Signal Processing Noise

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.

• Describes a generalized approach to signal processing noise that represents a major advance in signal detection theory and signal processing
• Shows that it may be possible to raise the upper bound of noise immunity in complex signal processing systems
• Details theories particularly useful in practice
• Includes observations and experimental results never before published

Contents

• Probability: Basic Concepts
• Random Variables
• Stochastic Processes
• Correlation Function
• Spectral Density
• Statistical Characteristics
• Conclusions

• 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

• 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

• 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

• Basic Concepts
• Criticism
• Initial Premises
• Likelihood Ratio
• Engineering Interpretation
• Generalized Detector
• Distribution Law
• Conclusions

• 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

• 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

• 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

• Estimation Criteria of Signal Resolution
• Signal Resolution by Woodward Criterion
• Statistical Criterion of Signal Resolution
• Conclusions