Download - Fundamentals of Statistical Signal Processing, Volume I Estimation Theory by Steven M.kay
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Digital Coding of waveforms Array Signal Processing: Concepts and Techniques
Fundamentals of Statistical Signal Processing: Estimation Theory
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Advanced Topics in Signal Processing Digital Spectral Analysis with Applications
Lessons in Digital Estimation Theory Number Theory an Digital Signal Processing
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Digital Signal Analysis, 2/E Seismic Applications of Homomorphic Signal Processing
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Fundamentals of Statistical Signal Processing:
Est imat ion Theory
Steven M. Kay University of Rhode Island
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Contents
Preface xi
1 Introduction 1 1.1 Estimation in Signal Processing . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Mathematical Estimation Problem . . . . . . . . . . . . . . . . . . 7 1.3 Assessing Estimator Performance . . . . . . . . . . . . . . . . . . . . . . 9 1.4 Some Notes to the Reader . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Minimum Variance Unbiased Estimation 15 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Unbiased Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Minimum Variance Criterion . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5 Existence of the Minimum Variance Unbiased Estimator . . . . . . . . . 20 2.6 Finding the Minimum Variance Unbiased Estimator . . . . . . . . . . . 21 2.7 Extension to a Vector Parameter . . . . . . . . . . . . . . . . . . . . . . 22
3 Cramer-Rao Lower Bound 27 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.3 Estimator Accuracy Considerations . . . . . . . . . . . . . . . . . . . . . 28 3.4 Cramer-Rao Lower Bound . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.5 General CRLB for Signals in White Gaussian Noise . . . . . . . . . . . . 35 3.6 Transformation of Parameters . . . . . . . . . . . . . . . . . . . . . . . . 37 3.7 Extension to a Vector Parameter . . . . . . . . . . . . . . . . . . . . . . 39 3.8 Vector Parameter CRLB for Transformations . . . . . . . . . . . . . . . 45 3.9 CRLB for the General Gaussian Case . . . . . . . . . . . . . . . . . . . 47 3.10 Asymptotic CRLB for WSS Gaussian Random Processes . . . . . . . . . 50 3.1 1 Signal Processing Examples . . . . . . . . . . . . . . . . . . . . . . . . . 53 3A Derivation of Scalar Parameter CRLB . . . . . . . . . . . . . . . . . . . 67 3B Derivation of Vector Parameter CRLB . . . . . . . . . . . . . . . . . . . 70 3C Derivation of General Gaussian CRLB . . . . . . . . . . . . . . . . . . . 73 3D Derivation of Asymptotic CRLB . . . . . . . . . . . . . . . . . . . . . . 77
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