Introduction Signal Processing Transforms, Serhan Yarkan and Khalid A. QaraqeIntroductionBasic TransformationsFourier Series and TransformSamplingCosine and Sine TransformsLaplace TransformHartley TransformHilbert TransformDiscrete-Time Fourier TransformThe Z-TransformConclusion and Further Reading Linear Algebra, Fatemeh Hamidi Sepehr and Erchin SerpedinVector SpacesLinear TransformationsOperator Norms and Matrix NormsSystems of Linear EquationsDeterminant, Adjoint, and Inverse of a MatrixCramer’s Rule Unitary and Orthogonal Operators and MatricesLU DecompositionLDL and Cholesky DecompositionQR DecompositionHouseholder and Givens TransformationsBest Approximations and Orthogonal ProjectionsLeast Squares ApproximationsAngles between SubspacesEigenvalues and EigenvectorsSchur Factorization and Spectral TheoremSingular Value Decomposition (SVD)Rayleigh QuotientApplication of SVD and Rayleigh Quotient: Principal Component AnalysisSpecial MatricesMatrix OperationsFurther Studies Elements of Galois Fields, Tolga DumanGroups, Rings, and FieldsGalois FieldsPolynomials with Coefficients in GF(2)Construction of GF(2m)Some Notes on Applications of Finite Fields Numerical Analysis, Vivek Sarin Numerical ApproximationSensitivity and ConditioningComputer ArithmeticInterpolationNonlinear EquationsEigenvalues and Singular ValuesFurther Reading Combinatorics, Walter D. WallisTwo Principles of EnumerationPermutations and CombinationsThe Principle of Inclusion and ExclusionGenerating FunctionsRecurrence RelationsGraphsPaths and Cycles in GraphsTreesEncoding and DecodingLatin SquaresBalanced Incomplete Block DesignsConclusion Probability, Random Variables, and Stochastic Processes, Dinesh RajanIntroduction to ProbabilityRandom VariablesJoint Random VariablesRandom ProcessesMarkov ProcessSummary and Further Reading Random Matrix Theory, Romain Couillet and Merouane DebbahProbability NotationsSpectral Distribution of Random MatricesSpectral AnalysisStatistical InferenceApplicationsConclusion Large Deviations, Hongbin Li IntroductionConcentration InequalitiesRate FunctionCramer’s TheoremMethod of TypesSanov’s TheoremHypothesis TestingFurther Readings Fundamentals of Estimation Theory, Yik-Chung WuIntroductionBound on Minimum Variance — Cramer-Rao Lower BoundMVUE Using RBLS TheoremMaximum Likelihood EstimationLeast Squares (LS) EstimationRegularized LS EstimationBayesian EstimationFurther Reading Fundamentals of Detection Theory, Venugopal V. VeeravalliIntroductionBayesian Binary DetectionBinary Minimax DetectionBinary Neyman-Pearson DetectionBayesian Composite DetectionNeyman-Pearson Composite DetectionBinary Detection with Vector ObservationsSummary and Further Reading Monte Carlo Methods for Statistical Signal Processing, Xiaodong WangIntroduction Monte Carlo MethodsMarkov Chain Monte Carlo (MCMC) MethodsSequential Monte Carlo (SMC) MethodsConclusions and Further Readings Factor Graphs and Message Passing Algorithms, Ahmad Aitzaz, Erchin Serpedin, and Khalid A. QaraqeIntroduction Factor GraphsModeling Systems Using Factor GraphsRelationship with Other Probabilistic Graphical ModelsMessage Passing in Factor GraphsFactor Graphs with CyclesSome General Remarks on Factor GraphsSome Important Message Passing AlgorithmsApplications of Message Passing in Factor Graphs Unconstrained and Constrained Optimization Problems, Shuguang Cui, Man-Cho Anthony So, and Rui ZhangBasics of Convex AnalysisUnconstrained vs. Constrained OptimizationApplication Examples Linear Programming and Mixed Integer Programming, Bogdan DumitrescuLinear ProgrammingModeling Problems via Linear ProgrammingMixed Integer Programming Majorization Theory and Applications, Jiaheng Wang and Daniel PalomarMajorization TheoryApplications of Majorization Theory Conclusions and Further Readings Queueing Theory, Thomas ChenIntroductionMarkov ChainsQueueing ModelsM/M/1 QueueM/M/1/N QueueM/M/N/N QueueM/M/1 Queues in TandemM/G/1 QueueConclusions Network Optimization Techniques, Michal PioroIntroduction Basic Multicommodity Flow Networks Optimization ModelsOptimization Methods for Multicommodity Flow NetworksOptimization Models for Multistate NetworksConcluding Remarks Game Theory, Erik G. Larsson and Eduard JorswieckIntroduction Utility TheoryGames on the Normal FormNoncooperative Games and the Nash EquilibriumCooperative GamesGames with Incomplete InformationExtensive Form GamesRepeated Games and Evolutionary StabilityCoalitional Form/Characteristic Function FormMechanism Design and Implementation TheoryApplications to Signal Processing and CommunicationsAcknowledgments A Short Course on Frame Theory, Veniamin I. Morgenshtern and Helmut Bölcskei Examples of Signal ExpansionsSignal Expansions in Finite Dimensional Hilbert SpacesFrames for General Hilbert SpacesThe Sampling TheoremImportant Classes of Frames Index Exercises and References appear at the end of each chapter.
