726 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



z ■= 



10 



12 



0.2 



0.4 



0.6 



1.6 



U 

 30 S 



Z 



20 I 



< 



10 z 



< 

 1.8 2.0 



0.8 1.0 1.2 1.4 



Fig. 1 — Low-pass transmission frequency characteristic with sharp cut-off. 



In Fig. 2 the attenuation and phase characteristics are shown as a 

 function of co/wc for w < coc and as a function of the inverse ratio coc/w 

 for CO > coc . It will be noticed that for the above case the phase charac- 

 teristic is infinite for co/coc ^ 1 and has even sjonmetry about this point, 

 while the attenuation characteristic has odd symmetry with respect to 

 the midpoint of the amplitude discontinuity. The phase characteristic 

 may be modified by a gradual cutoff in the attenuation characteristic, 

 as illustrated in the figure. It is possible to shape the attenuation char- 

 acteristic to obtain a linear phase characteristic in the transmission 

 band, i.e. between co/wc = and 1. Since transmission systems with a 



0.8 



0.6 0.4 



0.2 0.4 0.6 



Fig. 2 — Solid curves same as in Fig. 1, l>ut with inverse scale for aj/oj^ > 1. 

 Dashed curves illustrate modification in phase characteristic with gradual cut-off 

 in attenuation (not computed). 



