TELEPHONY BY PULSE CODE MODULATION 397 



mitted as a pulse of corresponding amplitude. In order to transmit both 

 positive and negative values a constant or d-c value of pulse amplitude can 

 be added. (See Fig. 1.) When this is done positive values of the informa- 

 tion wave correspond to pulse amplitudes greater than the constant value 

 while negative values correspond to pulse amplitudes less than the constant 

 value. At the receiver a reproduction of the original speech wave will be 

 obtained at the output of a low-pass filter. 



The PCM system considered in this paper starts with a PAM system and 

 adds equipment at the terminals to enable the transmission of a group of 

 ON-OFF pulses or binary digits to represent each instantaneous pulse 

 amplitude of the PAM system. Representation of the amplitude of a single 

 PAM pulse by a finite group of ON-OFF pulses or binary digits requires 

 quantization of the audio wave. In other words, we cannot represent the 

 actual amplitude closer than ^ "quantum". The number of amplitude 

 levels required depends upon the grade of circuit desired. The disturbance 

 which results from the quantization process has been termed quantizing 

 noise. For this type of noise a signal-to-noise ratio of 33 db would be ob- 

 tained for 32 amplitude levels and this grade of circuit was deemed suffi- 

 ciently good for a preliminary study. These 32 amplitude levels can be 

 obtained with 5 binary digits, since 32 = 2^. 



Figure 2 shows how several values of PAM pulse amplitude can be 

 represented by this binary code. The first column gives the digit pulses 

 which are sent between the transmitter and receiver while the second column 

 shows the same pulse pattern with each pulse weighted according to its 

 assigned value, and the final column shows the sum of the weighted values. 

 The sum, of course, represents the PAM pulse to the nearest lower amplitude 

 unit. The top row where all the digits are present shows, in the middle 

 wave form, the weighted equivalent of each digit pulse. By taking different 

 combinations of the five digits all integer amphtudes between 31 and can 

 be represented. The examples shown are for 31, 18, 3, and 0. 



Referring to Fig. 3 sampling of the audio wave (a) yields the PAM wave 

 (b). The PAM pulses are coded to produce the code groups or PCM 

 signal (c) . The PCM pulses are the ones sent over the transmission medium . 

 For a sampling rate of 8000 per second, there would be 8000 PAM pulses 

 per second for a single channel. The digit pulse rate would be 40,000 pps 

 for a five-digit code. For a time-division multiplex of N channels both of 

 these pulse rates would be multiplied by N. 



Wave form (d) shows the decoded PAM pulses where the amplitudes are 

 shown under the pulses. The original audio wave is repeated as wave 

 form (e). It will be noted that the received signal is delayed by one PAM 

 pulse interval. It is also seen that the decoded pulses do not fit exactly on 

 this curve. This is the result of quantization and the output of the low-pass 



