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Introduction to Random Signals and Noise

Book Description

Random signals and noise are present in many engineering systems and networks. Signal processing techniques allow engineers to distinguish between useful signals in audio, video or communication equipment, and interference, which disturbs the desired signal.

With a strong mathematical grounding, this text provides a clear introduction to the fundamentals of stochastic processes and their practical applications to random signals and noise. With worked examples, problems, and detailed appendices, Introduction to Random Signals and Noise gives the reader the knowledge to design optimum systems for effectively coping with unwanted signals.

Key features:

  • Considers a wide range of signals and noise, including analogue, discrete-time and bandpass signals in both time and frequency domains.

  • Analyses the basics of digital signal detection using matched filtering, signal space representation and correlation receiver.

  • Examines optimal filtering methods and their consequences.

  • Presents a detailed discussion of the topic of Poisson processes and shot noise.

An excellent resource for professional engineers developing communication systems, semiconductor devices, and audio and video equipment, this book is also ideal for senior undergraduate and graduate students in Electronic and Electrical Engineering.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright
  4. Dedication
  5. Contents
  6. Preface
  7. Chapter 1: Introduction
    1. 1.1 RANDOM SIGNALS AND NOISE
    2. 1.2 MODELLING
    3. 1.3 THE CONCEPT OF A STOCHASTIC PROCESS
    4. 1.4 SUMMARY
  8. Chapter 2: Stochastic Processes
    1. 2.1 STATIONARY PROCESSES
    2. 2.2 CORRELATION FUNCTIONS
    3. 2.3 GAUSSIAN PROCESSES
    4. 2.4 COMPLEX PROCESSES
    5. 2.5 DISCRETE-TIME PROCESSES
    6. 2.6 SUMMARY
    7. 2.7 PROBLEMS
  9. Chapter 3: Spectra of Stochastic Processes
    1. 3.1 THE POWER SPECTRUM
    2. 3.2 THE BANDWIDTH OF A STOCHASTIC PROCESS
    3. 3.3 THE CROSS-POWER SPECTRUM
    4. 3.4 MODULATION OF STOCHASTIC PROCESSES
    5. 3.5 SAMPLING AND ANALOGUE-TO-DIGITAL CONVERSION
    6. 3.6 SPECTRUM OF DISCRETE-TIME PROCESSES
    7. 3.7 SUMMARY
    8. 3.8 PROBLEMS
  10. Chapter 4: Linear Filtering of Stochastic Processes
    1. 4.1 BASICS OF LINEAR TIME-INVARIANT FILTERING
    2. 4.2 TIME DOMAIN DESCRIPTION OF FILTERING OF STOCHASTIC PROCESSES
    3. 4.3 SPECTRA OF THE FILTER OUTPUT
    4. 4.4 NOISE BANDWIDTH
    5. 4.5 SPECTRUM OF A RANDOM DATA SIGNAL
    6. 4.6 PRINCIPLES OF DISCRETE-TIME SIGNALS AND SYSTEMS
    7. 4.7 DISCRETE-TIME FILTERING OF RANDOM SEQUENCES
    8. 4.8 SUMMARY
    9. 4.9 PROBLEMS
  11. Chapter 5: Bandpass Processes
    1. 5.1 DESCRIPTION OF DETERMINISTIC BANDPASS SIGNALS
    2. 5.2 QUADRATURE COMPONENTS OF BANDPASS PROCESSES
    3. 5.3 PROBABILITY DENSITY FUNCTIONS OF THE ENVELOPE AND PHASE OF BANDPASS NOISE
    4. 5.4 MEASUREMENT OF SPECTRA
    5. 5.5 SAMPLING OF BANDPASS PROCESSES
    6. 5.6 SUMMARY
    7. 5.7 PROBLEMS
  12. Chapter 6: Noise in Networks and Systems
    1. 6.1 WHITE AND COLOURED NOISE
    2. 6.2 THERMAL NOISE IN RESISTORS
    3. 6.3 THERMAL NOISE IN PASSIVE NETWORKS
    4. 6.4 SYSTEM NOISE
    5. 6.5 SUMMARY
    6. 6.6 PROBLEMS
  13. Chapter 7: Detection and Optimal Filtering
    1. 7.1 SIGNAL DETECTION
    2. 7.2 FILTERS THAT MAXIMIZE THE SIGNAL-TO-NOISE RATIO
    3. 7.3 THE CORRELATION RECEIVER
    4. 7.4 FILTERS THAT MINIMIZE THE MEAN-SQUARED ERROR
    5. 7.5 SUMMARY
    6. 7.6 PROBLEMS
  14. Chapter 8: Poisson Processes and Shot Noise
    1. 8.1 INTRODUCTION
    2. 8.2 THE POISSON DISTRIBUTION
    3. 8.3 THE HOMOGENEOUS POISSON PROCESS
    4. 8.4 INHOMOGENEOUS POISSON PROCESSES
    5. 8.5 THE RANDOM-PULSE PROCESS
    6. 8.6 SUMMARY
    7. 8.7 PROBLEMS
  15. References
  16. Further Reading
  17. Appendix A: Representation of Signals in a Signal Space
    1. A.1 LINEAR VECTOR SPACES
    2. A.2 THE SIGNAL SPACE CONCEPT
    3. A.3 GRAM-SCHMIDT ORTHOGONALIZATION
    4. A.4 THE REPRESENTATION OF NOISE IN SIGNAL SPACE
    5. A.5 SIGNAL CONSTELLATIONS
    6. A.6 PROBLEMS
  18. Appendix B: Attenuation, Phase Shift and Decibels
  19. Appendix C: Mathematical Relations
    1. C.1 TRIGONOMETRIC RELATIONS
    2. C.2 DERIVATIVES
    3. C.3 INDEFINITE INTEGRALS
    4. C.4 DEFINITE INTEGRALS
    5. C.5 SERIES
    6. C.6 LOGARITHMS
  20. Appendix D: Summary of Probability Theory
  21. Appendix E: Definition of a Few Special Functions
  22. Appendix F: The Q(.) and erfc Functions
  23. Appendix G: Fourier Transforms
  24. Appendix H: Mathematical and Physical Constants
  25. Index