fundamentals of statistical signal processing, volume i estimation theory by steven m.kay
TRANSCRIPT
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PRENTICE HALL SIGNAL PROCESSING SERIES
Alan V. Oppenheim, Series Editor
ANDREWS AND HUNT BRIGHAM The Fast Fourier Tmnsform BRIGHAM BURDIC CASTLEMAN Digital Image Processing COWAN AND GRANT Adaptive Filters CROCHIERE AND RABINER DUDGEON AND MERSEREAU HAMMING Digital Filters, 3 /E HAYKIN, ED. HAYKIN, ED. Array Signal Processing JAYANT AND NOLL JOHNSON A N D DUDGEON KAY KAY Modern Spectral Estimation KINO LEA, ED. LIM LIM, ED. Speech Enhancement LIM AND OPPENHEIM, EDS. MARPLE MCCLELLAN AND RADER MENDEL OPPENHEIM, ED. OPPENHEIM AND NAWAB, EDS. OPPENHEIM, WILLSKY, WITH YOUNG OPPENHEIM AND SCHAFER Digital Signal Processing OPPENHEIM AND SCHAFER Discrete- Time Signal Processing QUACKENBUSH ET AL. Objective Measures of Speech Quality RABINER AND GOLD RABINER AND SCHAFER Digital Processing of Speech Signals ROBINSON AND TREITEL STEARNS AND DAVID STEARNS AND HUSH TRIBOLET VAIDYANATHAN WIDROW AND STEARNS
Digital Image Restomtion
The Fast Fourier Transform and Its Applications Underwater Acoustic System Analysis, 2/E
Multimte Digital Signal Processing Multidimensional Digital Signal Processing
Advances in Spectrum Analysis and Array Processing, Vols. I € 5 II
Digital Coding of waveforms Array Signal Processing: Concepts and Techniques
Fundamentals of Statistical Signal Processing: Estimation Theory
Acoustic Waves: Devices, Imaging, and Analog Signal Processing Trends in Speech Recognition
Two-Dimensional Signal and Image Processing
Advanced Topics in Signal Processing Digital Spectral Analysis with Applications
Lessons in Digital Estimation Theory Number Theory an Digital Signal Processing
Applications of Digital Signal Processing Symbolic and Knowledge-Based Signal Processing
Signals and Systems
Theory and Applications of Digital Signal Processing
Geophysical Signal Analysis Signal Processing Algorithms
Digital Signal Analysis, 2/E Seismic Applications of Homomorphic Signal Processing
Multimte Systems and Filter Banks Adaptive Signal Processing
Fundamentals of Statistical Signal Processing:
Est imat ion Theory
Steven M. Kay University of Rhode Island
For book and bookstore information
I I http://wmn.prenhrll.com gopher to gopher.prenhall.com
Upper Saddle River, NJ 07458
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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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