situation which may provide conditions well outside the scope of the BF insta- 

 bility. Similarly, the waves can be expected to be more organized spatially 

 and modulation processes would be operating over relatively long time scales. 

 This reasoning is qualitatively supported by the time series which show 

 evidence of very long modulation periods . The advantage to be gained from 

 such a data sample is that a record with a given length (e.g., 512 seconds) 

 is very likely stationary in terms of any underlying modulation phenomenon. 

 Because the modulation time scale is large, the 40-minute gap between 1,024- 

 second records is not expected to be a severe shortcoming, provided the modu- 

 lation time scale is short enough to be identifiable in the record. The 

 stationarity of the meteorological system generating the waves also helps to 

 justify this expectation. 



IV. ANALYSIS PROCEDURES 



1. Data Editing. 



The first step in the analysis of field records is editing the data. 

 Although the field records selected for this study were relatively free of 

 signal contamination, past experience has indicated that field records should 

 be checked for data points excessively far from the mean and for large differ- 

 ences between successive data points (Thompson, 1974). These checks identify 

 the electronic contamination occasionally found in field records . Bad data 

 points are defined in this study as points more than 5.0 standard deviations 

 from the mean and successive points which differ by more than 2.5 standard 

 deviations. Bad points are removed from the record and replaced with points 

 obtained by interpolation between good points. 



2. Component Frequencies , Amplitudes , and Phases . 



a. Background Discussion of Fourier Transform Techniques . Frequency com- 

 ponents of a time-series record were initially estimated from a fast Fourier 

 transform (FFT) computer program following the development of Harris (1974). 

 Let the finite time series with zero mean be represented as 



y = y(nAt) , n = 1, 2, 3, ..., N 



|y(nAt)| < L ^^^ 



where At is the constant time interval between data points, N the number 

 of data points, and L a finite constant. The time series can be represented 

 as a sum of N linearly independent, bounded functions 



N 

 y(nAt) = I c^f^(nAt) (6) 



i=l 



where Cj is a constant and f^ a known function. 



Since ocean waves have a quasi-periodic form, it seems sensible to choose 

 periodic functions for the f^ in equation (6). If the trigonometric func- 

 tions are used, equation (6) becomes 



N/2 

 y(nAt) = I (a^ cos o^ nAt + b^^^ sin a^ nAt) (7) 



m=i 



27 



