Mathematical Foundations for Signal Processing, Communications, and Networking: 1st Edition (Paperback) book cover

Mathematical Foundations for Signal Processing, Communications, and Networking

1st Edition

Edited by Erchin Serpedin, Thomas Chen, Dinesh Rajan

CRC Press

858 pages | 54 Color Illus. | 138 B/W Illus.

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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.


"Here is a book providing the mathematical tools for a large range of researchers, more precisely for future researchers. First, we remark that the involved range is quite new, since many books give mathematical tools for signal processing, for communications or for networking. But this volume gives the tools for all three domains. In this way, a large group of students and researchers is addressed. Therefore the diversity of the subjects is larger. … the chapters are written by well-known active workers in the domain. … The included examples are interesting and suggestive. … The book will be helpful for students and researchers to be acquainted with the recent trends in the areas included in the book. We think we are faced with an excellent book that will soon become a standard reference in the respective areas."

—Dumitru Stanomir (Bucuresti), Zentralblatt MATH, 1254 — 1

Table of Contents


Signal Processing Transforms, Serhan Yarkan and Khalid A. Qaraqe


Basic Transformations

Fourier Series and Transform


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(2m)

Some Notes on Applications of Finite Fields

Numerical Analysis, Vivek Sarin

Numerical Approximation

Sensitivity and Conditioning

Computer Arithmetic


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


Paths and Cycles in Graphs


Encoding and Decoding

Latin Squares

Balanced Incomplete Block Designs


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



Large Deviations, Hongbin Li


Concentration Inequalities

Rate Function

Cramer’s Theorem

Method of Types

Sanov’s Theorem

Hypothesis Testing

Further Readings

Fundamentals of Estimation Theory, Yik-Chung Wu


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


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


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


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


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


Network Optimization Techniques, Michal Pioro


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


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


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


Exercises and References appear at the end of each chapter.

About the Editors

Erchin Serpedin is a professor in the Department of Electrical Engineering at Texas A&M University. Dr. Serpedin has been an associate editor of several journals and has received numerous honors, including a National Science Foundation CAREER Award, a National Research Council Fellow Award, and an American Society for Engineering Education Fellow Award. His research focuses on statistical signal processing, wireless communications, and bioinformatics.

Thomas Chen is a professor of networks at Swansea University. Dr. Chen is technical editor for IEEE Press, editor-in-chief of IEEE Network, senior editor of IEEE Communications Magazine, and associate editor of International Journal of Security and Networks, Journal on Security and Communication Networks, and International Journal of Digital Crime and Forensics. His research areas encompass web filtering, web classification, traffic classification, smart grid security, privacy, cyber crime, and malware.

Dinesh Rajan is an associate professor in the Department of Electrical Engineering at Southern Methodist University. An IEEE senior member, Dr. Rajan has received several awards, including a National Science Foundation CAREER Award. His research interests include communications theory, wireless networks, information theory, and computational imaging.

Subject Categories

BISAC Subject Codes/Headings:
COMPUTERS / Networking / General