TRANSMISSION OF INFORMATION ■ 551 



medium. Other forms of energy storage give to the admittance- 

 frequency curves shapes which are characteristic of the particular 

 system. This alteration of these curves is commonly spoken of as 

 frequency distortion. Their form may in most cases be deduced 

 fairly readily from the values of the energy-storing and energy-dissi- 

 pating elements of the system. This fact makes such a description 

 of the system particularly useful for design purposes. 



This physical description is, of course, useful as a criterion of 

 performance only in so far as it can be related to the satisfactoriness 

 with which the system performs its primary function of transmitting 

 information. In the case of telephony it has been found practical 

 to establish such a correlation by purely empirical means. Until 

 fairly recently adequate results have been obtained by considering 

 the amplitude-frequency function only. With the use of lines of 

 increasing length and with increasingly severe standards of performance 

 it is coming to be necessary to take account of the phase-frequency 

 function as well. 



In attempting to extend this method of treatment to telegraphy it 

 was not found desirable to establish the correlation between steady 

 state properties and overall performance by purely empirical methods. 

 One reason for this was that a considerable fund of information has 

 been accumulated with reference to the correlation between the 

 overall performance and the transient properties of the system. A 

 correlation therefore between steady state and transient properties 

 would offer a means of bringing this empirical information to bear on 

 the design of apparatus and systems on a steady state basis. For 

 bridging this gap between steady state and transient phenomena 

 there was already available one arch in the form of the Fourier Integral. 

 This integral may be thought of as a mathematical fiction for expressmg 

 a transient phenomenon in terms of steady state phenomena. It 

 permits the determination, for any magnitude-time function, of the 

 relative amplitudes and the phases of an infinite succession of sustained 

 sinusoids whose resultant is at any instant equal to the magnitude of 

 the function at that instant. The amplitudes of the sinusoids are 

 infinitesimal and the frequencies of successive components differ from 

 each other by infinitesimal increments. The relative amplitudes and 

 the phases of these components expressed as functions of the frequency 

 constitute a steady state description of the magnitude-time function. 



Suppose then we have given the magnitude-time function repre- 

 senting an impressed transient driving force and wish to obtain the 

 magnitude-time function of the received current. We deduce the 

 steady state description of the driving force, modify the amplitudes 

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