578 



BELL SYSTEM TECHNICAL JOURNAL 



output as the signal wave plus a wide spectrum of distortion frequencies 

 representing the effect of the steps. From this point of view, it is clear that 

 only a high sampling frequency prevents lower sidebands associated with 

 the sampling frequency and its harmonics from overlapping the signal band. 

 Quantizing noise decreases with increase of sampling frequency at an initial 

 rate of approximately 3 db per octave and continues until correlation of suc- 

 cessive errors becomes appreciable. This occurs at a sampling frequency 

 which is dependent upon the spectral distribution of the signal, being lower 

 for signals having a predominately low-frequency spectral density. An 

 increase of step size also reduces the lowest sampling frequency at which 

 effects of correlation are observed. Figure 35 shows curves calculated for an 



D-m 



6 8 10 20 40 60 80 100 200 



SAMPLING FREQUENCY 



400 600 1000 



WIDTH OF SIGNAL BAND 



Fig. 35 — Variation of quantizing noise with sampling frequency. 



input consisting, in fact, of thermal noise. Such an input is a rough ap- 

 proximation to a speech wave. 



The asymptotic values shown for five and seven digits represent the quan- 

 tizing noise corresponding to transmission of the thermal noise signal through 

 stepped transducers having 32 and 128 steps, respectively. The curves 

 suggest that sampUng is a penalty such that 32-step granularity without 

 sampling is about equivalents^ to 128-step granularity with sampling at the 

 minimum rate. However, sending information which designates the irregu- 

 lar instants of time at which the signal enters and leaves each step interval 

 is far less efficient than designating the steps at the regular instants of the 

 minimum sampling rate. 



"" The equivalence would he in terms of total noise power; the properties of the asymp- 

 totic noise are different than were described earlier in this appendix, for sampling at the 

 minimum rate. 



