638 



BELL SYSTEM TECHNICAL JOURNAL 



sures that oo and thus the displacement error will be zero, leaving prin- 

 cipally the velocity and acceleration errors to be considered. 



The coefficients Co , ai , 02 , etc. may be calculated easily for any particu- 

 lar case. For illustration, the three common forms of fi characteristic shown 

 in Fig. 11 will be examined. (As previously discussed, the designated forms 

 of fj. need hold only for | /x | ;^ 1.) 



\ 



LOG OJ m~ 



Fig. 11 — Elementarj' /x forms. 



Type 1. —6 db/ octave, n = ooo/joi 

 The error expansion becomes, 



A(/) =-f,{t) -\f\{t) + 



0)0 Wo 



(12.1; 



For the combination of high accuracy and rapidly converging input spec- 

 trum, the first term is the only one of importance. Thus this type of sys- 

 tem has essentially a velocity error. 



Type 2. —12 db/ octave, 11 — {uq/juY 

 Here the error is 



A(/) = -.f,{t) 



Cx^O 





(12.2) 



