## Book description

Mathematical Foundations for Signal Processing, Communications, and Networking describes mathematical concepts and results important in the design, analysis, and optimization of signal processing algorithms, modern communication systems, and networks. Helping readers master key techniques and comprehend the current research literature, the book offers a comprehensive overview of methods and applications from linear algebra, numerical analysis, statistics, probability, stochastic processes, and optimization.

From basic transforms to Monte Carlo simulation to linear programming, the text covers a broad range of mathematical techniques essential to understanding the concepts and results in signal processing, telecommunications, and networking. Along with discussing mathematical theory, each self-contained chapter presents examples that illustrate the use of various mathematical concepts to solve different applications. Each chapter also includes a set of homework exercises and readings for additional study.

This text helps readers understand fundamental and advanced results as well as recent research trends in the interrelated fields of signal processing, telecommunications, and networking. It provides all the necessary mathematical background to prepare students for more advanced courses and train specialists working in these areas.

1. Cover
2. Half Title
3. Title Page
6. List of Figures
7. List of Tables
8. Preface
9. Editors
10. List of Contributors
11. List of Acronyms
12. Notations and Symbols
13. 1 Introduction
14. 2 Signal Processing Transforms
1. 2.1 Introduction
2. 2.2 Basic Transformations
3. 2.3 Fourier Series and Transform
4. 2.4 Sampling
5. 2.5 Cosine and Sine Transforms
6. 2.6 Laplace Transform
7. 2.7 Hartley Transform
8. 2.8 Hilbert Transform
9. 2.9 Discrete-Time Fourier Transform
10. 2.10 The Z-Transform
11. 2.11 Conclusion and Further Reading
12. 2.12 Exercises
13. References
15. 3 Linear Algebra
1. 3.1 Vector Spaces
2. 3.2 Linear Transformations
3. 3.3 Operator Norms and Matrix Norms
4. 3.4 Systems of Linear Equations
5. 3.5 Determinant, Adjoint, and Inverse of a Matrix
6. 3.6 Cramer’s Rule
7. 3.7 Unitary and Orthogonal Operators and Matrices
8. 3.8 LU Decomposition
9. 3.9 LDL and Cholesky Decomposition
10. 3.10 QR Decomposition
11. 3.11 Householder and Givens Transformations
12. 3.12 Best Approximations and Orthogonal Projections
13. 3.13 Least Squares Approximations
14. 3.14 Angles Between Subspaces
15. 3.15 Eigenvalues and Eigenvectors
16. 3.16 Schur Factorization and Spectral Theorem
17. 3.17 Singular Value Decomposition (SVD)
18. 3.18 Rayleigh Quotient
19. 3.19 Application of SVD and Rayleigh Quotient: Principal Component Analysis
20. 3.20 Special Matrices
21. 3.21 Matrix Operations
22. 3.22 References and Further Studies
23. 3.23 Exercises
24. References
16. 4 Elements of Galois Fields
1. 4.1 Groups, Rings, and Fields
2. 4.2 Galois Fields
3. 4.3 Polynomials with Coefficients in GF(2)
4. 4.4 Construction of GF(2m)
5. 4.5 Some Notes on Applications of Finite Fields
6. 4.6 Exercises
7. References
17. 5 Numerical Analysis
1. 5.1 Numerical Approximation
2. 5.2 Sensitivity and Conditioning
3. 5.3 Computer Arithmetic
4. 5.4 Interpolation
5. 5.5 Nonlinear Equations
6. 5.6 Eigenvalues and Singular Values
8. 5.8 Exercises
9. References
18. 6 Combinatorics
19. 7 Probability, Random Variables, and Stochastic Processes
1. 7.1 Introduction to Probability
2. 7.2 Random Variables
3. 7.3 Joint Random Variables
4. 7.4 Random Processes
5. 7.5 Markov Process
6. 7.6 Summary and Further Reading
7. 7.7 Exercises
8. References
20. 8 Random Matrix Theory
1. 8.1 Probability Notations
2. 8.2 Spectral Distribution of Random Matrices
3. 8.3 Spectral Analysis
4. 8.4 Statistical Inference
5. 8.5 Applications
