MEASUREMENT OF PHASE DISTORTION 525 



ranges where the attenuation is not a function of frequency; that is, 

 the envelope delay in seconds is 



where 



and 



doi df 



(8 = the phase shift measured in radians, 



B = the phase shift measured in cycles, 



/ = the frequency measured in cycles per second, 



CO 



= 2x/. 



Hereafter in this paper this notation will be used. 



For a distortionless system this quantity is the actual delay of the 

 signal transmitted through the system. However, for a system which 

 introduces phase distortion, the received envelope is usually quite 

 different from the impressed envelope; and the delay of this envelope 

 through the system is then quite indefinite depending upon what 

 particular feature of the envelope is taken for observation. Neverthe- 

 less, the quantity defined as envelope delay is perfectly definite for such 

 a system. 



The significance of phase shift and envelope delay and the relation 

 between the two is considered at some length in other papers.®*-^ 

 The use of phase shift and delay data as a measure of phase distortion 

 is also considered there. Phase shift itself is a rather fundamental 

 quantity and various means of measuring it can be devised when both 

 ends of the system under consideration are available. In this paper, 

 one method of doing this is referred to which has proved very useful in 

 laboratory measurements in the design of apparatus. However, for 

 field measurements on telephone circuits, envelope delay seems to be a 

 more useful quantity with which to work. The derived nature of this 

 quantity makes its measurement somewhat complicated and conse- 

 quently considerable space is given to methods for this purpose. 



The envelope delay is determined from the difference in the steady- 

 state phase shift for a definite interval of frequency. In practical 

 cases finite intervals are used instead of infinitesimally small intervals 

 which would be required for the determination of the derivative, or of 

 the slope of the phase shift-frequency curve. This means then that 

 the measured value is actually the slope of the secant of the curve and 

 is simply an approximate value for the envelope delay, the amount of 

 approximation depending on the size of the interval chosen. The value 

 of envelope delay arrived at in this way will be called Ts so that 



^* I.e. Appendix I. 



