Book contents
- Time Series Data Analysis in Oceanography
- Time Series Data Analysis in Oceanography
- Copyright page
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Introduction to MATLAB
- 3 Time and MATLAB Functions for Time
- 4 Deterministic and Random Functions
- 5 Error and Variability Propagation
- 6 Taylor Series Expansion and Application in Error Estimate
- 7 Spherical Trigonometry and Distance Computation
- 8 A System of Linear Equations and Least Squares Method
- 9 Base Functions and Linear Independence
- 10 Generic Least Squares Method and Orthogonal Functions
- 11 Harmonic Analysis of Tide
- 12 Fourier Series
- 13 Fourier Transform
- 14 Discrete Fourier Transform and Fast Fourier Transform
- 15 Properties of Fourier Transform
- 16 More Discussion on the Harmonic Analysis and Fourier Analysis
- 17 Effect of Finite Sampling
- 18 Power Spectrum, Cospectrum, and Coherence
- 19 Window Functions for Reducing Side Lobes
- 20 Convolution, Filtering with the Window Method
- 21 Digital Filters
- 22 Rotary Spectrum Analysis
- 23 Short-Time Fourier Transform and Introduction to Wavelet Analysis
- 24 Empirical Orthogonal Function Analysis
- References
- Index
16 - More Discussion on the Harmonic Analysis and Fourier Analysis
Published online by Cambridge University Press: 21 April 2022
- Time Series Data Analysis in Oceanography
- Time Series Data Analysis in Oceanography
- Copyright page
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Introduction to MATLAB
- 3 Time and MATLAB Functions for Time
- 4 Deterministic and Random Functions
- 5 Error and Variability Propagation
- 6 Taylor Series Expansion and Application in Error Estimate
- 7 Spherical Trigonometry and Distance Computation
- 8 A System of Linear Equations and Least Squares Method
- 9 Base Functions and Linear Independence
- 10 Generic Least Squares Method and Orthogonal Functions
- 11 Harmonic Analysis of Tide
- 12 Fourier Series
- 13 Fourier Transform
- 14 Discrete Fourier Transform and Fast Fourier Transform
- 15 Properties of Fourier Transform
- 16 More Discussion on the Harmonic Analysis and Fourier Analysis
- 17 Effect of Finite Sampling
- 18 Power Spectrum, Cospectrum, and Coherence
- 19 Window Functions for Reducing Side Lobes
- 20 Convolution, Filtering with the Window Method
- 21 Digital Filters
- 22 Rotary Spectrum Analysis
- 23 Short-Time Fourier Transform and Introduction to Wavelet Analysis
- 24 Empirical Orthogonal Function Analysis
- References
- Index
Summary
Harmonic analysis and Fourier analysis are fundamental tools for oceanographic time series data analysis. Both can be derived from the least squares method. They are different, however, in one major respect: Fourier analysis is based on a complete set of base functions, such that the convergence of relevant Fourier series is guaranteed for continuous functions. In contrast, harmonic analysis almost always has non-zero total error squared unless for pure deterministic functions with tidal frequencies only. This chapter provides additional discussion and some examples aimed at a better understanding of the concepts and techniques. The discussion will involve tidal harmonic analysis and Fourier analysis by contrasting them in concept and through some examples for harmonic analysis.
- Type
- Chapter
- Information
- Time Series Data Analysis in OceanographyApplications using MATLAB, pp. 279 - 307Publisher: Cambridge University PressPrint publication year: 2022