(11.8) 



20 ' zj [20 - 



f = 1,58 -^-41 1^ -"2 



= 1.58(6) = 9.48 

 For Data Set 3C, the number of degrees of freedom is given by equation 



ai.9)« 



= 9=48 

 Thus each individual spectral estimate is distributed according to a Chi- 

 square distribution witli slightly more than 9 degrees of freedom. A ratio 

 as large as 2.57 for two variances so distributed is quite possible since at 

 the 5 percent level of significance the ratio can be 3.18, and therefore these 

 values are not unusual. They simply represent sampling variation. 



The plan for the analysis of the results 

 The average of the two covariance surfaces as shown in figure 11.15 is 

 the best available estimate of the covariance surface. The sum of the two 

 independently determined spectra as shown in figure II0I8 is the best avail- 

 able estimate of the energy spectrum. This energy spectrum has only 19 

 degrees of freedom per spectral estimate. Also it obviously has some dis- 

 tortions in it caused by columm noise (naainly) and curvature. It also has a 

 white noise background due to the original spot hejght reading errors. The 

 planof the analysis of the data as represented byfigures 11,15 and 11,18 is to: 

 1- Remove the column noise from the directional spectrum. 

 2., Sum around circles of constant frequency in order to connpare the 



]89 



