r = 



cosh nkg 



i+1 



[W ' 1 / (X C (A 1 ) - Q sin nk£ d£ 



. A 

 + IV s ' 1 / (X S (A 1 ) - O sin nk£ d?] 

 x o 



[W ' 1 / Y^CA^D cos nk? d£ 



w s,i j. ySfA 1 ) cos nk? d?] 

 y o 



(19) 



The W terms are weighting factors used to distribute the error pro- 

 portionally between the components of the transform generated and 

 specified curves. 



It can be shown that the above relations result from minimizing 

 the following error function: 



E. , = W 5 ' 1 E S ' i+1 + W 5 ' 1 E S ' i+1 

 1+1 xx v y 



„.c,i „c.i+l ,.,c,i ^c.i+1 

 + W ' E + W E 

 xx v v 



(20) 



where 



2y j[X i, (A ± U,-e)) - x 1 X (5,-B)] 2 d? , 



-A 



(21) 



,s,i+l _ J_ 



V ~ 2\ 



i+1 



Dr(A x (£,-B)) - y X (?,-B)] 2 d? , 



(22) 



,c,i+l J_ 

 : x 2\ 



i+1 



IX (A x (£,+£)) - x 1 ^f^ + B)] 2 d? , 



(23) 



and 



17 



