Probability and Random Processes with Applications to Signal Processing

【实例简介】
第三版 作者是Henry Stark 和 John. W. Woods UCSD指定教科书
To my father P D. Stark(in memoriam From darkness to light (1941-1945) To harriet J. W. Woods Contents reface 1 Introduction to Probability 1.1.. Introduction: Why Study Probability? 1.2 The Different Kinds of Probability A. Probability as intuition B Probability as the Ratio of Favorable to Total Outcomes Classical Theory C. Probability as a Measure of Frequency of occurrence D. Probability Based on an Axiomatic Theory 1.3 Misuses, Miscalculations, and Paradoxes in Probability 1122345577 1.4 Sets, Fields, and Events Examples of Sample spaces 1.5 Axiomatic Definition of Probability 11 1.6 Joint, Conditional, and Total Probabilities; Independence 16 1.7 Bayes'Theorem and Applications 1. 8 Combinatorics 24 Occupancy Problems Extensions and Applications 30 1.9 Bernoulli Trials--Binomial and Multinomial Probability Laws 32 Multinomial Probability law 36 1.10 Asymptotic Behavior of the Binomial Law: The Poisson Law 1.11 Normal Approximation to the Binomial Law 45 1.12 Summary 47 Problems References 57 Contents 2 Random variable 58 2.1 Introduction 2.2 Definition of a Random variable 59 2.3 Probability Distribution Function 62 2. 4 Probability Density Function(PDF) 66 Four Other Common Density Functions More Advanced Density Functions 74 2.5 Continuous, Discrete, and Mixed Random Variables 75 Examples of Probability Mass Functions 77 2.6 Conditional and Joint, Distributions and Densities 80 2.7 Failure rates 105 2.8 Sumary 108 Problems 109 References 115 Additional reading 115 3 Functions of Random Variables 116 3.1 Introduction 116 Functions of a, Random Variable(Several views 119 3.2 Solving Problems of the Type Y=g(X) 120 General Formula of Determining the pdf of y=g(X 3.3 Solving Problems of the Type Z=g(x,r) 134 3.4 Solving Problems of the Type V=gX,Y),w=h(X,Y) 152 Fundamental Problem 152 Obtaining fvw Directly from fXy 154 3.5 Additional Examples 157 3.6 Summary 161 Problems 162 Refe 168 Additional Reading 168 4 Expectation and Introduction to Estimation 169 4.1 Expected Value of a Random variable 169 On the validity of Equation 4. 1-8 172 4.2 Conditional Expectations 183 Conditional Expectation as a Random Variable 190 4.3 Moments 192 Joint moments 196 Properties of Uncorrelated Random Variables 198 Jointly gaussian Random Variables 201 Contours of Constant Density of the Joint Gaussian pdf 203 4.4 Chebyshev and Schwarz Inequalities 205 Random Variables with Nonnegative values 207 The Schwarz Inequality 208 Contents 4.5 Moment-Generating Functions 211 4.6 Chernoff bound 214 4.7 Characteristic Functions 216 Joint Characteristic Functions 222 The Central Limit Theorem 225 4.8 Estimators for the Mean and Variance of the normal law 230 Confidence intervals for the mean 231 Confidence interval for the variance 234 4.9 Summar 236 Problems 237 Refe 243 Additional reading 243 5 Random Vectors and Parameter Estimation 244 5.1 Joint Distribution and densities 5.2 Multiple Transformation of Random Variables 248 5.3 Expectation Vectors and Covariance Matrices 251 5.4 Properties of Covariance Matrices 254 5.5 Simultaneous Diagonalization of Two Covariance Matrices and Applications in Pattern Recognition 259 Projection 262 Maximization of Quadratic Forms 263 5.6 The Multidimensional Gaussian Law 269 5.7 Characteristic Functions of Random Vectors 277 The Characteristic Function of the Normal law 5.8 Parameter Estimation 282 Estimation of EX 284 5.9 Estimation of Vector Means and Covariance Matrices 286 Estimation of 286 Estimation of the covariance K 287 5.10 Maximum Likelihood Estimators 290 5. 11 Linear Estimation of Vector Parameters 294 5. 12 Summary 297 P roblems References Additional reading 303 6 Random sequences 304 6. 