554 BELL SYSTEM TECHNICAL JOURNAL 



transient distortion corresponding to this steady state distortion must 

 result in intersymbol interference; hence it places a limit on the rate at 

 which distinguishable symbols may be selected, that is, on the rate 

 of transmitting information. 



It does not necessarily follow, however, that the rate of transmission 

 with such a system is the maximum attainable for systems whose 

 transmission is limited to the frequency-range determined by the 

 cut-off of the filter. It is conceivable that by the introduction of 

 additional energy-storing elements the transfer admittance curves 

 for frequencies within the transmitted range may be altered in such a 

 way as to reduce the total intersymbol interference and so permit an 

 increased rate of selection. The maximum rate of transmission of 

 information which can be secured by such methods represents the 

 maximum rate corresponding to that range of frequencies. 



Let us consider next the way in which this possible rate of trans- 

 mission varies with the cut-off frequency of the filter. The theory of 

 filter design teaches us that the cut-off frequency may be changed 

 without altering the required terminating resistances if we change all 

 inductances and capacities in the inverse ratio of the desired change 

 in cut-off frequency. Suppose this change in energy-storing elements, 

 with no change in dissipative elements, is made not only for the filter 

 but for the entire system. We have already seen that such a modifi- 

 cation changes the rate of transmission in the inverse ratio of the 

 change in energy-storing elements; that is, in the direct ratio of the 

 change in cut-off frequency in the present case. That the new rate 

 is the maximum for the new frequency-range is evident when we 

 consider that the transfer admittance curves of the new system bear 

 the same relation to its cut-off frequency as held in the original system. 



This brings us to the important conclusion that the maximum rate 

 at which information may be transmitted over a system whose trans- 

 mission is limited to frequencies lying in a restricted range is propor- 

 tional to the extent of this frequency-range. From this it follows that 

 the total amount of information which may be transmitted over such a 

 system is proportional to the product of the frequency-range which it 

 transmits by the time during which it is available for the transmission. 

 This product of transmitted frequency-range by time available is the 

 quantitative criterion for comparing transmission systems to which I 

 referred at the beginning of this discussion. The significance of this 

 criterion can perhaps best be brought out by applying it to some 

 typical situations. 



