DESIGN OF REACTIVE EQUALIZERS 



ni 



may he written in thec^^ (loniaiu as a I'ourier cosine series, 



/l(v?) = <7o + (?! COS(^ + 02 cos 2^ + ' ' • + «« COS IKp = ^ fl^ COS k(p. (22) 



In particular, the correspondence of the x domain and <p domain may be 

 conveniently illustrated as in Fig. 21. It is to be noted that the compara- 

 tively limited region of the useful band, < .v < 1, in the .v domain goes 



into half of the available range, < (^ < - , in the ip domain. It is apparent, 



then, that some advantage has already been gained by this transformation. 



Before attention can be confined to the evaluation of the coefficients, au , 



it is necessary to establish the form of the approximating function in the cp 



domain which corresponds to /(.v-) in the frequency domain, and to relate 



-00-1 1 00 



I I LJ L_ 



I I I I 

 I'll 

 I I I I 



— I I I I r 

 -n n n TT 



"2 2 



-►y> 



Fig. 21 — Graphical representation of the transformation x = tan ^. 



the Ak in eq. (14) to the au in eq. (22). This is accomplished by means of the 

 following relationships: 



X = tan 



/; 



— cos (f 



+ cos (p 



1 2 



1 -~ X 



COS Hip = Vn (cos (p). 



Thus, the corresponding expression for eq. (22) in the frequency domain 

 becomes 



fi{<p) = ao + aiVi {cos<p) -f- 02^2 (cos^?) 



+ azVz {cos(p) + 



-f dnVn {C0S<p) 



