Details

Statistical Signal Processing in Engineering


Statistical Signal Processing in Engineering


1. Aufl.

von: Umberto Spagnolini

110,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 15.11.2017
ISBN/EAN: 9781119293958
Sprache: englisch
Anzahl Seiten: 608

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Beschreibungen

<p><b>A problem-solving approach to statistical signal processing for practicing engineers, technicians, and graduate students</b> </p> <p>This book takes a pragmatic approach in solving a set of common problems engineers and technicians encounter when processing signals. In writing it, the author drew on his vast theoretical and practical experience in the field to provide a quick-solution manual for technicians and engineers, offering field-tested solutions to most problems engineers can encounter. At the same time, the book delineates the basic concepts and applied mathematics underlying each solution so that readers can go deeper into the theory to gain a better idea of the solution’s limitations and potential pitfalls, and thus tailor the best solution for the specific engineering application. </p> <p>Uniquely, <i>Statistical Signal Processing in Engineering</i> can also function as a textbook for engineering graduates and post-graduates. Dr. Spagnolini, who has had a quarter of a century of experience teaching graduate-level courses in digital and statistical signal processing methods, provides a detailed axiomatic presentation of the conceptual and mathematical foundations of statistical signal processing that will challenge students’ analytical skills and motivate them to develop new applications on their own, or better understand the motivation underlining the existing solutions.  </p> <p>Throughout the book, some real-world examples demonstrate how powerful a tool statistical signal processing is in practice across a wide range of applications.</p> <ul> <li>Takes an interdisciplinary approach, integrating basic concepts and tools for statistical signal processing</li> <li>Informed by its author’s vast experience as both a practitioner and teacher</li> <li>Offers a hands-on approach to solving problems in statistical signal processing</li> <li>Covers a broad range of applications, including communication systems, machine learning, wavefield and array processing, remote sensing, image filtering and distributed computations</li> <li>Features numerous real-world examples from a wide range of applications showing the mathematical concepts involved in practice</li> <li>Includes MATLAB code of many of the experiments in the book</li> </ul> <p><i>Statistical Signal Processing in Engineering</i> is an indispensable working resource for electrical engineers, especially those working in the information and communication technology (ICT) industry. It is also an ideal text for engineering students at large, applied mathematics post-graduates and advanced undergraduates in electrical engineering, applied statistics, and pure mathematics, studying statistical signal processing.</p>
