راهنمای تحلیل سری‌های زمانی، پردازش سیگنال و دینامیک

The aim of this book is to serve as a graduate text and reference in time series analysis and signal processing, two closely related subjects that are the concern of a wide range of disciplines, such as statistics, electrical engineering, mechanical engineering and physics. The book provides a CD-ROM containing codes in PASCAL and C for the computer procedures printed in the book. It also furnishes a complete program devoted to the statistical analysis of time series, which will be attractive to a wide range of academics working in diverse mathematical disciplines. Preface......Page 25 Introduction......Page 27 The Frequency Domain and the Time Domain......Page 29 Harmonic Analysis......Page 30 Autoregressive and Moving-Average Models......Page 33 Generalised Harmonic Analysis......Page 36 The Equivalence of the Two Domains......Page 38 The Maturing of Time-Series Analysis......Page 40 Mathematical Appendix......Page 42 Polynomial Methods......Page 47 Sequences......Page 49 Linear Convolution......Page 52 Circular Convolution......Page 54 Time-Series Models......Page 56 Transfer Functions......Page 57 The Lag Operator......Page 59 Periodic Polynomials and Circular Convolution......Page 61 Polynomial Factorisation......Page 63 Complex Roots......Page 64 The Roots of Unity......Page 68 The Polynomial of Degree n......Page 69 Matrices and Polynomial Algebra......Page 71 Lower-Triangular Toeplitz Matrices......Page 72 Circulant Matrices......Page 74 The Factorisation of Circulant Matrices......Page 76 Euclid's Algorithm......Page 81 Partial Fractions......Page 85 The Expansion of a Rational Function......Page 88 Recurrence Relationships......Page 90 Laurent Series......Page 93 Analytic Functions......Page 96 Complex Line Integrals......Page 98 The Cauchy Integral Theorem......Page 100 Multiply Connected Domains......Page 102 Integrals and Derivatives of Analytic Functions......Page 103 Series Expansions......Page 104 Residues......Page 108 The Autocovariance Generating Function......Page 110 The Argument Principle......Page 112 Polynomial Computations......Page 115 Polynomials and their Derivatives......Page 116 The Division Algorithm......Page 120 Roots of Polynomials......Page 124 Real Roots......Page 125 Complex Roots......Page 130 Müller's Method......Page 135 Polynomial Interpolation......Page 140 Lagrangean Interpolation......Page 141 Divided Differences......Page 143 Difference Equations and Differential Equations......Page 147 Linear Difference Equations......Page 148 Solution of the Homogeneous Difference Equation......Page 149 Complex Roots......Page 150 Particular Solutions......Page 152 Solutions of Difference Equations with Initial Conditions......Page 155 Alternative Forms for the Difference Equation......Page 159 Linear Differential Equations......Page 161 Solution of the Homogeneous Differential Equation......Page 162 Differential Equation with Complex Roots......Page 163 Particular Solutions for Differential Equations......Page 165 Solutions of Differential Equations with Initial Conditions......Page 170 Difference and Differential Equations Compared......Page 173 Conditions for the Stability of Differential Equations......Page 174 Conditions for the Stability of Difference Equations......Page 177 The State-Space Equations......Page 187 Conversions of Difference Equations to State-Space Form......Page 189 Controllable Canonical State-Space Representations......Page 191 Observable Canonical Forms......Page 194 Reduction of State-Space Equations to a Transfer Function......Page 196 Controllability......Page 197 Observability......Page 202 Least-Squares Methods......Page 205 Matrix Computations......Page 207 Solving Linear Equations by Gaussian Elimination......Page 208 Inverting Matrices by Gaussian Elimination......Page 214 The Direct Factorisation of a Nonsingular Matrix......Page 215 The Cholesky Decomposition......Page 217 Householder Transformations......Page 221 The Q--R Decomposition of a Matrix of Full Column Rank......Page 222 The Linear Regression Model......Page 227 The Decomposition of the Sum of Squares......Page 228 Some Statistical Properties of the Estimator......Page 230 Estimating the Variance of the Disturbance......Page 231 Some Matrix Identities......Page 232 Computing a Regression