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BELL SYSTEM TECHNICAL JOURNAL 



the loss requirement with a large margin of safety, but the phase 

 shift curve departs seriously from linearity near the last useful fre- 

 quencies, which fall in the shortened intervals of the transition factors. 



With these two attempts as guides, a compromise frequency pattern 

 which exactly suits the conditions of the problem is readily arrived at. 

 In contrast to the transition factor spacings of 0.853q: and 0.353q:, 

 as shown by the solution for m = 2, those actually adopted are 0.94a 

 and 0.375a so as to make the first transition spacing more nearly 

 uniform with those in the pass-band. The indicated frequency 

 pattern is shown in the third column of the table. 



As the values of these transition factors near the band edges are 

 somewhat too large they lead to larger undulations of the phase 

 characteristic in those regions than near the band center. The 

 approximations can be rendered more uniform throughout the band 

 without serious consequence to the loss characteristic by multiplying 

 the tangent expression by a constant slightly smaller than unity. In 

 this case the value chosen was Ki = 0.9975. 



The final "delay" and loss characteristics, corrected for the effects 

 of dissipation, are exhibited by Figs. 16 and 17. A noteworthy result 



12 13 



FREQUENCY IN KILOCYCLES PER SECOND 



Fig. 16 — Variation in the phase slope of a band pass liUer. 



