Frequency Spectrum

A frequency spectrum is the distribution of variance (energy) of a fluctuating signal as a function of frequency, computed from a time series by Fourier transform. For ocean surface waves the spectrum S(f) partitions the variance of sea-surface elevation across frequency, with the area under the curve equal to the total variance; the significant wave height is four times its square root. Wave spectra show a sharp peak at the dominant frequency and a high-frequency tail near f^-4 to f^-5. Empirical forms include the Pierson-Moskowitz spectrum for a fully developed sea and JONSWAP for fetch-limited seas. The same method analyzes current and turbulence records.