638 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1952 



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 



Fig. 9 — Comparison of design procedures — four natural modes equalizing two 

 natural modes at po = — r^ uc. 



approximating network gain is generalized, by introducing arbitrary 

 frequencies of infinite loss, in addition to the arbitrary natural modes. 

 The methods are also modified for approximation to an assigned phase, 

 instead of gain, or to phase and gain simultaneously. Finally, the anal- 

 ysis is modified to permit useful intervals of the "high-pass" type, or 

 (in the case of gain simulation) of the "band-pass" type. 



16. APPROXIMATION TO A GENERAL ASSIGNED GAIN a 



If we now permit the assigned gain a to be general, in the sense of 

 Section 8, we must return to the formulation: 



J2C2kz"' = log [R(z)R{-z)] 



(50) 



