LEADER 05552nam 2200745 450 001 996213244803316 005 20210209174349.0 010 $a1-118-61549-2 010 $a1-280-84785-9 010 $a9786610847853 010 $a0-470-39493-5 010 $a0-470-61229-0 010 $a1-84704-624-X 035 $a(CKB)1000000000393366 035 $a(EBL)700768 035 $a(SSID)ssj0000294102 035 $a(PQKBManifestationID)11206492 035 $a(PQKBTitleCode)TC0000294102 035 $a(PQKBWorkID)10303539 035 $a(PQKB)10394051 035 $a(MiAaPQ)EBC700768 035 $a(MiAaPQ)EBC5205684 035 $a(MiAaPQ)EBC275632 035 $a(Au-PeEL)EBL275632 035 $a(OCoLC)520990378 035 $a(CaSebORM)9781905209743 035 $a(EXLCZ)991000000000393366 100 $a20180130h20072005 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDiscrete stochastic processes and optimal filtering /$fJean-Claude Bertein, Roger Ceschi 205 $a1st edition 210 1$aNewport Beach, California :$cISTE,$d2007. 210 4$dİ2005 215 $a1 online resource (303 p.) 225 1 $aISTE ;$vv.670 300 $a"First published in France in 2005 by Hermes Science/Lavoisier entitled "Processus stochastiques discrets et filtrages optimaux"." 311 $a1-905209-74-6 320 $aIncludes bibliographical references and index. 327 $aDiscrete Stochastic Processes and Optimal Filtering; Table of Contents; Preface; Introduction; Chapter 1. Random Vectors; 1.1. Definitions and general properties; 1.2. Spaces L1(dP) and L2(dP); 1.2.1. Definitions; 1.2.2. Properties; 1.3. Mathematical expectation and applications; 1.3.1. Definitions; 1.3.2. Characteristic functions of a random vector; 1.4. Second order random variables and vectors; 1.5. Linear independence of vectors of L2(dP); 1.6. Conditional expectation (concerning random vectors with density function); 1.7. Exercises for Chapter 1; Chapter 2. Gaussian Vectors 327 $a2.1. Some reminders regarding random Gaussian vectors2.2. Definition and characterization of Gaussian vectors; 2.3. Results relative to independence; 2.4. Affine transformation of a Gaussian vector; 2.5. The existence of Gaussian vectors; 2.6. Exercises for Chapter 2; Chapter 3. Introduction to Discrete Time Processes; 3.1. Definition; 3.2. WSS processes and spectral measure; 3.2.1. Spectral density; 3.3. Spectral representation of a WSS process; 3.3.1. Problem; 3.3.2. Results; 3.3.2.1. Process with orthogonal increments and associated measurements; 3.3.2.2. Wiener stochastic integral 327 $a3.3.2.3. Spectral representation3.4. Introduction to digital filtering; 3.5. Important example: autoregressive process; 3.6. Exercises for Chapter 3; Chapter 4. Estimation; 4.1. Position of the problem; 4.2. Linear estimation; 4.3. Best estimate - conditional expectation; 4.4. Example: prediction of an autoregressive process AR (1); 4.5. Multivariate processes; 4.6. Exercises for Chapter 4; Chapter 5. The Wiener Filter; 5.1. Introduction; 5.1.1. Problem position; 5.2. Resolution and calculation of the FIR filter; 5.3. Evaluation of the least error 327 $a5.4. Resolution and calculation of the IIR filter5.5. Evaluation of least mean square error; 5.6. Exercises for Chapter 5; Chapter 6. Adaptive Filtering: Algorithm of the Gradient and the LMS; 6.1. Introduction; 6.2. Position of problem; 6.3. Data representation; 6.4. Minimization of the cost function; 6.4.1. Calculation of the cost function; 6.5. Gradient algorithm; 6.6. Geometric interpretation; 6.7. Stability and convergence; 6.8. Estimation of gradient and LMS algorithm; 6.8.1. Convergence of the algorithm of the LMS; 6.9. Example of the application of the LMS algorithm 327 $a6.10. Exercises for Chapter 6Chapter 7. The Kalman Filter; 7.1. Position of problem; 7.2. Approach to estimation; 7.2.1. Scalar case; 7.2.2. Multivariate case; 7.3. Kalman filtering; 7.3.1. State equation; 7.3.2. Observation equation; 7.3.3. Innovation process; 7.3.4. Covariance matrix of the innovation process; 7.3.5. Estimation; 7.3.6. Riccati's equation; 7.3.7. Algorithm and summary; 7.4. Exercises for Chapter 7; Table of Symbols and Notations; Bibliography; Index 330 $aOptimal filtering applied to stationary and non-stationary signals provides the most efficient means of dealing with problems arising from the extraction of noise signals. Moreover, it is a fundamental feature in a range of applications, such as in navigation in aerospace and aeronautics, filter processing in the telecommunications industry, etc. This book provides a comprehensive overview of this area, discussing random and Gaussian vectors, outlining the results necessary for the creation of Wiener and adaptive filters used for stationary signals, as well as examining Kalman filters which ar 410 0$aISTE 606 $aSignal processing$xMathematics 606 $aDigital filters (Mathematics) 606 $aStochastic processes 615 0$aSignal processing$xMathematics. 615 0$aDigital filters (Mathematics) 615 0$aStochastic processes. 676 $a621.382/2 700 $aBertein$b Jean-Claude$0888976 702 $aCeschi$b Roger 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996213244803316 996 $aDiscrete stochastic processes and optimal filtering$91985745 997 $aUNISA