564 



BELL SYSTEM TECHNICAL JOURNAL 



Phase and Attenuation Distortion 



To illustrate how phase and attenuation distortion operate to reduce 

 the effective transmitted frequency range, the filter characteristics 

 shown in Figs. 9 and 10 will be considered.*^ One of the uses of filters 

 in telephone systems is to provide a number of channels for one trans- 

 mission line by using filters in parallel, each filter transmitting a dif- 

 ferent frequency range. In a long line as many as twenty or twenty- 

 five filters may be used in series for each channel. In this use it is 



a 



z 

 o 

 o 



UJ 

 If) 



0.05 



0X34 



0.03 



x|3 

 ■o|-o 



>- 

 < 



III 

 o 



0.02 



0.01 



50 



40 



-0 



30 - 



Z 



o 



20 



lO 



2500 



500 1000 1500 2000 

 -EFFECTIVE BAND 20 FILTERS Q = 200 



-EFFECTIVE BAND 20 FILTERS Q=200 (EiQuALfzED)" 

 -EFFECTIVE BAND I FILTER Q = 200 (NEGLIGIBLEV 



3000 3500 4000 



FRECUENCY IN 

 CYCLES PER SECOND 



-ALLOTTED BAND- 



Fig. 9 — Transmission for a filter ha\ing a slow rate of attenuation increase. 



desirable that the attenuation at the edge of the transmitted band 

 should increase at a very rapid rate, and that the delay distortion at 

 the edge should be small. 



The solid curve in Fig. 9 shows the attenuation distortion, i.e., the 

 difference between the minimum attenuation and the attenuation for 

 any frequency/, for a filter having a slow rate of attenuation increase. 

 The delay for one filter is not shown, but it is about 1/20 of the delay 

 shown by the dotted curve. The allotted frequency band is determined 

 by the frequency value at which the attenuation curve of the filter 

 crosses that of the filter transmitting the adjacent band. The attenu- 

 ation at the crossover for the purposes of this discussion may be taken as 



•> For a discussion of the relation between these characteristics and the type of 

 filter section, the reader is referred to the previously cited paper by C. E. Lane. 



