PHASE DISTORTION IN TELEPHONE APPARATUS 521 



We may consider the signal as operated on successively by different 

 portions of the phase characteristic. The first term aio) delays the 

 signal without distortion by time ai, the remaining terms distorting it. 



The phase characteristic of a constant K band pass filter and those 

 derived from it may, in the transmitting range, be written 



Let flo = fli^w CLi again defines delay of the signal without distor- 

 tion provided ao = Nt. If ao 7^ Ntt there is a delay ai and in addition 

 every component is shifted through an angle ao and then distorted by 

 the remaining terms. Let us see what the constant phase shift ao 

 of itself does to the signal. , 



We may write 



Ih = S y cos(co/ -\- Q — ao)d(ji} (13) 



or 



lb = cosao y y cos (cot + d)dci: -f sin Oo J^ y sin(aj/ + 6)doo. (14) 



The wave resulting from this distortion only may be resolved into 

 two components one undelayed and exactly like the original but modi- 

 fied by the amplitude factor cos ao and another w^hich may be derived 

 from the original by shifting all of the components through an angle 

 7r/2 and modifying by a factor sin ao. 



The phase characteristics of a high pass filter may be written 



B = ai^co-i + ao'o:- + aa^w-^ • • -. (15) 



Here there is no term producing a delay without distortion to the 

 signal as a whole nor is there a constant term producing a constant 

 phase shift at all frequencies as in band filters. The distortion de- 

 pends upon the values of aiao etc. 



The phase characteristic of an all pass network may in the lower 

 frequency range be represented by the same expression as for the low- 

 pass filter and in the upper frequency range as for the high-pass filter 

 but no such series as above will cover the entire range. 



