508 



BELL SYSTEM TECHNICAL JOURNAL 



rising attenuation at the edge of the band. These curves show that 

 the delay distortion in the transmitting band is increased by increasing 

 the slope of the attenuation curve at the cut-off although the minimum 

 value — i.e. the delay which applies to the signal as a whole, does not 

 increase appreciably. The effective band width transmitted depends 

 upon both the delay and attenuation characteristics since especially 



0.032 

 0.030 

 0.028 

 0.026 

 0.024 

 0.022 



^ 0.020 

 o 



z 



O 0.018 



o 



UJ 



0.016 



^ 0.014 



_I 



UJ 



° 0.012 



0.010 

 0.006 

 0.006 

 0.004 

 0.002 



400 



800 



1,200 1,600 2,000 2,400 



FREQUENCY IN CYCLES PER SECOND 



2,800 3,200 



Fig. 16 — Insertion delay characteristics corresponding to the phase characteristics of 



Fig. 14. 



for a number of filters like these in tandem the delay of the frequency 

 components of the wave near the cut-off may be so great that these 

 components contribute little to articulation. Therefore in the design 

 of filters a proper balance must be determined between the rate of 

 attenuation and the delay distortion. A more complete discussion 

 of the relation between delay, attenuation, and the effective cut-oft' is 

 given in the paper by J. C. Steinberg.-" When low pass filters are to 

 be designed with sharper cut-offs from the standpoint of both delay 

 and attenuation, there are two ways in which this is usually done, one 

 20 Loc. cit. 



