For a more strict analysis^ the degrees of freedom should be compute,4 

 from the data with the white noise still present since at each value it is also 

 distributed according to Chi square with 19 degrees of freedom. The error 

 made in the above computations is small for low values of k, but for large k 

 the variation in white noise naay be falsely reflected into variation in spectral 

 estimates because the white noise is a rather large proportion of the total 

 contribution. 



The degrees of freedom for low valuer of k are quite low. For k equal 

 to 11, there are only 22 degrees of freedom. Had all these stereo pairs been 

 satisfactory for analysis and had there been no distortion at the edges of the 

 stereo data, the 19 degrees of freedom for each value of U(r,s) actually ob- 

 tained would have been raised to 50 degrees of freedom, and the 22 degrees of 

 freedom for k = 11 would have been close to 50 degrees of freedom. 



The number of degrees of freedom given by equation (11.15) can be com" 

 bined with the entries in Table 11.5 to give the 90 percent confidence bounds 

 on the estimates of AE as corrected for white noise. The results are shown 

 in Table 11.8. The values given at the 90 percent confidence bounds will 

 enclose the true value of AE nine times out of ten in repeated tests of this 

 same type under the same conditions. Of course, for a given set of data, the 

 true value either does or does not fall within the confidence bounds and one 

 can never know whether it did or did not. 



The entries shown in Table 11,8 can be connbined with the entries in 



Table 10.1 to compare the wave pole data and the stereo data. The result is 



205 



