(2) Description of wave spectral analysis.

(a) Unlike the wave train or wave-by-wave analysis, the spectral analysis method determines the

distribution of wave energy and average statistics for each wave frequency by converting time series of the

wave record into a wave spectrum. This is essentially a transformation from time-domain to the frequency-

domain, and is accomplished most conveniently using a mathematical tool known as the Fast Fourier

Transform (FFT) technique (Cooley and Tukey 1965). Here we will treat analysis of the time recording ofthe

surface at a point, in order to obtain a frequency spectrum of the record. In a later section, we will describe

how to obtain a frequency-directional spectrum.

(b) The *wave energy spectral density E(f) *or simply the *wave spectrum *may be obtained directly from

a continuous time series of the surface *η(t) *with the aid of the Fourier analysis. Using a Fourier analysis, the

II-1-80

Water Wave Mechanics

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