segments of 2,048 points. Each segment is tapered with a Kaiser-Bessel window 

 (a modified Bessel function of the first kind, compensated uniformly for loss 

 of variance because of windowing) to reduce leakage. The segments are then 

 fast Fourier transformed to the frequency domain. An intermediate-resolution 

 transform is found by averaging the 15 transformed segments, frequency by 

 frequency. Final resolution transforms are found by averaging results over 

 10 adjacent frequency bands. The final resolution bandwidth is 0.00976 Hz. 

 Transform estimates are retained for 28 frequency bands ranging from band- 

 center frequency 0.054 to 0.318 Hz, i.e., the wind wave frequencies of 

 interest. Resulting degrees of freedom are at least 150 (assuming 8 con- 

 tiguous segments and ignoring any gain from lapped segments) for which the 

 Chi-square confidence limits are nearly Gaussian. They equal approximately 

 ±19 percent at the 95 -percent level and ±15 percent at the 90 -percent level. 

 Conversion of pressure signals 



109. Conversion of pressure signals measured near the ocean bottom to 

 water surface displacement is done through the linear wave theory pressure 

 response factor as described in the SPM (1984). It is a frequency- dependent 

 function of water depth and gage elevation which provides the amplification 

 necessary to compensate for attenuation of wave properties with depth. It is 

 larger for high-frequency waves since the pressure signal of these waves 

 attenuates more rapidly with depth. In 8 m of water, the factor ranges from 

 about 1.05 for 0.054-Hz signals to about 13.1 for 0.318-Hz signals. Note that 

 any noise in the higher frequency signals is also amplified by the larger 

 factor. If the signal-to-noise ratio drops at these frequencies (as it does 

 in low-wind conditions when the wave field is mostly relict swell) , noise can 

 become important and can contaminate the high-frequency parts of the spectra. 

 This possibility needs to be considered in interpretation of results. 

 Computing cross spectra 



110. Cross spectra are computed from products at corresponding frequen- 

 cies of Fourier transforms of data from two different gages. They have two 

 parts, called coincident and quadrature spectra. The two parts contain 

 information about the products of the amplitudes of the Fourier transforms and 

 the phase difference of a signal at one gage relative to a signal at the 

 other. This phase difference contains wave directional information. At a 

 given frequency, the cross spectra can be computed for all gage pairs. As 

 mentioned above, there are 36 pairs possible with 9 gages. When the 



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