<p>List of Figures xvii</p> <p>List of Tables xxiii</p> <p>Preface xxv</p> <p>List of Abbreviations xxix</p> <p>How to Use the Book xxxi</p> <p>About the Companion Website xxxiii</p> <p>Prerequisites xxxv</p> <p>Why are there so many matrixes in this book? xxxvii</p> <p><b>1 Manipulations on Matrixes 1</b></p> <p>1.1 Matrix Properties 1</p> <p>1.1.1 Elementary Operations 2</p> <p>1.2 Eigen-Decomposition 6</p> <p>1.3 Eigenvectors in Everyday Life 9</p> <p>1.3.1 Conversations in a Noisy Restaurant 9</p> <p>1.3.2 Power Control in a Cellular System 12</p> <p>1.3.3 Price Equilibrium in the Economy 14</p> <p>1.4 Derivative Rules 15</p> <p>1.4.1 Derivative with respect to x 16</p> <p>1.4.2 Derivative with respect to x 17</p> <p>1.4.3 Derivative with respect to the Matrix X 18</p> <p>1.5 Quadratic Forms 19</p> <p>1.6 Diagonalization of a Quadratic Form 20</p> <p>1.7 Rayleigh Quotient 21</p> <p>1.8 Basics of Optimization 22</p> <p>1.8.1 Quadratic Function with Simple Linear Constraint (M=1) 23</p> <p>1.8.2 Quadratic Function with Multiple Linear Constraints 23</p> <p>Appendix A: Arithmetic vs. Geometric Mean 24</p> <p><b>2 Linear Algebraic Systems 27</b></p> <p>2.1 Problem Definition and Vector Spaces 27</p> <p>2.1.1 Vector Spaces in Tomographic Radiometric Inversion 29</p> <p>2.2 Rotations 31</p> <p>2.3 Projection Matrixes and Data-Filtering 33</p> <p>2.3.1 Projections and Commercial FM Radio 34</p> <p>2.4 Singular Value Decomposition (SVD) and Subspaces 34</p> <p>2.4.1 How to Choose the Rank of Afor Gaussian Model? 35</p> <p>2.5 QR and Cholesky Factorization 36</p> <p>2.6 Power Method for Leading Eigenvectors 38</p> <p>2.7 Least Squares Solution of Overdetermined Linear Equations 39</p> <p>2.8 Efficient Implementation of the LS Solution 41</p> <p>2.9 Iterative Methods 42</p> <p><b>3 Random Variables in Brief 45</b></p> <p>3.1 Probability Density Function (pdf), Moments, and Other Useful Properties 45</p> <p>3.2 Convexity and Jensen Inequality 49</p> <p>3.3 Uncorrelatedness and Statistical Independence 49</p> <p>3.4 Real-Valued Gaussian Random Variables 51</p> <p>3.5 Conditional pdf for Real-Valued Gaussian Random Variables 54</p> <p>3.6 Conditional pdf in Additive Noise Model 56</p> <p>3.7 Complex Gaussian Random Variables 56</p> <p>3.7.1 Single Complex Gaussian Random Variable 56</p> <p>3.7.2 Circular Complex Gaussian Random Variable 57</p> <p>3.7.3 Multivariate Complex Gaussian Random Variables 58</p> <p>3.8 Sum of Square of Gaussians: Chi-Square 59</p> <p>3.9 Order Statistics for N rvs 60</p> <p><b>4 Random Processes and Linear Systems 63</b></p> <p>4.1 Moment Characterizations and Stationarity 64</p> <p>4.2 Random Processes and Linear Systems 66</p> <p>4.3 Complex-Valued Random Processes 68</p> <p>4.4 Pole-Zero and Rational Spectra (Discrete-Time) 69</p> <p>4.4.1 Stability of LTI Systems 70</p> <p>4.4.2 Rational PSD 71</p> <p>4.4.3 Paley–Wiener Theorem 72</p> <p>4.5 Gaussian Random Process (Discrete-Time) 73</p> <p>4.6 Measuring Moments in Stochastic Processes 75</p> <p>Appendix A: Transforms for Continuous-Time Signals 76</p> <p>Appendix B: Transforms for Discrete-Time Signals 79</p> <p><b>5 Models and Applications 83</b></p> <p>5.1 Linear Regression Model 84</p> <p>5.2 Linear Filtering Model 86</p> <p>5.2.1 Block-Wise Circular Convolution 88</p> <p>5.2.2 Discrete Fourier Transform and Circular Convolution Matrixes 89</p> <p>5.2.3 Identification and Deconvolution 90</p> <p>5.3 MIMO systems and Interference Models 91</p> <p>5.3.1 DSL System 92</p> <p>5.3.2 MIMO in Wireless Communication 92</p> <p>5.4 Sinusoidal Signal 97</p> <p>5.5 Irregular Sampling and Interpolation 97</p> <p>5.5.1 Sampling With Jitter 100</p> <p>5.6 Wavefield Sensing System 101</p> <p><b>6 Estimation Theory 105</b></p> <p>6.1 Historical Notes 105</p> <p>6.2 Non-Bayesian vs. Bayesian 