List of Contributors
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
Aitzaz Ahmad
Texas A&M University
College Station, USA
Helmut Bölcskei
ETH Zurich
Switzerland
Thomas Chen
Swansea University
Wales, UK
Romain Couillet
L’École Supérieure D’Électricité (SUPELEC)
France
Shuguang Cui
Texas A&M University
College Station, USA
Merouane Debbah
L’École Supérieure D’Électricité (SUPELEC)
France
Tolga M. Duman
Arizona State University
Tempe, USA
Bogdan Dumitrescu
Tampere University of Technology
Finland
Eduard Jorswieck
Technical University of Dresden
Germany
Erik G. Larsson
Linkoping University
Sweden
Hongbin Li
Stevens Institute of Technology
Hoboken, NJ, USA
Veniamin I. Morgenshtern
ETH Zurich
Switzerland
Daniel Palomar
Hong Kong University of Science and Technology
Michał Pióro
Lund University
Sweden
Warsaw University of Technology
Poland
Khalid Qaraqe
Texas A&M University at Qatar
Dinesh Rajan
Southern Methodist University
Dallas, USA
Vivek Sarin
Texas A&M University
College Station, USA
Erchin Serpedin
Texas A&M University
College Station, USA
Anthony Man-Cho So
The Chinese University of Hong Kong
Hong Kong, China
Fatemeh Hamidi Sepehr
Texas A&M University
College Station, USA
Venugopal V. Veeravalli
University of Illinois at Urbana-Champaign
USA
Walter D. Wallis
Southern Illinois University
Carbondale, USA
Jiaheng Wang
KTH Royal Institute of Technology
Stockholm, Sweden
Xiaodong Wang
Columbia University
New York, USA
Yik-Chung Wu
University of Hong Kong
Serhan Yarkan
Texas A&M University
College Station, USA
Rui Zhang
National University of Singapore
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