Extraction of Harmonic Components From Intermittent and Aperiodic Wave Elevation Measurements

Sea waves never repeat so any measurement of irregular wave elevation time history should be treated as an aperiodic function. Furthermore, wave elevation measurements might also be intermittent. The objective of this study is to extract harmonic components from an aperiodic and intermittent wave elevation measurement. A mathematically sound method, which is completely different from the traditional Fourier method, is developed for extracting all harmonic components from an aperiodic and intermittent wave elevation measurement. The method involves two main steps. In the first step, the number of harmonic components in the wave elevation measurement and the frequency of each component are estimated. After knowing the frequencies, the amplitude and phase angle of each harmonic component are computed at the second step using a least squares method. The superiority of the newly developed method over the traditional DFT analysis on extracting harmonic components is demonstrated using simulated aperiodic wave elevation signals. Whereas using the proposed method can nicely recover all target harmonic components, the Fourier analysis fails to decompose the signal into the target harmonic components due to its periodicity assumption imposed on the aperiodic wave elevation signal. In addition, the new method also performs well with a simulated aperiodic/intermittent wave elevation signal, and can accurately recover the missing part of the aperiodic/intermittent signal.