INSTANTANEOUS COMPANDING OF QUANTIZED SIGNALS 659 



increase in size and approach the full range, +F to —V, (to accommo- 

 date stronger signals), the excitation of extremely large steps might re- 

 sult in an rms step size exceeding the uniform size shown in Fig. 1(a). 



Fig. 1 also indicates that signals (including unwanted noise) too weak 

 to excite even the first quantizing step (and therefore absolutely incapa- 

 ble of transmission) when uniformly quantized, may successfully be 

 transmitted as a result of the excitation of a few steps following non- 

 uniform quantization. 



Although the assumption that the average value of the signal is zero 

 is quite proper for speech, subsequent discussion will disclose the possi- 

 bility that the quiescent value of the signal, as it appears at the input 

 to the quantizing equipment, may not always coincide with the exact 

 center of the voltage range depicted in Fig. 1. This effect may formally 

 be described in terms of the addition of an equivalent dc bias to the 

 speech input at the quantizer. As shown in Fig. 1, the addition of such 

 a dc component, eo , to the signal which previously excited the band of 

 steps labeled X — X', transforms X — X' into an array of equal extent 

 Y— Y', centered about e = Co instead of e = 0. This causes the excitation 

 of some larger steps, in Fig. 1(b), as well as the assignment of greatest 

 weight'* to the steps in the vicinity of e = Co , which are larger than those 

 near e = 0; the net result is an increase in the rms excited step size, and 

 the quantizing error power. This effect will depend on the comparative 

 size of Co and the signal as well as on the degree of step size variation. 

 In particular, Fig. 1(a) indicates that the presence of eo does not afl'ect 

 the rms excited step size under conditions of uniform quantization. 



It is clear from the foregoing that the effect of nonuniform quantiza- 

 tion of PCM signals will vary greatly with the strength of the signal; 

 greatest improvement is to be expected for weak signals, whereas an 

 actual impairment may be experienced by strong signals. The range of 

 signal volumes is therefore of prime importance in the choice of the 

 proper distribution of step sizes. 



D. Nonuniform Quantization Through Uniform Quantization of a Com- 

 pressed Signal 



Nonuniform quantization is logically equivalent to uniform quantiza- 

 tion of a 'V'ompressed version" of the original input signal. When applied 

 directly, tapered quantization provides an acceptably high ratio of sam- 

 ple amplitude to sample error for weak pulses, by decreasing the errors 

 (i.e., the step sizes) assigned to small amplitudes. Signal compression 

 achieves the same goal bj^ increasing weak pulse amplitudes without 

 altering the step size. 



