G62 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



Under these circumstances it is appropriate to resolve companding 

 improvement into the separate contributions of an increased signal to 

 noise ratio for weak speech by the compressor, and a quieting of the 

 circuit in the absence of speech by the expandor. The introduction of an 

 independent source of noise in the channel between the compressor and 

 expandor is the key to such behavior. 



2. Instantaneous Companding of Unquantized Pulse Signals 



Time division systems, emplojdng unquantized pulse modulation 

 (e.g., PAM) are admirably suited to the application of instantaneous 

 companding to the individual pulse samples. Since each pulse is ampli- 

 fied to a degree which varies with its input amplitude, the compressor 

 output is a sampled version of a distorted signal. 



As in the S3dlabic case, the location of the noise source in the channel 

 between the compressor and expandor permits an improvement of the 

 received signal-to-noise ratio for weak signals. Furthermore, the ex- 

 pandor again assumes the separate and distinct task of suppressing 

 channel noise in the absence of speech. 



Unfortunately, quantitative expression of the companding improve- 

 ment is not as simple as in the syllabic case. The response to instan- 

 taneous amplitudes much lower than the rms threshold signal (including 

 zero) becomes important and the improvement factor may not (except 

 in the special case of a linear compression characteristic) simply be read 

 from a graph relating instantaneous values of v and e. Instead, one must 

 employ the probability density of the signal in order properl}^ to account 

 for the distinctive treatment accorded individual pvilse amplitudes in a 

 complex signal. 



3. Instantaneous Companding of Quantized Signals 



Although the same physical devices which serve as an instantaneous 

 compressor and expandor in a PAM system may also be used in a PC^NI 

 system, the functional description of companding improvement is differ- 

 ent in the two applications. Whereas the compandor is used to combat 

 channel noise in a PAM sj^stem, encoded transmission permits a PCM 

 sj^stem to assign this task to the devices which transmit and regenerate 

 code pulses. Thus, assuming that error-free encoded transmission is 

 realized, the quantized signal may be regarded as completely impervious 

 to noise in the transmission medium. Quantization is required to permit 

 such transmission. The sole purpose of the PCM compandor is to reduce 

 the (juantizing impairment of the signal by comerting uniform to effec- 

 tivel}' nonuniform cjuantization. 



