Q*(p, q) = 2Q(p, q) 



for p = 1 to 19, q = -19 to +19 



that 



Q*(0, q) = Q(0, q) q = -19 to +19 



Q*{20, q) = Q(20, q) q = -19 to +19 



/ Q*(p, 20) = Q{p. 20) p = 1 to 19 



Q*(p,-20) = Q(p,-20) p= 1 to 19 

 and that 



Q*(0, 20) =-iQ(0, 20) 



Q*{0,-20) =1q(0,-20) 

 2 



Q*(20,20) = -iQ(20,20) 



Q*(20,-20)=-iQ(20,-20) . 



Thus points on the q-axis have unit weight (but since Q(0, q) = Q(0,-q), 



they could be considered as one set of values weighted twice). Points off the 



p-axis in the first and fourth quadrants are weighted twice due to extension into 



the -p quadrants, points on the sides are weighted once, (really 1/2 on four 



sides of the full expansion) and corner points are weighted one half (really 



1/4 on the four corners). 



The raw estimates of the spectrum are then found from equation (8.21). 



, +20 20 

 (8.21) L(r, s)=-I- 2 S Q*(p. q) cos [ JL (rp + sq)] 



800 q=_20 p=0 ^" 



where r = 0, 1, 2, . , . , 20 



s = -20, -19, .... +20 . 



Note that L(r, s) = L(-r^ -s) and that the spectral estimates have the same 



property as equation (8. 12)„ 



68 