106</p> <p>6.3 Performance Metrics and Bounds 107</p> <p>6.3.1 Bias 107</p> <p>6.3.2 Mean Square Error (MSE) 108</p> <p>6.3.3 Performance Bounds 109</p> <p>6.4 Statistics and Sufficient Statistics 110</p> <p>6.5 MVU and BLU Estimators 111</p> <p>6.6 BLUE for Linear Models 112</p> <p>6.7 Example: BLUE of the Mean Value of Gaussian rvs 114</p> <p><b>7 Parameter Estimation 117</b></p> <p>7.1 Maximum Likelihood Estimation (MLE) 117</p> <p>7.2 MLE for Gaussian Model 119</p> <p>7.2.1 Additive Noise Model with 119</p> <p>7.2.2 Additive Noise Model with 120</p> <p>7.2.3 Additive Noise Model with Multiple Observations with Known 121</p> <p>7.2.3.1 Linear Model 121</p> <p>7.2.3.2 Model 122</p> <p>7.2.3.3 Model 123</p> <p>7.2.4 Model 123</p> <p>7.2.5 Additive Noise Model with Multiple Observations with Unknown 124</p> <p>7.3 Other Noise Models 125</p> <p>7.4 MLE and Nuisance Parameters 126</p> <p>7.5 MLE for Continuous-Time Signals 128</p> <p>7.5.1 Example: Amplitude Estimation 129</p> <p>7.5.2 MLE for Correlated Noise 130</p> <p>7.6 MLE for Circular Complex Gaussian 131</p> <p>7.7 Estimation in Phase/Frequency Modulations 131</p> <p>7.7.1 MLE Phase Estimation 132</p> <p>7.7.2 Phase Locked Loops 133</p> <p>7.8 Least Square (LS) Estimation 135</p> <p>7.8.1 Weighted LS with 136</p> <p>7.8.2 LS Estimation and Linear Models 137</p> <p>7.8.3 Under or Over-Parameterizing? 138</p> <p>7.8.4 Constrained LS Estimation 139</p> <p>7.9 Robust Estimation 140</p> <p><b>8 Cramér–Rao Bound 143</b></p> <p>8.1 Cramér–Rao Bound and Fisher Information Matrix 143</p> <p>8.1.1 CRB for Scalar Problem (P=1) 143</p> <p>8.1.2 CRB and Local Curvature of Log-Likelihood 144</p> <p>8.1.3 CRB for Multiple Parameters (p 1) 144</p> <p>8.2 Interpretation of CRB and Remarks 146</p> <p>8.2.1 Variance of Each Parameter 146</p> <p>8.2.2 Compactness of the Estimates 146</p> <p>8.2.3 FIM for Known Parameters 147</p> <p>8.2.4 Approximation of the Inverse of FIM 148</p> <p>8.2.5 Estimation Decoupled From FIM 148</p> <p>8.2.6 CRB and Nuisance Parameters 149</p> <p>8.2.7 CRB for Non-Gaussian rv and Gaussian Bound 149</p> <p>8.3 CRB and Variable Transformations 150</p> <p>8.4 FIM for Gaussian Parametric Model 151</p> <p>8.4.1 FIM for with 151</p> <p>8.4.2 FIM for Continuous-Time Signals in Additive White Gaussian Noise 152</p> <p>8.4.3 FIM for Circular Complex Model 152</p> <p>Appendix A: Proof of CRB 154</p> <p>Appendix B: FIM for Gaussian Model 156</p> <p>Appendix C: Some Derivatives for MLE and CRB Computations 157</p> <p><b>9 MLE and CRB for Some Selected Cases 159</b></p> <p>9.1 Linear Regressions 159</p> <p>9.2 Frequency Estimation 162</p> <p>9.3 Estimation of Complex Sinusoid 164</p> <p>9.3.1 Proper, Improper, and Non-Circular Signals 165</p> <p>9.4 Time of Delay Estimation 166</p> <p>9.5 Estimation of Max for Uniform pdf 170</p> <p>9.6 Estimation of Occurrence Probability for Binary pdf 172</p> <p>9.7 How to Optimize Histograms? 