
One major acceptable results of the e-book comprises arriving at a basic approach to the canonical detection challenge for energetic sonar in a reverberation-limited atmosphere. still, the final difficulties handled within the textual content additionally offer an invaluable framework for discussing different present learn components, corresponding to wavelet decompositions, neural networks, and better order spectral analysis.
The constitution of the e-book, with the exposition proposing as many info as beneficial, was once selected to serve either these readers who're mainly drawn to the consequences and those that are looking to research the fabric from scratch. therefore, the textual content could be precious 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
2 Reproducing Kernel Hilbert Spaces of Measurable Functions .. 3 Representations of Reproducing Kernels . . . .. . . . . . . . . 4 Embeddings of Reproducing Kernel Hilbert Spaces . . . . . . . 5 Reproducing Kernel Hilbert Spaces of Functions with Integrable Power .. . . . . . . . . . . . . .. . . . . . . . . 6 Reproducing Kernel Hilbert Spaces of Continuous Functions .. 7 Spectral Theory: A Vademecum .. . . . . . . . . . . . . . . . . 8 Reproducing Kernel Hilbert Spaces as Images of Ranges of Square Roots of Linear Operators .
1 Definitions, Characterization, and Properties . . . . . . 2 Ocone Martingales and Exponentials ... . . . . . . . . 3 Ocone Martingales, More Properties, and Some Examples . . . . . . . . . . . . . . . . . . . 8 The Uniqueness Class of Continuous Local Martingales . . . . 993 993 996 1011 1012 1022 1043 1047 1047 1055 1058 1064 17 Likelihoods for Signal Plus Gaussian Noise Versus Gaussian Noise . . . . . . . .
1 Evaluation Maps and Borel Sets in the Fréchet Case . . 2 Evaluation Maps and Borel Sets in the Banach Case . . 3 Measures for Sample Spaces . . . . . . . . . . . . . . . . . . . xxxiii 851 851 854 857 869 874 875 876 884 888 903 903 904 905 908 908 909 910 13 Likelihoods for Signal Plus “White Noise” Versus “White Noise” .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A Version of Girsanov’s Theorem .. .