The pattern employed, the values of the radii, and the numbers finally 

 obtained are shown in figure lloZO for a quarter sector of the full area of 

 the directional spectrum. All other points can be obtained by symmetry. 

 Note that half the values on the horizontal axis should be used on the vertical 

 axis. 



The values of U^Ai^i' ^) "^ ^SC^'"^' ^^ corrected for column noise were then 



entered in the corresponding squares. To determine U(k), the pereei^a-ges of the 



squares falling between circles with radii corresponding to k • -l arid k + — 



^ 2 



were multiplied by the AE values for the appropriate squares axbd all contri- 

 butions for that particular semicircular ring were summed. 



The results are shown in Figure 11.21, The values of AE in (ft) ^ obtained 

 upon summation are plotted as a function of k in the upper curve, Tlje spec- 

 trum obtained from the wave pole data is also shown. 



An additional correction is needed before the two curves can. b^ coynpared. 

 The effect of the white noise variance of 0„54 (ft) must be removed. Since 

 this error variance is spread evenly over the entire plane of the directional 

 spectrum each square in this analysis has an expected value of 1,08/800 (ft)'' 

 assigned to it in terms of E value. When the entries in Table 11,4 are 

 multiplied by 1.08/800 and subtracted from the values shown on the top curve 

 in figure 11.21 the result is the middle curve which shows the frequensy . 

 spectrum corrected for the white noise estimate given previously. Tlie effect 

 of assuming that the white noise error variance is twice as great is shown by 

 a third curve in the figure. Such a correction would be much too big. 



197 