173</p> <p>9.8 Logistic Regression 176</p> <p><b>10 Numerical Analysis and Montecarlo Simulations 179</b></p> <p>10.1 System Identification and Channel Estimation 181</p> <p>10.1.1 Matlab Code and Results 184</p> <p>10.2 Frequency Estimation 184</p> <p>10.2.1 Variable (Coarse/Fine) Sampling 187</p> <p>10.2.2 Local Parabolic Regression 189</p> <p>10.2.3 Matlab Code and Results 190</p> <p>10.3 Time of Delay Estimation 192</p> <p>10.3.1 Granularity of Sampling in ToD Estimation 193</p> <p>10.3.2 Matlab Code and Results 194</p> <p>10.4 Doppler-Radar System by Frequency Estimation 196</p> <p>10.4.1 EM Method 197</p> <p>10.4.2 Matlab Code and Results 199</p> <p><b>11 Bayesian Estimation 201</b></p> <p>11.1 Additive Linear Model with Gaussian Noise 203</p> <p>11.1.1 Gaussian A-priori: 204</p> <p>11.1.2 Non-Gaussian A-Priori 206</p> <p>11.1.3 Binary Signals: MMSE vs. MAP Estimators 207</p> <p>11.1.4 Example: Impulse Noise Mitigation 210</p> <p>11.2 Bayesian Estimation in Gaussian Settings 212</p> <p>11.2.1 MMSE Estimator 213</p> <p>11.2.2 MMSE Estimator for Linear Models 213</p> <p>11.3 LMMSE Estimation and Orthogonality 215</p> <p>11.4 Bayesian CRB 218</p> <p>11.5 Mixing Bayesian and Non-Bayesian 220</p> <p>11.5.1 Linear Model with Mixed Random/Deterministic Parameters 220</p> <p>11.5.2 Hybrid CRB 222</p> <p>11.6 Expectation-Maximization (EM) 223</p> <p>11.6.1 EM of the Sum of Signals in Gaussian Noise 224</p> <p>11.6.2 EM Method for the Time of Delay Estimation of Multiple Waveforms 227</p> <p>11.6.3 Remarks 228</p> <p>Appendix A: Gaussian Mixture pdf 229</p> <p><b>12 Optimal Filtering 231</b></p> <p>12.1 Wiener Filter 231</p> <p>12.2 MMSE Deconvolution (or Equalization) 233</p> <p>12.3 Linear Prediction 234</p> <p>12.3.1 Yule–Walker Equations 235</p> <p>12.4 LS Linear Prediction 237</p> <p>12.5 Linear Prediction and AR Processes 239</p> <p>12.6 Levinson Recursion and Lattice Predictors 241</p> <p><b>13 Bayesian Tracking and Kalman Filter 245</b></p> <p>13.1 Bayesian Tracking of State in Dynamic Systems 246</p> <p>13.1.1 Evolution of the A-posteriori pdf 247</p> <p>13.2 Kalman Filter (KF) 249</p> <p>13.2.1 KF Equations 251</p> <p>13.2.2 Remarks 253</p> <p>13.3 Identification of Time-Varying Filters in Wireless Communication 255</p> <p>13.4 Extended Kalman Filter (EKF) for Non-Linear Dynamic Systems 257</p> <p>13.5 Position Tracking by Multi-Lateration 258</p> <p>13.5.1 Positioning and Noise 260</p> <p>13.5.2 Example of Position Tracking 263</p> <p>13.6 Non-Gaussian Pdf and Particle Filters264</p> <p><b>14 Spectral Analysis 267</b></p> <p>14.1 Periodogram 268</p> <p>14.1.1 Bias of the Periodogram 268</p> <p>14.1.2 Variance of the Periodogram 271</p> <p>14.1.3 Filterbank Interpretation 273</p> <p>14.1.4 Pdf of the Periodogram (White Gaussian Process) 274</p> <p>14.1.5 Bias and Resolution 275</p> <p>14.1.6 Variance Reduction and WOSA 278</p> <p>14.1.7 Numerical Example: Bandlimited Process and (Small) Sinusoid 280</p> <p>14.2 Parametric Spectral Analysis 282</p> <p>14.2.1 MLE and CRB 284</p> <p>14.2.2 General Model for AR, MA, ARMA Spectral Analysis 285</p> <p>14.3 AR Spectral Analysis 286</p> <p>14.3.1 MLE and CRB 286</p> <p>14.3.2 A Good Reason to Avoid Over-Parametrization in AR 289</p> <p>14.3.3 Cramér–Rao Bound of Poles in AR Spectral Analysis 291</p> <p>14.3.4 Example: Frequency Estimation by AR Spectral Analysis 293</p> <p>14.4 MA Spectral Analysis 296</p> <p>14.5 ARMA Spectral Analysis 298</p> <p>14.5.1 Cramér–Rao Bound for ARMA Spectral Analysis 300</p> <p>Appendix A: Which Sample Estimate of the Autocorrelation to Use? 302</p> <p>Appendix B: Eigenvectors and Eigenvalues of Correlation Matrix 303</p> <p>Appendix C: Property of Monic Polynomial 306</p> <p>Appendix D: Variance of Pole in AR(1) 307</p> <p><b>15 Adaptive Filtering 309</b></p> <p>15.1 Adaptive Interference Cancellation 311</p> <p>15.2 Adaptive Equalization in Communication Systems 313</p> <p>15.2.1 Wireless Communication