Half Title
by Dinesh Rajan, Thomas Chen, Erchin Serpedin
Mathematical Foundations for Signal Processing, Communications, and Networking
- Cover
- Half Title
- Title Page
- Copyright Page
- Table of Contents
- List of Figures
- List of Tables
- Preface
- Editors
- List of Contributors
- List of Acronyms
- Notations and Symbols
- 1 Introduction
- 2 Signal Processing Transforms
- 2.1 Introduction
- 2.2 Basic Transformations
- 2.3 Fourier Series and Transform
- 2.4 Sampling
- 2.5 Cosine and Sine Transforms
- 2.6 Laplace Transform
- 2.7 Hartley Transform
- 2.8 Hilbert Transform
- 2.9 Discrete-Time Fourier Transform
- 2.10 The Z-Transform
- 2.11 Conclusion and Further Reading
- 2.12 Exercises
- References
- 3 Linear Algebra
- 3.1 Vector Spaces
- 3.2 Linear Transformations
- 3.3 Operator Norms and Matrix Norms
- 3.4 Systems of Linear Equations
- 3.5 Determinant, Adjoint, and Inverse of a Matrix
- 3.6 Cramer’s Rule
- 3.7 Unitary and Orthogonal Operators and Matrices
- 3.8 LU Decomposition
- 3.9 LDL and Cholesky Decomposition
- 3.10 QR Decomposition
- 3.11 Householder and Givens Transformations
- 3.12 Best Approximations and Orthogonal Projections
- 3.13 Least Squares Approximations
- 3.14 Angles Between Subspaces
- 3.15 Eigenvalues and Eigenvectors
- 3.16 Schur Factorization and Spectral Theorem
- 3.17 Singular Value Decomposition (SVD)
- 3.18 Rayleigh Quotient
- 3.19 Application of SVD and Rayleigh Quotient: Principal Component Analysis
- 3.20 Special Matrices
- 3.20.1 Block Matrices
- 3.20.2 Circulant Matrices
- 3.20.3 Toeplitz Matrices
- 3.20.4 Hankel Matrices
- 3.20.5 Vandermonde Matrices
- 3.20.6 Normal Matrices
- 3.20.7 Stochastic Matrices
- 3.20.8 Positive and Negative Definite Matrices
- 3.20.9 Matrix Condition Number
- 3.20.10 Sherman-Morrison-Woodbury Identity
- 3.20.11 Schur Complement
- 3.20.12 Generalized Inverses
- 3.21 Matrix Operations
- 3.22 References and Further Studies
- 3.23 Exercises
- References
- 4 Elements of Galois Fields
- 5 Numerical Analysis
- 6 Combinatorics
- 6.1 Two Principles of Enumeration
- 6.2 Permutations and Combinations
- 6.3 The Principle of Inclusion and Exclusion
- 6.4 Generating Functions
- 6.5 Recurrence Relations
- 6.6 Graphs
- 6.7 Paths and Cycles in Graphs
- 6.8 Trees
- 6.9 Encoding and Decoding
- 6.10 Latin Squares
- 6.11 Balanced Incomplete Block Designs
- 6.12 Conclusion
- 6.13 Exercises
- References
- 7 Probability, Random Variables, and Stochastic Processes
- 8 Random Matrix Theory
- 9 Large Deviations
- 10 Fundamentals of Estimation Theory
- 11 Fundamentals of Detection Theory
- 12 Monte Carlo Methods for Statistical Signal Processing
- 13 Factor Graphs and Message Passing Algorithms
- 13.1 Introduction
- 13.2 Factor Graphs
- 13.3 Modeling Systems Using Factor Graphs
- 13.4 Relationship with Other Probabilistic Graphical Models
- 13.5 Message Passing in Factor Graphs
- 13.6 Factor Graphs with Cycles
- 13.7 Some General Remarks on Factor Graphs
- 13.8 Some Important Message Passing Algorithms
- 13.9 Applications of Message Passing in Factor Graphs
- 13.10 Exercises
- References
- 14 Unconstrained and Constrained Optimization Problems
- 15 Linear Programming and Mixed Integer Programming
- 16 Majorization Theory and Applications
- 17 Queueing Theory
- 18 Network Optimization Techniques
- 19 Game Theory
- 19.1 Introduction
- 19.2 Utility Theory
- 19.3 Games on the Normal Form
- 19.4 Noncooperative Games and the Nash Equilibrium
- 19.5 Cooperative Games
- 19.6 Games with Incomplete Information
- 19.7 Extensive Form Games
- 19.8 Repeated Games and Evolutionary Stability
- 19.9 Coalitional Form/Characteristic Function Form
- 19.10 Mechanism Design and Implementation Theory
- 19.11 Applications to Signal Processing and Communications
- 19.12 Acknowledgments
- 19.13 Exercises
- References
- 20 A Short Course on Frame Theory
- Index
Mathematical Foundations
for
SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING
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