Additive and multiplicative noise in the information signal can significantly limit the potential of complex signal processing systems, especially when those systems use signals with complex phase structure. During the last few years this problem has been the focus of much research, and its solution could lead to profound improvements in applications of complex signals and coherent signal processing.
Signal Processing Noise sets forth a generalized approach to signal processing in multiplicative and additive noise that represents a remarkable advance in signal processing and detection theory. This approach extends the boundaries of the noise immunity set by classical and modern signal processing theories, and systems constructed on this basis achieve better detection performance than that of systems currently in use. Featuring the results of the author's own research, the book is filled with examples and applications, and each chapter contains an analysis of recent observations obtained by computer modelling and experiments.
Tables and illustrations clearly show the superiority of the generalized approach over both classical and modern approaches to signal processing noise. Addressing a fundamental problem in complex signal processing systems, this book offers not only theoretical development, but practical recommendations for raising noise immunity in a wide range of applications.
Probability: Basic Concepts
Random Variables
Stochastic Processes
Correlation Function
Spectral Density
Statistical Characteristics
Conclusions
References
CLASSICAL AND MODERN APPROACHES TO SIGNAL DETECTION THEORY
Gaussian Approach
Markov Approach
Bayes' Decision-Making Rule
Unbiased and Invariant Decision-Making Rules
Mini-Max Decision-Making Rule
Sequential Signal Detection
Signal Detection in Non-Gaussian Noise
Non-Parametric Signal Detection
Conclusions
References
MAIN CHARACTERISTICS OF MULTIPLICATIVE NOISE
Classification of the Noise and Interference
Sources of the Multiplicative Noise
Classification and Main Properties of Multiplicative Noise
Correlation Function and Energy Spectrum of Multiplicative Noise
Generalized Statistical Model of Multiplicative Noise
Conclusions
References
STATISTICAL CHARACTERISTICS OF SIGNALS UNDER THE STIMULUS OF MULTIPLICATIVE NOISE
Deterministic and Quasideterministic Multiplicative Noise
Stationary Fluctuating Multiplicative Noise
Ensemble and Individual Realizations of the Signal
Probability Distribution Density of the Signal in the Additive Gaussian Noise under the Stimulus of Multiplicative Noise
Multivariate Probability Distribution Density of Instantaneous Values of the Signal under the Stimulus of Fluctuating Multiplicative Noise
Conclusions
References
MAIN THEORETICAL PRINCIPLES OF THE GENERALIZED APPROACH TO SIGNAL PROCESSING UNDER THE STIMULUS OF MULTIPLICATIVE NOISE
Basic Concepts
Criticism
Initial Premises
Likelihood Ratio
Engineering Interpretation
Generalized Detector
Distribution Law
Conclusions
References
GENERALIZED APPROACH TO SIGNAL PROCESSING UNDER THE STIMULUS OF MULTIPLICATIVE NOISE AND LINEAR SYSTEMS
Signal Characteristics at the Output of Linear System of the Generalized Detector under the Stimulus of Multiplicative Noise
Signal Characteristics at the Generalized Detector Output under under the Stimulus of Multiplicative Noise
Signal Noise Component for Some Types of Signals
Signal Noise Component under the Stimulus of the Slow and Rapid Multiplicative Noise
Signal Distribution Law under the Stimulus of Multiplicative Noise
Conclusions
References
GENERALIZED APPROACH TO SIGNAL DETECTION IN THE PRESENCE OF MULTIPLICATIVE AND ADDITIVE GAUSSIAN NOISE
Statistical Characteristics of Signals at the Output of the Generalized Detector
Detection Performances of the Generalized Detector
Known Correlation Function of the Multiplicative Noise
One-Channel Generalized Detector
Diversity Signal Detection
Conclusions
References
SIGNAL PARAMETER MEASUREMENT PRECISION
A Single Signal Parameter Measurement under a Combined Stimulus of Weak Multiplicative and Additive Gaussian Noise
Simultaneous Measurement of Two Signal Parameters under a Combined Stimulus of Weak Multiplicative and Additive Gaussian Noise
A Single Parameter Measurement under a Combined Stimulus of High Multiplicative and Additive Gaussian Noise
Conclusions
References
SIGNAL RESOLUTION UNDER THE GENERALIZED APPROACH TO SIGNAL PROCESSING IN THE PRESENCE OF NOISE
Estimation Criteria of Signal Resolution
Signal Resolution by Woodward Criterion
Statistical Criterion of Signal Resolution
Conclusions
References
APPENDIX I: Delta Function
APPENDIX II: Correlation Function and Energy Spectrum of Noise Modulation Function
NOTATION INDEX
INDEX
Biography
Tuzlukov\, Vyacheslav