via Gaussian Elimination......Page 234 Calculating the Corrected Sum of Squares......Page 237 Computing the Regression Parameters via the Q--R Decomposition......Page 241 The Normal Distribution and the Sampling Distributions......Page 244 Hypothesis Concerning the Complete Set of Coefficients......Page 245 Hypotheses Concerning a Subset of the Coefficients......Page 247 An Alternative Formulation of the F statistic......Page 249 Recursive Least-Squares Regression......Page 253 The Matrix Inversion Lemma......Page 254 Prediction Errors and Recursive Residuals......Page 255 The Updating Algorithm for Recursive Least Squares......Page 257 Initiating the Recursion......Page 261 Estimators with Limited Memories......Page 262 The Kalman Filter......Page 265 Filtering......Page 267 A Summary of the Kalman Equations......Page 270 An Alternative Derivation of the Kalman Filter......Page 271 Innovations and the Information Set......Page 273 Conditional Expectations and Dispersions of the State Vector......Page 275 The Classical Smoothing Algorithms......Page 276 Variants of the Classical Algorithms......Page 280 Multi-step Prediction......Page 283 Polynomial Regression......Page 287 The Gram--Schmidt Orthogonalisation Procedure......Page 289 A Modified Gram--Schmidt Procedure......Page 292 Uniqueness of the Gram Polynomials......Page 294 Recursive Generation of the Polynomials......Page 296 The Polynomial Regression Procedure......Page 298 Grafted Polynomials......Page 304 B-Splines......Page 307 Recursive Generation of B-spline Ordinates......Page 310 Regression with B-Splines......Page 316 Smoothing with Cubic Splines......Page 319 Cubic Spline Interpolation......Page 320 Cubic Splines and Bézier Curves......Page 327 The Minimum-Norm Property of Splines......Page 331 Smoothing Splines......Page 333 A Stochastic Model for the Smoothing Spline......Page 339 Appendix: The Wiener Process and the IMA Process......Page 345 Conditions of Optimality......Page 349 Univariate Search......Page 352 Quadratic Interpolation......Page 354 Bracketing the Minimum......Page 361 Unconstrained Optimisation via Quadratic Approximations......Page 364 The Method of Steepest Descent......Page 365 The Newton--Raphson Method......Page 366 A Modified Newton Procedure......Page 367 The Minimisation of a Sum of Squares......Page 369 Quadratic Convergence......Page 370 The Conjugate Gradient Method......Page 373 Numerical Approximations to the Gradient......Page 377 Quasi-Newton Methods......Page 378 Rank-Two Updating of the Hessian Matrix......Page 380 Fourier Methods......Page 389 Fourier Series and Fourier Integrals......Page 391 Fourier Series......Page 393 Convolution......Page 397 Fourier Approximations......Page 400 Discrete-Time Fourier Transform......Page 403 Symmetry Properties of the Fourier Transform......Page 404 The Frequency Response of a Discrete-Time System......Page 406 The Fourier Integral......Page 410 The Uncertainty Relationship......Page 412 The Delta Function......Page 414 Impulse Trains......Page 417 The Sampling Theorem......Page 418 The Frequency Response of a Continuous-Time System......Page 420 Appendix of Trigonometry......Page 422 Orthogonality Conditions......Page 423 The Discrete Fourier Transform......Page 425 Trigonometrical Representation of the DFT......Page 426 Determination of the Fourier Coefficients......Page 429 The Periodogram and Hidden Periodicities......Page 431 The Periodogram and the Empirical Autocovariances......Page 434 The Exponential Form of the Fourier Transform......Page 436 Leakage from Nonharmonic Frequencies......Page 439 The Fourier Transform and the z-Transform......Page 440 The Classes of Fourier Transforms......Page 442 Sampling in the Time Domain......Page 444 Truncation in the Time Domain......Page 447 Sampling in the Frequency Domain......Page 448 Appendix: Harmonic Cycles......Page 449 Basic Concepts......Page 453 The Two-Factor Case......Page 457 The FFT for Arbitrary Factors......Page 460 Locating the Subsequences......Page 463 The Core of the Mixed-Radix Algorithm......Page 465 Unscrambling......Page 468 The Shell of the Mixed-Radix Procedure......Page 471 The Base-2 Fast Fourier Transform......Page 473 FFT Algorithms for Real Data......Page 476 FFT for a Single Real-valued Sequence......Page 478 Time-Series Models......Page 483 