PROBABILITY AND STATISTICS |
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Probability: Basic Concepts |
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Random Variables |
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Stochastic Processes |
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Correlation Function |
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Spectral Density |
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Statistical Characteristics |
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Conclusions |
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References |
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CLASSICAL AND MODERN APPROACHES TO SIGNAL DETECTION THEORY |
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Gaussian Approach |
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Markov Approach |
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Bayes' Decision-Making Rule |
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Unbiased and Invariant Decision-Making Rules |
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Mini-Max Decision-Making Rule |
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Sequential Signal Detection |
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Signal Detection in Non-Gaussian Noise |
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Non-Parametric Signal Detection |
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Conclusions |
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References |
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MAIN CHARACTERISTICS OF MULTIPLICATIVE NOISE |
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Classification of the Noise and Interference |
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Sources of the Multiplicative Noise |
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Classification and Main Properties of Multiplicative Noise |
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Correlation Function and Energy Spectrum of Multiplicative Noise |
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Generalized Statistical Model of Multiplicative Noise |
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Conclusions |
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References |
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STATISTICAL CHARACTERISTICS OF SIGNALS UNDER THE STIMULUS OF MULTIPLICATIVE NOISE |
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Deterministic and Quasideterministic Multiplicative Noise |
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Stationary Fluctuating Multiplicative Noise |
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Ensemble and Individual Realizations of the Signal |
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Probability Distribution Density of the Signal in the Additive Gaussian Noise under the Stimulus of Multiplicative Noise |
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Multivariate Probability Distribution Density of Instantaneous Values of the Signal under the Stimulus of Fluctuating Multiplicative Noise |
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Conclusions |
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References |
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MAIN THEORETICAL PRINCIPLES OF THE GENERALIZED APPROACH TO SIGNAL PROCESSING UNDER THE STIMULUS OF MULTIPLICATIVE NOISE |
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Basic Concepts |
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Criticism |
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Initial Premises |
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Likelihood Ratio |
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Engineering Interpretation |
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Generalized Detector |
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Distribution Law |
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Conclusions |
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References |
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GENERALIZED APPROACH TO SIGNAL PROCESSING UNDER THE STIMULUS OF MULTIPLICATIVE NOISE AND LINEAR SYSTEMS |
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Signal Characteristics at the Output of Linear System of the Generalized Detector under the Stimulus of Multiplicative Noise |
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Signal Characteristics at the Generalized Detector Output under under the Stimulus of Multiplicative Noise |
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Signal Noise Component for Some Types of Signals |
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Signal Noise Component under the Stimulus of the Slow and Rapid Multiplicative Noise |
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Signal Distribution Law under the Stimulus of Multiplicative Noise |
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Conclusions |
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References |
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GENERALIZED APPROACH TO SIGNAL DETECTION IN THE PRESENCE OF MULTIPLICATIVE AND ADDITIVE GAUSSIAN NOISE |
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Statistical Characteristics of Signals at the Output of the Generalized Detector |
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Detection Performances of the Generalized Detector |
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Known Correlation Function of the Multiplicative Noise |
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One-Channel Generalized Detector |
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Diversity Signal Detection |
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Conclusions |
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References |
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SIGNAL PARAMETER MEASUREMENT PRECISION |
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A Single Signal Parameter Measurement under a Combined Stimulus of Weak Multiplicative and Additive Gaussian Noise |
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Simultaneous Measurement of Two Signal Parameters under a Combined Stimulus of Weak Multiplicative and Additive Gaussian Noise |
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A Single Parameter Measurement under a Combined Stimulus of High Multiplicative and Additive Gaussian Noise |
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Conclusions |
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References |
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SIGNAL RESOLUTION UNDER THE GENERALIZED APPROACH TO SIGNAL PROCESSING IN THE PRESENCE OF NOISE |
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Estimation Criteria of Signal Resolution |
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Signal Resolution by Woodward Criterion |
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Statistical Criterion of Signal Resolution |
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Conclusions |
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References |
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APPENDIX I: Delta Function |
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APPENDIX II: Correlation Function and Energy Spectrum of Noise Modulation Function |
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NOTATION INDEX |
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INDEX |
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