Systems in Brief 313</p> <p>15.2.2 Adaptive Equalization 315</p> <p>15.3 Steepest Descent MSE Minimization 317</p> <p>15.3.1 Convergence Analysis and Step-Size 318</p> <p>15.3.2 An Intuitive View of Convergence Conditions 320</p> <p>15.4 From Iterative to Adaptive Filters 323</p> <p>15.5 LMS Algorithm and Stochastic Gradient 324</p> <p>15.6 Convergence Analysis of LMS Algorithm 325</p> <p>15.6.1 Convergence in the Mean 326</p> <p>15.6.2 Convergence in the Mean Square 326</p> <p>15.6.3 Excess MSE 329</p> <p>15.7 Learning Curve of LMS 331</p> <p>15.7.1 Optimization of the Step-Size 332</p> <p>15.8 NLMS Updating and Non-Stationarity 333</p> <p>15.9 Numerical Example: Adaptive Identification 334</p> <p>15.10 RLS Algorithm 338</p> <p>15.10.1 Convergence Analysis 339</p> <p>15.10.2 Learning Curve of RLS 341</p> <p>15.11 Exponentially-Weighted RLS 342</p> <p>15.12 LMS vs. RLS 344</p> <p>Appendix A: Convergence in Mean Square 344</p> <p><b>16 Line Spectrum Analysis 347</b></p> <p>16.1 Model Definition 349</p> <p>16.1.1 Deterministic Signals 350</p> <p>16.1.2 Random Signals 350</p> <p>16.1.3 Properties of Structured Covariance 351</p> <p>16.2 Maximum Likelihood and Cramér–Rao Bounds 352</p> <p>16.2.1 Conditional ML 353</p> <p>16.2.2 Cramér–Rao Bound for Conditional Model 354</p> <p>16.2.3 Unconditional ML 356</p> <p>16.2.4 Cramér–Rao Bound for Unconditional Model 356</p> <p>16.2.5 Conditional vs. Unconditional Model & Bounds 357</p> <p>16.3 High-Resolution Methods 357</p> <p>16.3.1 Iterative Quadratic ML (IQML) 358</p> <p>16.3.2 Prony Method 360</p> <p>16.3.3 MUSIC 360</p> <p>16.3.4 ESPRIT 363</p> <p>16.3.5 Model Order 365</p> <p><b>17 Equalization in Communication Engineering 367</b></p> <p>17.1 Linear Equalization 369</p> <p>17.1.1 Zero Forcing (ZF) Equalizer 370</p> <p>17.1.2 Minimum Mean Square Error (MMSE) Equalizer 371</p> <p>17.1.3 Finite-Length/Finite-Block Equalizer 371</p> <p>17.2 Non-Linear Equalization 372</p> <p>17.2.1 ZF-DFE 373</p> <p>17.2.2 MMSE–DFE 374</p> <p>17.2.3 Finite-Length MMSE–DFE 375</p> <p>17.2.4 Asymptotic Performance for Infinite-Length Equalizers 376</p> <p>17.3 MIMO Linear Equalization 377</p> <p>17.3.1 ZF MIMO Equalization 377</p> <p>17.3.2 MMSE MIMO Equalization 379</p> <p>17.4 MIMO–DFE Equalization 379</p> <p>17.4.1 Cholesky Factorization and Min/Max Phase Decomposition 379</p> <p>17.4.2 MIMO–DFE 380</p> <p>18 2D Signals and Physical Filters 383</p> <p>18.1 2D Sinusoids 384</p> <p>18.1.1 Moiré Pattern 386</p> <p>18.2 2D Filtering 388</p> <p>18.2.1 2D Random Fields 390</p> <p>18.2.2 Wiener Filtering 391</p> <p>18.2.3 Image Acquisition and Restoration 392</p> <p>18.3 Diffusion Filtering 394</p> <p>18.3.1 Evolution vs. Time: Fourier Method 394</p> <p>18.3.2 Extrapolation of the Density 395</p> <p>18.3.3 Effect of Phase-Shift 396</p> <p>18.4 Laplace Equation and Exponential Filtering 398</p> <p>18.5 Wavefield Propagation 400</p> <p>18.5.1 Propagation/Backpropagation 400</p> <p>18.5.2 Wavefield Extrapolation and Focusing 402</p> <p>18.5.3 Exploding Reflector Model 402</p> <p>18.5.4 Wavefield Extrapolation 404</p> <p>18.5.5 Wavefield Focusing (or Migration) 406</p> <p>Appendix A: Properties of 2D Signals 406</p> <p>Appendix B: Properties of 2D Fourier Transform 410</p> <p>Appendix C: Finite Difference Method for PDE-Diffusion 412</p> <p><b>19 Array Processing 415</b></p> <p>19.1 Narrowband Model 415</p> <p>19.1.1 Multiple DoAs and Multiple Sources 419</p> <p>19.1.2 