Frequency Response and Transfer Functions......Page 485 Computing the Gain and Phase Functions......Page 492 The Poles and Zeros of the Filter......Page 495 Inverse Filtering and Minimum-Phase Filters......Page 501 Linear-Phase Filters......Page 503 Locations of the Zeros of Linear-Phase Filters......Page 505 FIR Filter Design by Window Methods......Page 509 Truncating the Filter......Page 513 Cosine Windows......Page 518 Design of Recursive IIR Filters......Page 522 IIR Design via Analogue Prototypes......Page 524 The Butterworth Filter......Page 525 The Chebyshev Filter......Page 527 The Bilinear Transformation......Page 530 The Butterworth and Chebyshev Digital Filters......Page 532 Frequency-Band Transformations......Page 533 Autoregressive and Moving-Average Processes......Page 539 Stationary Stochastic Processes......Page 540 Moving-Average Processes......Page 543 Computing the MA Autocovariances......Page 547 MA Processes with Common Autocovariances......Page 548 Computing the MA Parameters from the Autocovariances......Page 549 The Autocovariances and the Yule--Walker Equations......Page 554 Computing the AR Parameters......Page 561 Autoregressive Moving-Average Processes......Page 566 Calculating the ARMA Parameters from the Autocovariances......Page 571 Time-Series Analysis in the Frequency Domain......Page 575 The Filtering of White Noise......Page 576 Cyclical Processes......Page 579 The Fourier Representation of a Sequence......Page 581 The Spectral Representation of a Stationary Process......Page 582 The Autocovariances and the Spectral Density Function......Page 585 The Theorem of Herglotz and the Decomposition of Wold......Page 587 The Frequency-Domain Analysis of Filtering......Page 590 The Spectral Density Functions of ARMA Processes......Page 592 Canonical Factorisation of the Spectral Density Function......Page 596 Prediction and Signal Extraction......Page 601 Mean-Square Error......Page 602 Predicting one Series from Another......Page 603 The Technique of Prewhitening......Page 605 Extrapolation of Univariate Series......Page 606 Forecasting with ARIMA Models......Page 609 Generating the ARMA Forecasts Recursively......Page 611 Physical Analogies for the Forecast Function......Page 613 Interpolation and Signal Extraction......Page 615 Extracting the Trend from a Nonstationary Sequence......Page 617 Finite-Sample Predictions: Hilbert Space Terminology......Page 619 Recursive Prediction: The Durbin--Levinson Algorithm......Page 620 A Lattice Structure for the Prediction Errors......Page 625 Recursive Prediction: The Gram--Schmidt Algorithm......Page 627 Signal Extraction from a Finite Sample: the Stationary Case......Page 633 Signal Extraction from a Finite Sample: the Nonstationary Case......Page 635 Time-Series Estimation......Page 643 Estimating the Mean of a Stationary Process......Page 645 Asymptotic Variance of the Sample Mean......Page 647 Estimating the Autocovariances of a Stationary Process......Page 648 Asymptotic Moments of the Sample Autocovariances......Page 650 Asymptotic Moments of the Sample Autocorrelations......Page 652 Calculation of the Autocovariances......Page 655 Inefficient Estimation of the MA Autocovariances......Page 658 Efficient Estimates of the MA Autocorrelations......Page 660 Representations of the ARMA Equations......Page 663 The Least-Squares Criterion Function......Page 665 The Yule--Walker Estimates......Page 667 Estimation of MA Models......Page 668 Representations via LT Toeplitz Matrices......Page 669 Representations via Circulant Matrices......Page 671 The Gauss--Newton Estimation of the ARMA Parameters......Page 674 An Implementation of the Gauss--Newton Procedure......Page 675 Asymptotic Properties of the Least-Squares Estimates......Page 681 The Sampling Properties of the Estimators......Page 683 The Burg Estimator......Page 686 Matrix Representations of Autoregressive Models......Page 693 The AR Dispersion Matrix and its Inverse......Page 695 Density Functions of the AR Model......Page 698 The Exact M-L Estimator of an AR Model......Page 699 Conditional M-L Estimates of an AR Model......Page 702 Matrix Representations of Moving-Average Models......Page 704 The MA Dispersion Matrix and its Determinant......Page 705 Density Functions of the MA Model......Page 706 The Exact M-L Estimator of an MA Model......Page 