3 Primary Data Analysis 



Primary data processing was done by checking data quality through a series of 

 spectral intercomparisons, and, for data of sufficient quality, computing 

 frequency-direction spectra. All steps rely on Fourier analysis of pressure gauge 

 time series data, and subsequent computation of cross-spectral densities. A dis- 

 cussion of error-checking procedures then leads logically to the subsequent steps 

 involved in frequency-direction spectral computation. 



Error Checking 



The first step in data processing is computation of discrete estimates of 

 frequency autospectra of pressure signals, and surface-corrected cross-spectral 

 densities of signals from all pairs of gauges. Cross spectra are denoted in complex 

 form as C. (f n ) - iQ r (f n ), where C. (f n ) is the coincident spectrum, 2, y (/ B ) is the 

 quadrature spectrum, i and j (as subscripts) are indices ranging in value from 1 

 to 6 that refer to the gauge numbers shown in Figure 2, and f n is the n ' of a set 

 of TV discrete frequencies. 1 Frequency autospectra are denoted S(f n ), and, if sur- 

 face corrected with the linear wave pressure response functions (Dean and Dal- 

 rymple 1984), are identically equal to C. t (f n ). All spectra are computed using 



Welch's method (Welch 1967) with standard Fourier analysis techniques (Bendat 

 andPiersol 1971). 



In a collection, the 8,192-sec time series from each gauge is analyzed in 15 

 half-lapped segments of 1,024 sec duration. Each segment is demeaned, tapered 

 with a variance-preserving window, and converted to the frequency domain with a 

 discrete Fourier transform. At this point, the analysis is split into two parts: esti- 

 mates of pressure autospectra from each gauge at depth, and estimates of surface- 

 corrected cross spectra of sea surface displacement. Raw cross-spectral estimates 

 are formed for all gauge pairs using temporally corresponding transformed seg- 

 ments of pressure data corrected to represent sea surface displacement. Raw auto- 

 spectral estimates are formed for each of the 15 transform segments for each indi- 

 vidual gauge. At the error-checking stage, autospectral estimates are not surface 

 corrected. 



For convenience, symbols and abbreviations are listed in the notation (Appendix E). 



Chapter 3 Primary Data Analysis 



