TM No. 377 



analyze using Fourier series approximations c Certain statistical pitfalls 

 associated with truncated series expansions and peculiarities in the spectrum 

 estimates have been avoided in the empirical formulations, making life rela- 

 tively easy for the geophysisto 



The following is a resume of the methods and formulation of the statistical 

 analysis used with the M.IcT. IBM-7090 and the NUWS IBM-1620 and CDC-3200 

 digital computers . The Fortran program suitable for these and similar com- 

 puters is listed in appendix D. 



The experimental data were presented at equally spaced time intervals 

 £Y > yielding a discreet time series, 



U 



') u i) ^3; ^ } (111=36) 



which had been previously edited and properly scaled. Other than the editing 

 for spurious points, no smoothing was done c It was hoped thus to preserve the 

 high frequency characteristics of the data. 



According to NUWS procedures^ the arithmetic mean must be removed from the 

 data, as indicated by equation (111-12). The mean value is given by: 



V 

 Cs^jl^*) i (lH-37) 



where N is the total number of samples ■ Subtracting the mean 1JL from each data 

 point ti-^d) } results in a new time series: 



KVW " 1A^(t)-U 5 (ni=38) 



and, by definition^ ^ 



Note that the total time over which the data are sampled is given by; 



T= 7^ rA/Af . (111=39) 



The auto-covariance function ^^Or) ( see eq^tion (111-1*0) is approximated by: 



(lH-40) 



59 



