More Discussion on the Harmonic Analysis and Fourier Analysis

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.