Analysis of ocean wave fields using the harmonic phase tracking parameter estimation technique

This study can be best summarized as the development of a new signal processing technique followed by its engineering application to ocean wind waves. The fundamental motivation was, are ocean waves random, or do they self-organize into a finite number of discrete sinusoids? And if they do self-organize, could their behavior be better understood with a more realistic mathematical decomposition?; A new harmonic retrieval technique called "Harmonic Phase Tracking" (HPT) was developed. Unlike the usual Fourier Series representation which uses a uniformly-spaced set of component frequencies, HPT estimates the true number of harmonics (signal rank) along with their (arbitrary) frequencies, amplitudes and phases. A very simple fact serves as the basis for HPT: for a harmonic signal, it is possible to recover the true phase using only an estimated frequency. HPT exploits this by finding a series of true phases for shifted windows of the time series; the slope of the unwrapped phase versus time equals the true frequency. For the general case with multiple sinusoids, total least squares is used and iteration is required to converge to the best-estimated parameter set.; HPT is applicable to any time series and parameters can be slowly-varying. Deterministic versus stochastic components are identified from inspection of parameter evolution versus time. HPT is a "high resolution" technique, meaning it is not a linear operator and that the frequency resolution exceeds the Rayleigh limit. Extensive validations are included for analytical and laboratory signals where the signal parameters are known.; Two sets of full-scale ocean waves are analyzed. The first control group corresponds to stationary conditions, while the second set corresponds to Hurricane Bob on August 18 and 19, 1991. Both data sets include waves at multiple gage positions in 8 meters of water. It was concluded that there is a coherent and discrete structure to the waves over space and time, as inferred from inspection of the evolution of mean frequency and amplitude versus time, and most importantly, from inspection of the continuous phase versus time for various components.