Sensor Spacing Design 420</p> <p>19.1.3 Spatial Resolution and Array Aperture 421</p> <p>19.2 Beamforming and Signal Estimation 422</p> <p>19.2.1 Conventional Beamforming 425</p> <p>19.2.2 Capon Beamforming (MVDR) 426</p> <p>19.2.3 Multiple-Constraint Beamforming 429</p> <p>19.2.4 Max-SNR Beamforming 431</p> <p>19.3 DoA Estimation 432</p> <p>19.3.1 ML Estimation and CRB 433</p> <p>19.3.2 Beamforming and Root-MVDR 434</p> <p><b>20 Multichannel Time of Delay Estimation 435</b></p> <p>20.1 Model Definition for ToD 440</p> <p>20.2 High Resolution Method for ToD (L=1) 441</p> <p>20.2.1 ToD in the Fourier Transformed Domain 441</p> <p>20.2.2 CRB and Resolution 444</p> <p>20.3 Difference of ToD (DToD) Estimation 445</p> <p>20.3.1 Correlation Method for DToD 445</p> <p>20.3.2 Generalized Correlation Method 448</p> <p>20.4 Numerical Performance Analysis of DToD 452</p> <p>20.5 Wavefront Estimation: Non-Parametric Method (L=1) 454</p> <p>20.5.1 Wavefront Estimation in Remote Sensing and Geophysics 456</p> <p>20.5.2 Narrowband Waveforms and 2D Phase Unwrapping 457</p> <p>20.5.3 2D Phase Unwrapping in Regular Grid Spacing 458</p> <p>20.6 Parametric ToD Estimation and Wideband Beamforming 460</p> <p>20.6.1 Delay and Sum Beamforming 462</p> <p>20.6.2 Wideband Beamforming After Fourier Transform 464</p> <p>20.7 Appendix A: Properties of the Sample Correlations 465</p> <p>20.8 Appendix B: How to Delay a Discrete-Time Signal? 466</p> <p>20.9 Appendix C: Wavefront Estimation for 2D Arrays 467</p> <p><b>21 Tomography 467</b></p> <p>21.1 X-ray Tomography 471</p> <p>21.1.1 Discrete Model 471</p> <p>21.1.2 Maximum Likelihood 473</p> <p>21.1.3 Emission Tomography 473</p> <p>21.2 Algebraic Reconstruction Tomography (ART) 475</p> <p>21.3 Reconstruction From Projections: Fourier Method 475</p> <p>21.3.1 Backprojection Algorithm 476</p> <p>21.3.2 How Many Projections to Use? 479</p> <p>21.4 Traveltime Tomography 480</p> <p>21.5 Internet (Network) Tomography 483</p> <p>21.5.1 Latency Tomography 484</p> <p>21.5.2 Packet-Loss Tomography 484</p> <p><b>22 Cooperative Estimation 487</b></p> <p>22.1 Consensus and Cooperation 490</p> <p>22.1.1 Vox Populi: The Wisdom of Crowds 490</p> <p>22.1.2 Cooperative Estimation as Simple Information Consensus 490</p> <p>22.1.3 Weighted Cooperative Estimation ( ) 493</p> <p>22.1.4 Distributed MLE ( ) 495</p> <p>22.2 Distributed Estimation for Arbitrary Linear Models (p>1) 496</p> <p>22.2.1 Centralized MLE 497</p> <p>22.2.2 Distributed Weighted LS 498</p> <p>22.2.3 Distributed MLE 500</p> <p>22.2.4 Distributed Estimation for Under-Determined Systems 501</p> <p>22.2.5 Stochastic Regressor Model 503</p> <p>22.2.6 Cooperative Estimation in the Internet of Things (IoT) 503</p> <p>22.2.7 Example: Iterative Distributed Estimation 505</p> <p>22.3 Distributed Synchronization 506</p> <p>22.3.1 Synchrony-States for Analog and Discrete-Time Clocks 507</p> <p>22.3.2 Coupled Clocks 510</p> <p>22.3.3 Internet Synchronization and the Network Time Protocol (NTP) 512</p> <p>Appendix A: Basics of Undirected Graphs 515</p> <p><b>23 Classification and Clustering 521</b></p> <p>23.1 Historical Notes 522</p> <p>23.2 Classification 523</p> <p>23.2.1 Binary Detection Theory 523</p> <p>23.2.2 Binary Classification of Gaussian Distributions 528</p> <p>23.3 Classification of Signals in Additive Gaussian Noise 529</p> <p>23.3.1 Detection of Known Signal 531</p> <p>23.3.2 Classification of Multiple Signals 532</p> <p>23.3.3 Generalized Likelihood Ratio Test (GLRT) 533</p> <p>23.3.4 Detection of Random Signals 535</p> <p>23.4 Bayesian Classification 536</p> <p>23.4.1 To Classify or Not to Classify? 