Evolutionary Fourier Analysis of Wave Data

by Leon E. Borgman, Univ of Wyoming, Laramie, United States,
Mihail Petrakos, Univ of Wyoming, Laramie, United States,
Chao Li, Univ of Wyoming, Laramie, United States,

Document Type: Proceeding Paper

Part of: Ocean Wave Measurement and Analysis


A new method is presented for analyzing nonstationary water level height time series. The usual assumption of pseudo-stationary intervals is avoided and the wave spectra can be changing very rapidly. The time series, η(t), is represented in a finite Fourier series, summed on m, for which the Fourier coefficients, A(m,t), are themselves functions of the time. The technique combines methods from finite element theory with Fourier analysis by representing the A(m,t) as linear combinations of basis function over each of sequence of finite intervals (or elements). The multipliers of the basis functions depend on m only, and not t. The method is applied here primarily to the estimation of frequency spectra, although some discussion is given for the use of the procedure in the estimation of directional wave spectra.

Subject Headings: Finite element method | Fourier analysis | Linear analysis | Water waves | Frequency response | Hydrologic models | Mathematical models | Time series analysis

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