Preface |
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xi | |
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1 Introduction to Measurement Systems |
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1 | (6) |
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1 | (2) |
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3 | (1) |
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4 | (3) |
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7 | (8) |
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7 | (2) |
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9 | (1) |
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2.3 Consequences of the Axioms |
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10 | (1) |
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2.4 Conditional Probability |
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11 | (1) |
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12 | (1) |
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2.6 Statistically Independent Events |
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13 | (1) |
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14 | (1) |
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3 Statistics of Random Processes |
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15 | (50) |
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3.1 Univariate Continuous Random Variables |
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16 | (4) |
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3.2 Discrete Random Variables |
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20 | (4) |
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3.3 Jointly Distributed Random Variables |
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24 | (2) |
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26 | (8) |
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3.5 Second-Order Statistics: Matrix Forms |
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34 | (5) |
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3.6 Stationary Random Processes |
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39 | (1) |
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3.7 Continuous-Time Covariance and Correlation |
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40 | (1) |
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41 | (2) |
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3.9 Multivariate Normal Density |
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43 | (2) |
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45 | (1) |
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3.11 Functions of Random Variables |
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46 | (4) |
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50 | (5) |
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3.13 Central Limit Theorem |
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55 | (1) |
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56 | (5) |
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61 | (4) |
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4 Spatiotemporal Models of the Measurement Process |
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65 | (27) |
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65 | (1) |
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4.2 Measurement Equations |
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65 | (7) |
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4.3 Signal Modeling Tools |
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72 | (9) |
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4.4 An Ultrasonic Measurement |
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81 | (3) |
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4.5 1-D Convolution by Matrix Multiplication |
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84 | (1) |
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4.6 2-D Direct Numerical Convolution |
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85 | (2) |
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4.7 2-D Convolution by Matrix Multiplication |
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87 | (2) |
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89 | (3) |
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92 | (57) |
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5.1 Introduction to Principal Components Analysis |
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92 | (5) |
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97 | (4) |
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101 | (2) |
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103 | (6) |
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5.5 Continuous-Time Fourier Transform |
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109 | (3) |
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5.6 Fourier Convolution Theorem |
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112 | (1) |
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5.7 Discrete-Time Fourier Transform |
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112 | (6) |
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5.8 Discrete Fourier Transform |
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118 | (4) |
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5.9 Fourier Analysis of 2-D LTI/LSI Measurement Systems |
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122 | (3) |
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5.10 Even-Odd Real-Imaginary Symmetries |
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125 | (1) |
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5.11 Short-Time Fourier Transform |
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126 | (1) |
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5.12 Power Spectral Density |
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127 | (3) |
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5.13 Passing Random Processes through Linear Systems |
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130 | (5) |
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5.14 Examples from Research |
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135 | (9) |
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144 | (5) |
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149 | (40) |
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6.1 Eigenanalysis with a Fourier Basis |
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150 | (1) |
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6.2 What Do Eigenstates Describe? |
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151 | (2) |
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6.3 Eigenanalysis Connections to DFT |
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153 | (7) |
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6.4 Measurements as Vector-Space Transformations |
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160 | (3) |
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6.5 Singular-Value Decomposition |
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163 | (8) |
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6.6 SVD Indicates Dimensionality of Motion |
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171 | (2) |
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6.7 Linear Shift-Varying Measurement Systems |
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173 | (2) |
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6.8 Compressed Sensing/Compressive Sampling Methods |
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175 | (5) |
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6.9 Analyzing Systems of Chemical Reactions |
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180 | (6) |
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186 | (3) |
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189 | (36) |
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7.1 Acquisition-Stage Processing: Modeling Photon Detection |
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189 | (5) |
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194 | (6) |
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200 | (2) |
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202 | (9) |
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7.5 Relating Quality Measures to Task Performance |
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211 | (4) |
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7.6 Display-Stage Processing |
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215 | (3) |
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218 | (7) |
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8 Statistical Decision-Making |
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225 | (23) |
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225 | (4) |
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229 | (8) |
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8.3 Receiver Operating Characteristic Analysis |
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237 | (5) |
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8.4 Other Performance Metrics |
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242 | (2) |
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244 | (4) |
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9 Statistical Pattern Recognition with Flow Cytometry Examples |
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248 | (23) |
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250 | (3) |
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9.2 Covariance Diagonalization and Whitening Transformations |
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253 | (7) |
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9.3 Discriminant Analysis |
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260 | (6) |
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266 | (2) |
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268 | (3) |
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10 ODE Models I: Biological Systems |
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271 | (40) |
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10.1 Mathematical Representations of Systems |
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272 | (7) |
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10.2 Linear Systems of Equations |
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279 | (1) |
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10.3 Differential Operators for Linear Systems |
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280 | (3) |
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10.4 Modeling Cell Growth |
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283 | (6) |
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10.5 Linearizing Equations via Taylor Series |
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289 | (2) |
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10.6 Nonlinear Continuous Models: Logistic Equation |
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291 | (3) |
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10.7 The Predator-Prey Problem |
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294 | (8) |
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10.8 Linear Stability, Model Limitations, and Generalizations |
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302 | (2) |
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10.9 Modeling Infectious Disease in Populations |
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304 | (4) |
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308 | (3) |
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11 ODE Models II: Sensors |
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311 | (12) |
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11.1 Second-Order Systems |
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311 | (2) |
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11.2 Sensor Impulse Response |
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313 | (7) |
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320 | (3) |
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1 1.4 MATLAB Solutions via Symbolic Math |
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323 | (6) |
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11.5 Laplace Transform Approach to Solving ODEs |
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326 | (3) |
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329 | (3) |
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330 | (2) |
Appendix A Review of Linear Algebra |
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332 | (26) |
Appendix B Properties of Dirac Deltas |
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358 | (2) |
Appendix C Signal Modulation |
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360 | (7) |
Appendix D Fourier Transform Theorems and Special Functions |
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367 | (6) |
Appendix E Constrained Optimization |
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373 | (3) |
Appendix F One-Sided Laplace Transforms |
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376 | (2) |
Appendix G Independent, Orthogonal, Uncorrelated |
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378 | (3) |
Bibliography |
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381 | (6) |
Index |
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387 | |