537</p> <p>23.4.2 Bayes Risk 537</p> <p>23.5 Pattern Recognition and Machine Learning 538</p> <p>23.5.1 Linear Discriminant 539</p> <p>23.5.2 Least Squares Classification 540</p> <p>23.5.3 Support Vectors Principle 541</p> <p>23.6 Clustering 543</p> <p>23.6.1 K-Means Clustering 544</p> <p>23.6.2 EM Clustering 545</p> <p>References 549</p> <p>Index 557</p>
<p><b>UMBERTO SPAGNOLINI</b> is Professor in Signal Processing and Telecommunications at Politecnico di Milano, Italy. Prof. Spagnolini's research focuses on statistical signal processing, communication systems, and advanced topics in signal processing for remote sensing and wireless communication systems. He is a Senior Member of the IEEE, engages in editorial activity for IEEE journals and conferences, and has authored 300 patents and papers in peer reviewed journals and conferences.
<p><b>A Problem-Solving Approach to Statistical Signal Processing for Practicing Engineers, Technicians, and Graduate Students</b> <p>This reference takes a pragmatic approach to solving a set of common problems encountered by engineers and technicians when processing signals. Drawing on the author's vast theoretical and practical experience, it offers field-tested solutions to most problems engineers and technicians can encounter. At the same time, it delineates the basic concepts and applied mathematics underlying each solution so that readers can go deeper into the theory to gain a better idea of the solution's limitations and potential pitfalls, thus tailoring the best solution for specific engineering applications. <p><i>Statistical Signal Processing in Engineering</i> also functions as a text for engineering graduate students. Dr. Spagnolini, who has 25 years' experience teaching graduate-level courses in digital and statistical signal processing methods, provides a detailed axiomatic presentation of the conceptual and mathematical foundations of statistical signal processing. This will challenge students' analytical skills and motivate them to develop their own new applications as well as understand the motivation underlining existing solutions. <p>This unique work <ul> <li>Takes an interdisciplinary approach, integrating basic concepts and tools for statistical signal processing</li> <li>Offers a hands-on approach to solving problems in statistical signal processing</li> <li>Covers a broad range of applications, including communication systems, machine learning, wavefield and array processing, remote sensing, image filtering and distributed computations</li> <li>Features numerous real-world examples across wide ranging applications to illustrate mathematical concepts involved in practice</li> <li>Includes MATLAB code of many of the experiments in the book</li> </ul> <p><i>Statistical Signal Processing in Engineering</i> is an indispensable working resource for electrical engineers, especially those working in the information and communication technology (ICT) industry. It is also an invaluable text for electrical engineering, applied statistics, and mathematics graduate and advanced undergraduate students studying statistical signal processing.

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von: Cenk Acar, Andrei Shkel
PDF ebook
149,79 €