PHASE DISTORTION AND PHASE DISTORTION CORRECTION 199 



explicit time function is sometimes essential, in the last analysis, to 

 indicate the degree of correction afforded. This information may be 

 supplied to sufficient precision by the first and succeeding derivatives 

 with respect to frequency of the steady state phase, which, as explained 



vM 



Fig. 4 — Distortion corrective circuit for long telegraph cable 



below, are extremely useful criteria of the improvement in the time 

 and steepness, respectively, of building-up over a finite range of 

 frequencies. Nevertheless, to visualize the actual effect of the applied 

 phase compensation upon the arrival current or voltage due to an 

 impressed e.m.f. of a specific frequency requires the evaluation of the 

 explicit time function. 



It is the object of this paper, following an analytical exposition of 

 the theory of phase distortion, to consider various methods of phase 

 distortion correction with particular reference to terminal phase com- 

 pensating networks and the application of the lattice network to the 

 loaded line as a terminal phase corrector. 



II. Phase Distortion 



1 . Steady State Theory of Phase Distortion 



The mathematical theory of phase distortion in signaling systems 



may be explained briefly from the steady state point of view. We 



suppose that it is required to transmit a signal /(/), which can be 



represented by the Fourier integral, 