707 Conditional M-L Estimates of an MA Model......Page 711 Matrix Representations of ARMA models......Page 712 Density Functions of the ARMA Model......Page 713 Exact M-L Estimator of an ARMA Model......Page 714 Nonparametric Estimation of the Spectral Density Function......Page 723 The Spectrum and the Periodogram......Page 724 The Expected Value of the Sample Spectrum......Page 728 Asymptotic Distribution of The Periodogram......Page 731 Smoothing the Periodogram......Page 736 Weighting the Autocovariance Function......Page 739 Weights and Kernel Functions......Page 740 Statistical Appendix: on Disc......Page 747 Multivariate Density Functions......Page 749 Functions of Random Vectors......Page 751 Expectations......Page 752 Moments of a Multivariate Distribution......Page 753 Degenerate Random Vectors......Page 755 The Multivariate Normal Distribution......Page 756 Distributions Associated with the Normal Distribution......Page 759 Quadratic Functions of Normal Vectors......Page 760 The Decomposition of a Chi-square Variate......Page 762 Limit Theorems......Page 765 Stochastic Convergence......Page 766 The Law of Large Numbers and the Central Limit Theorem......Page 771 Principles of Estimation......Page 775 Identifiability......Page 776 The Information Matrix......Page 779 The Efficiency of Estimation......Page 780 Unrestricted Maximum-Likelihood Estimation......Page 782 Restricted Maximum-Likelihood Estimation......Page 784 Tests of the Restrictions......Page 787 Index......Page 791 The CRC Materials Science and Engineering Handbook, Third Edition is the most comprehensive source available for data on engineering materials. Organized in an easy-to-follow format based on materials properties, this definitive reference features data verified through major professional societies in the materials field, such as ASM International and the American Ceramic Society. The third edition has been significantly expanded, most notably by the addition of new tabular material for a wide range of nonferrous alloys and various composite materials. For engineers making, selecting, or evaluating materials, this one, compact volume provides the ideal starting point. It is exceptionally easy to search-the authors have organized it according to materials properties, provided a key word indexing system, and placed many data sets in a convenient Selection Section where materials can be compared by property value, a feature ideal for design applications. A bestseller since its first edition, the CRC Materials Science and Engineering Handbook stands alone as a the consummate reference for data on the full spectrum of engineering materials. The aim of this book is to serve as a graduate text and reference in time series analysis and signal processing, two closely related subjects that are the concern of a wide range of disciplines, such as statistics, electrical engineering, mechanical engineering and physics.
The book provides a CD-ROM containing codes in PASCAL and C for the computer procedures printed in the book. It also furnishes a complete program devoted to the statistical analysis of time series, which will be attractive to a wide range of academics working in diverse mathematical disciplines.
Earlier editions of this work have established it as the definitive materials science reference for practically all scientists and engineers. This third edition retains the carefully thought out design and unique index format, and adds 700 pages of critical information in key areas of materials science, making it an indispensable source of useful information on important engineering materials. The aim of this book is to serve as a graduate text and reference in time series analysis and signal processing, two closely related subjects that are the concern of a wide range of disciplines, such as statistics, electrical engineering, mechanical engineering and physics. CD-ROM contains codes in PASCAL and C for the computer procedures printed in the book. Features data verified through major professional societies in the materials field, such as ASM International and the American Ceramic Society. This work covers a range of nonferrous alloys and various composite materials. It provides a key word indexing system and contains data sets in a single section that compares materials by property value.