576 BELL SYSTEM TECHNICAL JOURNAL 



tial portion of the total power in the distortion spectrum. If the signal is 

 not only weak but has its frequency near the low edge of the band, the distor- 

 tion spectrum has a decided downward slope on the frequency scale with a 

 major part of the distortion power concentrated in the lower harmonics of 

 the signal frequency. Similarly, a weak signal at the upper edge of the band 

 may cause a few scattered difference products to be outstanding. Stronger 

 signals with more centrally located frequencies give practically a uniform 

 distribution of distortion power throughout the signal band. For all except 

 the extreme cases of low ampUtudes and frequencies near the edges of the 

 band, the weighting network used to evaluate the telephonic interfering effect 

 of noise gives a reading equal to that obtained with a flat band of thermal 

 noise of the same mean power. The exceptional cases show a spread in the 

 readings which are sensitive to amplitude, frequency and disposition with 

 respect to step boundaries. The spread is reduced when complex signal 

 waves are applied. An operationally significant case is that in which the 

 noise is produced by residual power hum in the equipment. In such a case, 

 weighted noise readings range from approximately the value obtained for flat 

 noise of the same mean power, to several db lower. Connecting even a short 

 subscriber's loop to the input usually adds enough miscellaneous noise, if 

 the steps are as small as they need to be, to remove the variability and to 

 yield a reading within one db of the equivalent flat noise case. 



Thus, a PCM. system, like any other transmission system, possesses a 

 noise source and experiments show that this noise combines by power addi- 

 tion with that from another system connected to the input or output of the 

 PCM system. In tandem connections of PCM systems in which successive 

 quantizations may occur, the quantizing noise also adds like power, from sys- 

 tem to system, and soon becomes almost indistinguishable from thermal 

 noise. 



The quantizing noise consists of distortion products which maybe classified 

 as two kinds. One class includes those products which would be produced 

 by transmitting the wave through a transducer whose input-output charac- 

 teristic is stepped like a staircase. If such a transducer were actually used 

 the PCM process would be equivalent to sampling its output at a regular 

 rate and transmitting the step designations by code. This sampling process, 

 applied to the stepped transducer output, produces the other class of distor- 

 tion (or noise) and is illustrated in Fig. 34. Let us consider the sampled 

 value as the sum of the true value plus the step error, and focus attention on 

 the step error which is responsible for the distortion. .\t minimum permis- 

 sible sampling frequency (twice the highest signal frequency), the step errors 

 in consecutive samples are practically unrelated to each other. The low- 

 pass output filter passes most of the power in this sequence of random errors 



