OoOl second. If these time intervals seem quite small, it should be remembered that 

 they are measured in the reference system of the rapidly moving airborne platform „ 

 In general, each resulting time (space) series consisted of 1200 or 1700 points depend- 

 ing on the direction of plane traveL Each series was numerically filtered prior to 

 spectral analysis to remove extraneous low frequency noise „ The apparent power 

 spectra or spectra of encounter were computed on an IBM 7074 by the method of 

 Blackman and Tukey (1958)o These apparent spectra are designated by E (w ) where 

 «jj is the apparent frequency of encounter as seen by the plane. The apparent auto- 

 correlation function is given as follows: 

 +T/2 



r(T)=-:^ / h(t)h(t+T)dt 



' -T/2 



with h (t) being the time history of the sea surface as seen from the aircraft. The 

 spectrum of encounter is: 



I ® 



E (w)=— / r (t)cos (wt )dT . 



II o 



Each spectrum was independent of the other spectra in that any particular 

 time series did not overlap those ahead or behind it. The raw spectra were corrected 

 for instrument response and then smoothed using consecutive weighting factors of 

 .23, .54, .23 (hamming). Due to the nature of the sea and the manner in which the 

 measurements were made and digitized, "aliasing" did not introduce difficulties. 

 The spectra of the data digitized at 0.05 sec were estimated over 100 lags. The 

 corresponding 90 percent confidence limits are 0.65 and 1 .39 for the downwind run, 

 and for the upwind run, 0,71 and 1 .32, respectively. The spectra of the data digit- 

 ized at 0.10 sec have 90 percent confidence limits of 0.75 and 1 .26 for downwind 

 run and 0.76 and 1 .24 for upwind run. While the confidence limits (degrees of 

 freedom) for various runs and spectral estimates are not identical, they are not 

 different enough to introduce statistical variability into the final results. 



5.2 Numerical Filtering 



A sample spectrum from the raw data is shown in Figure 9. The large 

 amount of energy at low frequency precludes any meaningful statistical evaluation 

 of the data. Such an evaluation must be made to determine the maximum length of 

 record which can be considered as at least weakly homogeneous. The length of 

 record used to produce Figure 9 corresponded to 6 nautical miles of sea surface at a 

 distance of 150 nm from the coast. It will be shown that this interval is sufficient to 

 ensure homogeneity. 



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