Mathematical Foundations for Signal Processing, Communications, and Networking

✍ Scribed by Erchin Serpedin (Editor); Thomas Chen (Editor); Dinesh Rajan (Editor)

• Publisher: CRC Press
• Year: 2012
• Leaves: 852
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Introduction

Signal Processing Transforms, Serhan Yarkan and Khalid A. Qaraqe

Introduction

Basic Transformations

Fourier Series and Transform

Sampling

Cosine and Sine Transforms

Laplace Transform

Hartley Transform

Hilbert Transform

Discrete-Time Fourier Transform

The Z-Transform

Conclusion and Further Reading

Linear Algebra, Fatemeh Hamidi Sepehr and Erchin Serpedin

Vector Spaces

Linear Transformations

Operator Norms and Matrix Norms

Systems of Linear Equations

Determinant, Adjoint, and Inverse of a Matrix

Cramer’s Rule

Unitary and Orthogonal Operators and Matrices

LU Decomposition

LDL and Cholesky Decomposition

QR Decomposition

Householder and Givens Transformations

Best Approximations and Orthogonal Projections

Least Squares Approximations

Angles between Subspaces

Eigenvalues and Eigenvectors

Schur Factorization and Spectral Theorem

Singular Value Decomposition (SVD)

Rayleigh Quotient

Application of SVD and Rayleigh Quotient: Principal Component Analysis

Special Matrices

Matrix Operations

Further Studies

Elements of Galois Fields, Tolga Duman

Groups, Rings, and Fields

Galois Fields

Polynomials with Coefficients in GF(2)

Construction of GF(2^m)

Some Notes on Applications of Finite Fields

Numerical Analysis, Vivek Sarin

Numerical Approximation

Sensitivity and Conditioning

Computer Arithmetic

Interpolation

Nonlinear Equations

Eigenvalues and Singular Values

Further Reading

Combinatorics, Walter D. Wallis

Two Principles of Enumeration

Permutations and Combinations

The Principle of Inclusion and Exclusion

Generating Functions

Recurrence Relations

Graphs

Paths and Cycles in Graphs

Trees

Encoding and Decoding

Latin Squares

Balanced Incomplete Block Designs

Conclusion

Probability, Random Variables, and Stochastic Processes, Dinesh Rajan

Introduction to Probability

Random Variables

Joint Random Variables

Random Processes

Markov Process

Summary and Further Reading

Random Matrix Theory, Romain Couillet and Merouane Debbah

Probability Notations

Spectral Distribution of Random Matrices

Spectral Analysis

Statistical Inference

Applications

Conclusion

Large Deviations, Hongbin Li

Introduction

Concentration Inequalities

Rate Function

Cramer’s Theorem

Method of Types

Sanov’s Theorem

Hypothesis Testing

Further Readings

Fundamentals of Estimation Theory, Yik-Chung Wu

Introduction

Bound on Minimum Variance — Cramer-Rao Lower Bound

MVUE Using RBLS Theorem

Maximum Likelihood Estimation

Least Squares (LS) Estimation

Regularized LS Estimation

Bayesian Estimation

Further Reading

Fundamentals of Detection Theory, Venugopal V. Veeravalli

Introduction

Bayesian Binary Detection

Binary Minimax Detection

Binary Neyman-Pearson Detection

Bayesian Composite Detection

Neyman-Pearson Composite Detection

Binary Detection with Vector Observations

Summary and Further Reading

Monte Carlo Methods for Statistical Signal Processing, Xiaodong Wang

Introduction

Monte Carlo Methods

Markov Chain Monte Carlo (MCMC) Methods

Sequential Monte Carlo (SMC) Methods

Conclusions and Further Readings

Factor Graphs and Message Passing Algorithms, Ahmad Aitzaz, Erchin Serpedin, and Khalid A. Qaraqe

Introduction

Factor Graphs

Modeling Systems Using Factor Graphs

Relationship with Other Probabilistic Graphical Models

Message Passing in Factor Graphs

Factor Graphs with Cycles

Some General Remarks on Factor Graphs

Some Important Message Passing Algorithms

Applications of Message Passing in Factor Graphs

Unconstrained and Constrained Optimization Problems, Shuguang Cui, Man-Cho Anthony So, and Rui Zhang

Basics of Convex Analysis

Unconstrained vs. Constrained Optimization

Application Examples

Linear Programming and Mixed Integer Programming, Bogdan Dumitrescu

Linear Programming

Modeling Problems via Linear Programming

Mixed Integer Programming

Majorization Theory and Applications, Jiaheng Wang and Daniel Palomar

Majorization Theory

Applications of Majorization Theory

Conclusions and Further Readings

Queueing Theory, Thomas Chen

Introduction

Markov Chains

Queueing Models

M/M/1 Queue

M/M/1/N Queue

M/M/N/N Queue

M/M/1 Queues in Tandem

M/G/1 Queue

Conclusions

Network Optimization Techniques, Michal Pioro

Introduction

Basic Multicommodity Flow Networks Optimization Models

Optimization Methods for Multicommodity Flow Networks

Optimization Models for Multistate Networks

Concluding Remarks

Game Theory, Erik G. Larsson and Eduard Jorswieck

Introduction

Utility Theory

Games on the Normal Form

Noncooperative Games and the Nash Equilibrium

Cooperative Games

Games with Incomplete Information

Extensive Form Games

Repeated Games and Evolutionary Stability

Coalitional Form/Characteristic Function Form

Mechanism Design and Implementation Theory

Applications to Signal Processing and Communications

Acknowledgments

A Short Course on Frame Theory, Veniamin I. Morgenshtern and Helmut Bölcskei

Examples of Signal Expansions

Signal Expansions in Finite Dimensional Hilbert Spaces

Frames for General Hilbert Spaces

The Sampling Theorem

Important Classes of Frames

Index

Exercises and References appear at the end of each chapter.

✦ Subjects

Computer Science;Systems & Computer Architecture;Networks;Engineering & Technology;Electrical & Electronic Engineering;Digital Signal Processing;Mathematics & Statistics for Engineers