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Abstract

The fast Fourier transform (FFT) has been accepted as a tool for signal processing. This study conducted a series of numerical experiments using Matlab. By conducting FFT analysis on designated wave trains, the FFT results revealed that an extra phase shift of ��ሺ2�� ��⁄ ሻ , with N representing the number of data points for an i-th wave component, was implicitly added to the analyzed phases during the analysis. When extra phase shifts were subtracted from the analyzed phases of each component, signals could be completely reconstructed in the time domain with an acceptable difference. This study tested component and non-component waveforms, linear and nonlinear waveforms, multiple-component waveforms (one-, two-, three-, and four-waves), and several laboratory irregular wave records. The results confirmed a strong relation between the extra phase shift and the time shift of the wave profile. Accordingly, Fourier series used for wave profile recovery in the time domain should start from time 0 to avoid phase shifts. Although this study did not employ all possible FFT packages for experiments, except for Matlab and some alternatives, the time series definitions in the frequency and time domains were suggested to be identical; thus, water wave analyses in both domains can be closely connected. From the experiments, more understanding about characteristics of various waveforms were achieved, and more extensive researches and applications can be conducted using the procedure described herein.

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