non-normalized autocorrelation function. There are a total of 
m lags shown, and m numbers are the result, as designated by 
Qo? Ar Qoreeee-Qn gs and @.. 
Equation (10.31) is the finite difference analogue of 
equation (10.27) except that it yields increments in E(y#) in- 
stead of [a(n )]°. It yields the "raw" or uncorrected values 
of quantities related to [aCe )1°, (Tukey [1949]). 
Equation (10.32) finally yields the difference values between 
ECH 44/2) and E( Hy 4/2) It is a correction of the "raw" data 
which is necessitated by the inherent inaccuracies introduced in 
the procedure by taking only N points and by the finite difference 
procedures. It essentially smooths the values of Li by giving 
the correct factors which determine the interrelation between ad- 
jacent values. 
After the various multiplications and summations indicated 
by equations (10.30) through (10.32) have been carried out the re- 
sult is m numbers which represent the increments in E(#) from 
H equal to r(h - 1/2)/Atm to » equal to r(h + 1/2)/Atm as 
given by equation (10.34). The center of each band is at h 
equal to th/ Atm as given by equation (10.33). Note that the 
dimensions of the various quantities are correct. The most re- 
presentative value of [a(n 1° for the point, #,, is then given 
by equation (10.35). The period, T,, which corresponds to the 
spectral frequency #, is given by equation (10.36). 
For # equal to zero and / equal to / Nts the statements 
given above must be modified because of the edge effect. For h 
equal to zero in equation (10.32), @,, should be given by . 
EC Hy /o) - E(O) and the band is Only one half of those in the 
- 276 - 
