An Introduction to Communication Theory and Systems

This book was written as a first treatment of statistical com­ munication theory and communication systems at a senior­ graduate level. The only formal prerequisite is a knowledge of ele­ mentary calculus; however, some familiarity with linear systems and transform theory will be helpful. Chapter 1 is introductory and contains no substantial techni­ cal material. Chapter 2 is an elementary introduction to probability theory at a nonrigorous and non abstract level. It is essential to the remainder of the book but may be skipped (or reviewed has­ tily) by any student who has taken a one-semester undergraduate course in probability. Chapter 3 is a brief treatment of random processes and spec­ tral analysis. It includes an introduction to shot noise (Sections 3.14-3.17) which is not subsequently used explicitly. Chapter 4 considers linear systems with random inputs. It includes a considerable amount of material on narrow-band sys­ tems and on the representation of random processes. Chapter5 treats the matched filter and the linear least mean-squared-error filter at an elementary level but in some detail. Numerous examples are provided throughout the book. Many of these are of an elementary nature and are intended merely to illustrate textual material. A reasonable number of problems of varying difficulty are provided. Instructors who adopt the text for classroom use may obtain a Solutions Manual for most of the problems by writing to the author.

1-Introduction.- 1.1-Communication Systems.- 1.2-Statistical Communication Theory.- 1.3-Additional Reading.- 2-Probability and Random Variables.- 2.1-Introductory Remarks.- 2.2-Elements of Set Theory.- 2.3-A Classical Concept of Probability.- 2.4-Elements of Combinatorial Analysis.- 2.5-The Axiomatic Foundation of Probability Theory.- 2.6-Finite Sample Spaces.- 2.7-Fields,?-Fields, and Infinite Sample Spaces.- 2.8-Independence.- 2.9-Random Variables, Discrete and Continuous.- 2.10-Distribution Functions and Densities.- 2.11-The Transformation of Random Variables.- 2.12-Expectation.- 2.13-Moments.- 2.14-The Chebychev Inequality.- 2.15-Generating Functions.- 2.16-The Binomial Distribution.- 2.17- The Poisson Distribution.- 2.18- The Normal or Gaussian Distribution.- 2.19- Limit Theorems.- 2.20- Bivariate Distributions.- 2.21- The Bivariate Normal Distribution.- 2.22- The Multivariate Normal Distribution.- 2.23- Linear Transformations on Normal Random Variables.- Problems.- References.- 3-Random Processes and Spectral Analysis.- 3.1- Definition.- 3.2- Stationarity.- 3.3- Correlation Functions.- 3.4- Time Averages and Ergodicity.- 3.5- Convergence of Random Variables.- 3.6- Fourier Transforms.- 3.7- Integrals of Random Processes.- 3.8- Power Spectra.- 3.9- Shot Noise.- 3.10- Random Events in Time.- 3.11- The Mean and Autocorrelation Function of Shot Noise.- 3.12- The Amplitude Distribution of Shot Noise.- Problems.- References.- 4-Linear Filtering of Stationary Processes:Steady-State Analysis.- 4.1-Introduction.- 4.2-Discrete-Time Filters.- 4.3-Continuous-Time Filters.- 4.4-Complete Statistical Description of the Output of a Linear System.- 4.5-The Orthogonal Decomposition of Random Processes; Fourier Series.- 4.6-The Karhunen-Loeve Expansion.- 4.7-Optimal Truncation Properties of the Karhunen-Loeve Expansion.- 4.8-The Sampling Theorem.- 4.9-Narrow-Band Systems.- 4.10-Narrow-Band Systems with Added Sinusoids.- Problems.- References.- 5-Optimum Linear Systems: Steady-State Synthesis.- 5.1-Introduction.- I -The Matched Filter For Continuous-Time Inputs.- 5.2-Derivation.- 5.3-The Unrealizable Matched Filter in Continuous Time.- 5.4-Spectral Factorization for Continuous-Parameter Random Processes.- 5.5-Solution of the Integral Equation for the Continuous- Time Matched Filter.- II -The Matched Filter for Discrete-Time Inputs.- 5.6-Derivation.- 5.7-The Unrealizable Matched Filter in Discrete Time.- 5.8-Spectral Factorization for Discrete-Parameter Random Processes.- 5.9-Solution of the Integral Equation for the Discrete-Time Matched Filter.- III -The Linear Least-Mean-Squared-Error Filter for Continuous-Time Inputs.- 5.10-Formulation of the LLMSE Filtering and Prediction Problem in Continuous Time.- 5.11-The Unrealizable LLMSE Filter in Continuous Time.- 5.12-Solution of the Integral Equation for the Continuous- Time LLMSE Filter.- 5.13-The Mean-Squared Error for the Continuous-Time Case.- 5.14-The Pure Prediction Problem for the Continuous-Time Case.- IV -The Linear Least-Mean-Squared-Error Filter for Discrete-Time Inputs.- 5.15-Formulation of the LLMSE Filtering and Prediction Problem in Discrete Time.- 5.16-The Unrealizable LLMSE Filter in Discrete Time.- 5.17-Solution of the Integral Equation for the Discrete-Time LLMSE Filter.- 5.18-The Mean-Squared Error for the Discrete-Time Case.- 5.19-The Pure Prediction Problem for the Discrete-Time Case.- Problems.- Appendices.- Appendix A -The Riemann-Stieltjes Integral.- Appendix B -The Dirac Delta Function.- Appendix C -The Transformation of Coordinates.- Appendix D -Fourier Series and the Fourier and Laplace Transforms.- Appendix E -Some Inequalities Including Schwarz’s Inequality.- Appendix F -The Calculus of Variations.- Table-The Unit Normal Distribution.