INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 661 



curves, the central problem of choosing the proper distribution of step 

 sizes will be discussed in terms of the choice of the appropriate com- 

 pression characteristic; the reduction of quantizing error, corresponding 

 to nonuniform quantization without change in the total number of steps, 

 will be termed companding improvement. 



E. The Mechanism of Companding Improvement in Various Communica- 

 tion Systems 



1. Syllabic Companding of Continuous Signals^^- -"^ 



Originally, the compandor consisted of a compressor and comple- 

 mentary expander operating at a syllabic rather than instantaneous rate 

 in frequency division systems, since instantaneous companding was 

 found to imply an undesirable increase in bandwidth in such systems. ^^ 



In spite of the existence of syllabic power variations, a useful under- 

 standing of such compandor action ma}^ be inferred from the considera- 

 tion of the long-time average power. Thus, in its simplest form, the com- 

 pressor might provide amplification varjdng from a constant value within 

 the range of volumes corresponding to weak speech to little or no ampli- 

 fication for comparatively strong signals prior to transmission. Although 

 it is an amplifying device, the compressor takes its name from the con- 

 traction of the transmitted volume range which results from' selective 

 amplification of the weakest signals. Since the distortion of the signal 

 by the compressor may virtually be confined to a change in loudness, 

 the compressor output may be expected to be intelligible. 



In interpreting a compression characteristic, syllabic application per- 

 mits the identification of the ordinate and abscissa with -y/^ and -y/^, 

 rather than v and e as shown in Fig. 2. This substitution of rms for in- 

 stantaneous signals not only confines the significance of the compression 

 characteristic to the first quadrant but also removes the need for com- 

 pandor response to input signals below some small, nonzero, threshold 

 value. 



If we designate the mean square noise voltage in the transmission 

 medium bj^ i»„-, the amplification of weak signals prior to exposure to 

 this noise provides an increase in the transmitted signal to noise ratio 

 from (e2/y„2) to (y^/y^^), i.e., by a factor of (v^/e^). This increase in signal- 

 to-noise ratio may be read directly from the graph of the compression 

 characteristic, and is unaffected by the identical treatment accorded 

 signal and noise at the expandor. Furthermore, noise received during 

 the silent intervals, between speech bursts, is attenuated by the ex- 

 pandor. 



