Hence, equation (B-8) can be written approximately as: 



2 



P(fJ - 



a^NAt 



Tsin TTCmQ-ni) 1 J sin Tr(mQ- m) 1 ^ 1 



.1 TTrm„-m) J I fm^+ml J J 



(niQ+m) 



fsin iT(mQ-m]1 fsin TT(mQ+m)"l 

 (. TT(mQ-m) J I TT(mg+m) J 



cos (2 ttihq - 2(J)) 



(B-11) 



If 20£mQ+m << N, a reasonable assumption in many applications, then the 

 first term inside the square brackets will dominate the other two. This 

 fact is illustrated in the following computations, where 



^ _ r sin TT(mo-m) 1 

 1 I TT(mQ-m) J 



(B-12) 



{sin Tr(mQ+m) ~| 

 TT(mQ+m) J 



1 



400 tt2 



< 0.0003 



(B-13) 



I fsin TTrmn-mll fsin irrmn+m") ") 



2 \ " M - \ '-^—^ I cos (2 TTmo - 2(j)) 



' L TT(mQ-m) J L 7T(mQ+m) J 



1 



10 TT 



sin TT(mQ-m) 



iT(mQ-m] 



(B-14) 



m„-mj =0.5 



Upper bound 



1 



m^ 



m^-l 

 m, -2 

 m^-3 



0.405 0.0003 0.020 



0.045 0.0003 0.0068 



0.016 0.0003 0.0041 



0.0083 0.0003 0.0029 



91 



