28 February 2008 MAR 670 Course Introduction
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MAR 670 ADVANCED
TIME SERIES ANALYSIS OF OCEAN DATA
LECTURE NOTES
WENDELL S. BROWN
JANUARY 2008
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REFERENCES Code B Bracewell, R.; The Fourier Transform and its Application, McGraw-Hill, NY, 1965. BP1 Bendat, J. S. and A.G. Piersol; Random Data: Analysis and Measurement Procedures, Wiley Interscience, NY, 1971. BP2 Bendat, J. S. and A. G. Piersol; Random Data: Analysis and Measurement Procedures, Wiley Interscience, Second Edition, NY, 1986. BP3 Bendat, J. S. and A. G. Piersol; Random Data: Analysis and Measurement Procedures, Wiley Interscience, Second Edition, NY, ???????. JW Jenkins, G.M. and D. G. Watts; Spectral Analysis and its Applications, Holden-Day, San Francisco, 1968. H Haubrich, R., 1965. Earth noise, 5 to 500 millicycles per second, J. Geophys. Res., 70
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MAR 670 Topics in Advanced Time Series Analysis of Ocean Data CLASS NOTES
TABLE OF CONTENTS
CHAPTER TOPICS I. Title Page & Contents II. Introduction to Fourier Transforms A. Fourier Series B. Fourier Transformation C. Alternate Forms of Fourier Transform D. Interpretation of the Fourier Transform E. Properties of Fourier Transformation F. Special Functions G. Examples of Fourier Transform H. Convolution I. Sampling III. Random Process Theory A. Probability Density Functions B. Joint Probability Density Functions IV. Covariance Functions A. Auto-Covariance Functions B. Cross-Covariance Functions C. Cross-Covariance and Correlation D. Power-Spectral Density Functions E. Cross-Spectral Density Functions F. Coherence and Phase Functions V. Uncertainty of Statistical Estimators A. General Principles B. Sampling Distributions C. Confidence Intervals D. Definition of Errors VI. Data Sampling and Filtering A. Sampling and Aliasing B. Linear Filters and Filtering C. General Filtering D. Frequency Response and Transfer Functions
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VII. Spectral density Functions A. Power-Spectral Density Functions B. Cross-Spectral Density C. Discrete Spectral Density Functions D. Practical Uncertainty Considerations VIII. Coherence & Transfer Functions A. Coherence Function B. Frequency Response Function Estimates C. Estimating Tidal Transfer Function Error D. Summary of Error Relations IX. Advanced Statistical Analysis A. Empirical Orthogonal Functions EOF: Time Domain Scalars B. Empirical Orthogonal Functions EOF: Analysis X. Ocean Data Analysis A. Practical Data Processing Issues XI. Summary Appendix 1 Uncertainty Estimates Appendix 2 Data Analysis
