712 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



This is not true of the instantaneous compandor. While instantaneous com- 

 panding theoretically does not require an increase in bandwidth ^^ between 

 compressor and expandor, additional transmission requirements^' which 

 this path must satisfy usually would be regarded as very severe when this 

 band is no more than the bandwidth of the signal entering the compressor.* 

 This means, for example, that for practical reasons instantaneous com- 

 pandors cannot be applied to existing types of single-sideband carrier tele- 

 phone systems. On the other hand, if a pulse modulation or other type of 

 multi-channel time-division system is capable of operating without com- 

 pandors, the addition of instantaneous compandors will not alter matters. 

 Of course, the net over-all transmission will change more than one db for 

 each db change in the propagation from compressor output to expandor 

 input, but this is true for either type of compandor and depends essentially 

 upon the properties of the expandor. 



Application of Theory 



The theory will be used to evaluate the noise advantage of an instantane- 

 ous compandor in the PAM system shown in Fig. 1 when the signal is speech. 

 The result is applicable^" to other types of multi-channel pulse-modulation 

 systems. 



Choice of Expandor Characteristic 



The first step is to select a suitable characteristic. If the characteristic of 

 the compandor is logarithmic, the signal-to-noise ratio at the output of the 

 system will be independent of speech volume. It appears reasonable for 

 talkeis of different volume to be treated alike and so a logarithmic char- 

 acteristic will be chosen. Results of experimental observations on this type 

 of characteristic will be discussed in a later paragraph. 



A logarithmic compandor is one in which the output voltage of the com- 

 pressor is a logarithmic function of its input voltage. Conversely, the output 

 voltage of the expandor is an exponential function of its input voltage. This 

 relationship may be written: 



rL = ae 



where a and b are arbitrary constants, E is the expandor output voltage, 

 and V the expandor input voltage. 



* This implies suitable instrumentation which, for convenience, may utilize sampling. 

 If a signal be compressed by an instantaneous compressor, the bandwidth occupied by the 

 compressed signal obviously will be considerably increased. However, the information 

 content of the compressed signal is no more than before and accordingly may be repre- 

 sented by another appropriate information signal whose frequency range is restricted 

 to the bandwidth of the signal entering the compressor. 



