Transmission of Information^ 



By R. V. L. HARTLEY 



Synopsis: A quantitative measure of "information" is developed which 

 is based on physical as contrasted with psychological considerations. How 

 the rate of transmission of this information over a system is limited by the 

 distortion resulting from storage of energy is discussed from the transient 

 viewpoint. The relation between the transient and steady state viewpoints 

 is reviewed. It is shown that when the storage of energy is used to restrict 

 the steady state transmission to a limited range of frequencies the amount 

 of information that can be transmitted is proportional to the product of 

 the width of the frequency-range by the time it is available. Several 

 illustrations of the application of this principle to practical systems are 

 included. In the case of picture transmission and television the spacial 

 variation of intensity is analyzed by a steady state method analogous to 

 that commonly used for variations with time. 



WHILE the frequency relations involved in electrical communi- 

 cation are interesting in themselves, I should hardly be justified 

 in discussing them on this occasion unless we could deduce from them 

 something of fairly general practical application to the engineering 

 of communication systems. What I hope to accomplish in this 

 direction is to set up a quantitative measure whereby the capacities of 

 various systems to transmit information may be compared. In doing 

 this I shall discuss its application to systems of telegraphy, telephony, 

 picture transmission and television over both wire and radio paths. 

 It will, of course, be found that in very many cases it is not economi- 

 cally practical to make use of the full physical possibilities of a system. 

 Such a criterion is, however, often useful for estimating the possible 

 increase in performance which may be expected to result from im- 

 provements in apparatus or circuits, and also for detecting fallacies 

 in the theory of operation of a proposed system. 



Inasmuch as the results to be obtained are to represent the limits 

 of what may be expected under rather idealized conditions, it will be 

 permissible to simplify the discussion by neglecting certain factors 

 which, while often important in practice, have the efifect only of 

 causing the performance to fall somewhat further short of the ideal. 

 For example, external interference, which can never be entirely 

 eliminated in practice, always reduces the effectiveness of the system. 

 We may, however, arbitrarily assume it to be absent, and consider 

 the limitations which still remain due to the transmission system itself. 



In order to lay the groundwork for the more practical applications 

 of these frequency relationships, it will first be necessary to discuss a 

 few somewhat abstract considerations. 



1 Presented at the International Congress of Telegraphy and Telephony, Lake 

 Como, Italy, September 1927. 



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