6. 8.6 Conclusion
7. 8.7 Exercises
8. References
21. 9 Large Deviations
22. 10 Fundamentals of Estimation Theory
1. 10.1 Introduction
2. 10.2 Bound on Minimum Variance – Cramér-Rao Lower Bound
3. 10.3 MVUE Using RBLS Theorem
4. 10.4 Maximum Likelihood Estimation
5. 10.5 Least Squares Estimation
6. 10.6 Regularized LS Estimation
7. 10.7 Bayesian Estimation
8. 10.8 References and Further Reading
9. 10.9 Exercises
10. References
23. 11 Fundamentals of Detection Theory
1. 11.1 Introduction
2. 11.2 Bayesian Binary Detection
3. 11.3 Binary Minimax Detection
4. 11.4 Binary Neyman-Pearson Detection
5. 11.5 Bayesian Composite Detection
6. 11.6 Neyman-Pearson Composite Detection
7. 11.7 Binary Detection with Vector Observations
8. 11.8 Summary and Further Reading
9. 11.9 Exercises
10. References
24. 12 Monte Carlo Methods for Statistical Signal Processing
1. 12.1 Introduction
2. 12.2 Monte Carlo Methods
3. 12.3 Markov Chain Monte Carlo (MCMC) Methods
4. 12.4 Sequential Monte Carlo (SMC) Methods
5. 12.5 Conclusions and Further Readings
6. 12.6 Exercises
7. References
25. 13 Factor Graphs and Message Passing Algorithms
1. 13.1 Introduction
2. 13.2 Factor Graphs
3. 13.3 Modeling Systems Using Factor Graphs
4. 13.4 Relationship with Other Probabilistic Graphical Models
5. 13.5 Message Passing in Factor Graphs
6. 13.6 Factor Graphs with Cycles
7. 13.7 Some General Remarks on Factor Graphs
8. 13.8 Some Important Message Passing Algorithms
9. 13.9 Applications of Message Passing in Factor Graphs
10. 13.10 Exercises
11. References
26. 14 Unconstrained and Constrained Optimization Problems
1. 14.1 Basics of Convex Analysis
2. 14.2 Unconstrained vs. Constrained Optimization
3. 14.3 Application Examples
4. 14.4 Exercises
5. References
27. 15 Linear Programming and Mixed Integer Programming
1. 15.1 Linear Programming
2. 15.2 Modeling Problems via Linear Programming
3. 15.3 Mixed Integer Programming
4. 15.4 Historical Notes and Further Reading
5. 15.5 Exercises
6. References
28. 16 Majorization Theory and Applications
1. 16.1 Majorization Theory
2. 16.2 Applications of Majorization Theory
3. 16.3 Conclusions and Further Readings
4. 16.4 Exercises
5. References
29. 17 Queueing Theory
1. 17.1 Introduction
2. 17.2 Markov Chains
3. 17.3 Queueing Models
4. 17.4 M/M/1 Queue
5. 17.5 M/M/1/N Queue
6. 17.6 M/M/N/N Queue
7. 17.7 M/M/1 Queues in Tandem
8. 17.8 M/G/1 Queue
9. 17.9 Conclusions
10. 17.10 Exercises
11. References
30. 18 Network Optimization Techniques
1. 18.1 Introduction
2. 18.2 Basic Multicommodity Flow Networks Optimization Models
3. 18.3 Optimization Methods for Multicommodity Flow Networks
4. 18.4 Optimization Models for Multistate Networks
5. 18.5 Concluding Remarks
6. 18.6 Exercises
7. References
31. 19 Game Theory
1. 19.1 Introduction
2. 19.2 Utility Theory
3. 19.3 Games on the Normal Form
4. 19.4 Noncooperative Games and the Nash Equilibrium
5. 19.5 Cooperative Games
6. 19.6 Games with Incomplete Information
7. 19.7 Extensive Form Games
8. 19.8 Repeated Games and Evolutionary Stability
9. 19.9 Coalitional Form/Characteristic Function Form
10. 19.10 Mechanism Design and Implementation Theory
11. 19.11 Applications to Signal Processing and Communications
12. 19.12 Acknowledgments
13. 19.13 Exercises
14. References
32. 20 A Short Course on Frame Theory
1. 20.1 Examples of Signal Expansions
2. 20.2 Signal Expansions in Finite-Dimensional Spaces
3. 20.3 Frames for General Hilbert Spaces
4. 20.4 The Sampling Theorem
5. 20.5 Important Classes of Frames
6. 20.6 Exercises
7. References
33. Index

## Product information

• Title: Mathematical Foundations for Signal Processing, Communications, and Networking
• Author(s): Erchin Serpedin, Thomas Chen, Dinesh Rajan
• Release date: December 2017
• Publisher(s): CRC Press
• ISBN: 9781466514089