552 BELL SYSTEM TECHNICAL JOURNAL 



and phases of its various components in accordance with the known 

 admittance-frequency functions of the system, and obtain the ampU- 

 tude- and phase-frequency curves which represent the steady state 

 description of the received current. From these we deduce the magni- 

 tude-time function representing the received wave. 



A sHghtly different point of view, however, leads to results which 

 fit in better with our method of measuring information. We may 

 apply the method just outlined to deduce the magnitude-time function 

 which results when the applied wave consists merely of an instan- 

 taneous change in a steadily applied electromotive force from one 

 value which may be zero to another value differing from it by one unit. 

 The resulting wave form is characteristic of the system and has been 

 called by J. R. Carson its indicial admittance. We may think of this 

 as a transient description of the system. If we regard a continuously 

 varying applied wave as being formed by a succession of steps, we 

 may think of the received wave at any instant as being the resultant 

 of a series of waves each corresponding to a single step. The wave 

 form of each is that of the indicial admittance, its magnitude is 

 proportional to the size of the particular step and its location on the 

 time axis is determined by the time at which the particular step or 

 selection was made. When the steps are made infinitely close together, 

 a summation of these components becomes a process of integration 

 whereby the resulting magnitude-time function may be accurately 

 determined from the applied function. For the incompletely deter- 

 mined waves involved in communication where the separation of the 

 steps is finite a corresponding summation of the indicial admittance 

 curves resulting from all selections other than the one being observed 

 gives a measure of the intersymbol interference. 



Still another viewpoint, while it has, perhaps, less direct application 

 to the present problem, is of interest in that it brings out the signifi- 

 cance from the transient standpoint of the steady state characteristics 

 of the system. If we take as the applied wave a mathematical impulse, 

 that is to say, a disturbance which lasts for an infinitesimal time, 

 we find that the amplitudes of its steady state components are the 

 same for all frequencies. If the impulse occurs at zero time the 

 phase-frequency curve coincides with the axis of frequency, and if not 

 it is a straight line through the origin whose slope is proportional to 

 the time of occurrence. In order to find the current resulting from 

 such an impulse applied at zero time we multiply the constant ampli- 

 tude-frequency curve of its steady state components by the amplitude- 

 frequency curve of the system and obtain as the amplitude-frequency 

 curve of the received wave a function of the same form as the ampli- 



