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by Wim C. Van Etten
Introduction to Random Signals and Noise
Cover Page
Title Page
Copyright
Dedication
Contents
Preface
Chapter 1: Introduction
1.1 RANDOM SIGNALS AND NOISE
1.2 MODELLING
1.3 THE CONCEPT OF A STOCHASTIC PROCESS
1.4 SUMMARY
Chapter 2: Stochastic Processes
2.1 STATIONARY PROCESSES
2.2 CORRELATION FUNCTIONS
2.3 GAUSSIAN PROCESSES
2.4 COMPLEX PROCESSES
2.5 DISCRETE-TIME PROCESSES
2.6 SUMMARY
2.7 PROBLEMS
Chapter 3: Spectra of Stochastic Processes
3.1 THE POWER SPECTRUM
3.2 THE BANDWIDTH OF A STOCHASTIC PROCESS
3.3 THE CROSS-POWER SPECTRUM
3.4 MODULATION OF STOCHASTIC PROCESSES
3.5 SAMPLING AND ANALOGUE-TO-DIGITAL CONVERSION
3.6 SPECTRUM OF DISCRETE-TIME PROCESSES
3.7 SUMMARY
3.8 PROBLEMS
Chapter 4: Linear Filtering of Stochastic Processes
4.1 BASICS OF LINEAR TIME-INVARIANT FILTERING
4.2 TIME DOMAIN DESCRIPTION OF FILTERING OF STOCHASTIC PROCESSES
4.3 SPECTRA OF THE FILTER OUTPUT
4.4 NOISE BANDWIDTH
4.5 SPECTRUM OF A RANDOM DATA SIGNAL
4.6 PRINCIPLES OF DISCRETE-TIME SIGNALS AND SYSTEMS
4.7 DISCRETE-TIME FILTERING OF RANDOM SEQUENCES
4.8 SUMMARY
4.9 PROBLEMS
Chapter 5: Bandpass Processes
5.1 DESCRIPTION OF DETERMINISTIC BANDPASS SIGNALS
5.2 QUADRATURE COMPONENTS OF BANDPASS PROCESSES
5.3 PROBABILITY DENSITY FUNCTIONS OF THE ENVELOPE AND PHASE OF BANDPASS NOISE
5.4 MEASUREMENT OF SPECTRA
5.5 SAMPLING OF BANDPASS PROCESSES
5.6 SUMMARY
5.7 PROBLEMS
Chapter 6: Noise in Networks and Systems
6.1 WHITE AND COLOURED NOISE
6.2 THERMAL NOISE IN RESISTORS
6.3 THERMAL NOISE IN PASSIVE NETWORKS
6.4 SYSTEM NOISE
6.5 SUMMARY
6.6 PROBLEMS
Chapter 7: Detection and Optimal Filtering
7.1 SIGNAL DETECTION
7.2 FILTERS THAT MAXIMIZE THE SIGNAL-TO-NOISE RATIO
7.3 THE CORRELATION RECEIVER
7.4 FILTERS THAT MINIMIZE THE MEAN-SQUARED ERROR
7.5 SUMMARY
7.6 PROBLEMS
Chapter 8: Poisson Processes and Shot Noise
8.1 INTRODUCTION
8.2 THE POISSON DISTRIBUTION
8.3 THE HOMOGENEOUS POISSON PROCESS
8.4 INHOMOGENEOUS POISSON PROCESSES
8.5 THE RANDOM-PULSE PROCESS
8.6 SUMMARY
8.7 PROBLEMS
References
Further Reading
Appendix A: Representation of Signals in a Signal Space
A.1 LINEAR VECTOR SPACES
A.2 THE SIGNAL SPACE CONCEPT
A.3 GRAM-SCHMIDT ORTHOGONALIZATION
A.4 THE REPRESENTATION OF NOISE IN SIGNAL SPACE
A.5 SIGNAL CONSTELLATIONS
A.6 PROBLEMS
Appendix B: Attenuation, Phase Shift and Decibels
Appendix C: Mathematical Relations
C.1 TRIGONOMETRIC RELATIONS
C.2 DERIVATIVES
C.3 INDEFINITE INTEGRALS
C.4 DEFINITE INTEGRALS
C.5 SERIES
C.6 LOGARITHMS
Appendix D: Summary of Probability Theory
Appendix E: Definition of a Few Special Functions
Appendix F: The Q(.) and erfc Functions
Appendix G: Fourier Transforms
Appendix H: Mathematical and Physical Constants
Index
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