Such, a function is given by 



N 



(11,18> f(Hi, 0)^^[1+ S a„(iJL)cos2n8 + bn(M.)sin2ne] 



ir n=l " 



for e^(M.) ~ TT < e < BnidJ-), and zero otherwise if a.^ and b^ can be so chosen 



that f(|j., 8) 5^ and if 8 (|a.) is the angle in the first quadrant where f(|i, 8) is 



a minimum as a function of [jl. 



If the values of the entries in Table 11,6 are divided by the sum for each 



If the Fourier series given by equation (11.18) is truncated at some parti- 

 cular N as indicated, the effect is to smooth out som.e of the sampling vari- 

 ation in the data under the assumption that the spectrum is not too complex a 

 function. Since there are only 36 points to fit for a given k, for N large 

 enough a perfect fit within the resolution of the data could be obtained. 



The coefficients, a (ji) and b^(|x), in equation (11.18) can be computed 

 for a given |x, = 2iTk/96, by equations (11.21]^ and (11.22):. 



(11,21) 



+ 17 / (m+-^)Tr\ (znim+jyA 



+ 17 / (m+^ 

 (11,22) b (k) = 2 S F k, 



"" m=^18 » 36 



227 