1 Basic Concepts 304 Infinite-Length Bernoulli Trials 310 Continuity of Probability Measure 315 Statistical Specification of a Random Sequence 317 6.2 Basic Principles of Discrete-Time Linear Systems 334 6.3 Random Sequences and Linear Systems 340 Contents 6.4 WSS Random Sequences 348 Power Spectral Density 351 Interpretation of the PsD 352 Synthesis of Random Sequences and Discrete-Time Simulation 355 Decimation Interpolation 359 6.5 Markov Random Sequences 362 ARMA Models 365 Markov chains 366 6.6 Vector Random Sequences and State Equations 6.7 Convergence of Random Sequences 375 6.8 Laws of Large Numbers 383 6.9 Summary 387 P roblems 388 References 399 7 Random Processes 401 7.1 Basic Definitions 7.2 Some Important Random Processes 406 Asynchronous Binary Signaling 406 Poisson Counting Process 408 Alternative Derivation of Poisson Process 412 Random Telegraph Signal 414 Digital Modulation Using Phase-Shift Keying 416 Wiener process or Brownian Motion 418 Markov Random Processes 421 Birth-Death Markov Chains 425 Chapman-Kolmogorov Equations 42 Random process Generated from Random Sequences 430 7. 3 Continuous-Time Linear Systems with Random Inputs 430 White noise 436 7.4 Some Useful Classifications of Random Processes 437 stationarity 437 7.5 Wide-Sense Stationary Processes and LSI Systems 439 Wide-Sense Stationary Case 440 Power Spectral Density 443 An Interpretation of the psd 444 More on white noise 448 Stationary Processes and Differential Equations 455 7.6 Periodic and Cyclostationary P1 458 7.7 Vector Processes and State Equations 464 State Equations 466 7. 8 Summary 469 Cont X Problems 46 References 486 8 Advanced Topics in Random Processes 487 8.1 Mean-Square(ms ) Calculus 487 Stochastic Continuity and Derivatives [8-1 487 Further Results on m.s. Convergence[8-11 497 8.2 m.S. Stochastic Integrals 502 8.3 m.s. Stochastic Differential equations 506 8.4 Ergodicity [8-3 511 8.5 Karhunen-Loeve Expansion [8-5 518 8.6 Representation of Bandlimited and Periodic Processes 524 Bandlimited processes 525 Bandpass random Processes 528 WSS Periodic Processes 530 Fourier series for WsS Processes 533 8.7 Summary 535 8. 8 Appendix: Integral Equations 535 Existence Theorem 536 Problems 540 References 551 9 Applications to Statistical Signal Processing 552 9.1 Estimation of Random Variables 552 More on the conditional mean 558 Orthogonality and Linear estimation 560 Some Properties of the Operator E 9.2 Innovation Sequences and Kalman Filtering 570 Predicting Gaussian Random Sequences 574 Kalman predictor and Filter Error- Co ce equati 581 9. 3 Wiener Filters for Random Sequences 585 Unrealizable Case(Smoothing) 585 Causal wiener Filter 587 9.4 Expectation-Maximization Algorithm 589 Log-Likelihood for the Linear Transformation 592 Summary of the E-m algorithm 594 E-M Algorithm for Exponential Probability Functions 594 A pplication to Emission Tomography 595 Log-likelihood Function of Complete Data 598 E-step 598 M-step 599 9.5 Hidden Markov Models(HMm Specification of an hMM 601 Contents Application to Speech Processing 604 Efficient Computation of P[E!M with a Recursive Algorithm 605 Viterbi algorithm and the most likely state Sequence for the Observations 607 9.6 Spectral Estimation 610 The periodogram 611 Bartlett s Procedure--Averaging Periodograms 614 Parametric Spectral Estimate 616 Maximum Entropy Spectral Density 620 9.7 Simulated Annealing 623 Gibbs sampler 624 Noncausal Gauss-Markov Models 625 Compound Markov Models 629 Gibbs Line Sequence 630 8 St 633 Problems 635 References Appendix A Review of Relevant Mathematics 641 A 1 Basic mathematics 641 Sequences 641 Convergence 642 Summations 643 Z-Transform 643 A 2 Continuous Mathematics 644 Definite and Indefinite Integrals Differentiation of Integrals Integration by Parts 646 Completing the Square 647 Double Integration Functions 648 A3 Residue Method for Inverse Fourier Transformation 649 Fact 650 Inverse Fourier Transform for psd of Random Sequence 653 A4 Mathenatical Induction [A-4 656 Axiom of Induction 656 References 657 Appendix B Gamma and Delta Functions 658 B. 1 Gamma Function 658 B2 Dirac Delta Function 659 Appendix C Functional Transformations and Jacobians 662 C 1 Introduction 【实例截图】
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