6 BELL SYSTEM TECHNICAL JOURNAL 



To afford time for coding, the instantaneous samples may be maintained at 

 constant value for an appropriate interval — a process here referred to as 

 "holding." 



Quantization. The fundamental operation of PCM is the conversion of a 

 signal sample into a code combination of on-off pulses. In any practical 

 system a continuous range of signal values cannot be reproduced since only a 

 finite number of combinations can be made available. Each combination 

 stands for a specific value, of course, so that we wind up by representing a con- 

 tinuous range of amplitudes by a finite number of discrete steps. This process 

 is spoken of as quantization, a quantum being the difference between two 

 adjacent discrete values. Graphically this means that a straight line repre- 

 senting the relation between input and output samples in a linear continuous 



SIDEBANDS ON SIDEBANDS ON 



SAMPLING SAMPLING 



FUNDAMENTAL 2ND HARMONIC 



AUDIO 

 BAND 



FREQUENCY 



SAMPLING 2ND HARMONIC 



FREQUENCY OF SAMPLING 



FREQUENCY 



Fig. 3. Spectrum of a sampled audio band, illustrating separation of components when 

 the sampling frequency is at least twice the top audio frequency. 



system is here replaced by a flight of steps as in Fig. 4a. The midpoints of the 

 treads fall on the straight line, and the height of the step is the quantum. 



Manifestly the greatest error inherent in quantization amounts to half a step. 

 Hence the quality of reproduction may be measured by the size of that inter- 

 val, which depends upon the total number of steps in the amplitude range 

 covered. With n pulses assigned to represent an amplitude range, the maxi- 

 mum number of discrete steps is 2", and the size of each step is proportional to 

 2~" times the amplitude range. 



This error shows up as a noiselike form of distortion, affecting background 

 noise in the absence of speech, and accompanying speech as well. The dis- 

 tortion actually consists of a multiplicity of harmonics and high order modu- 

 lation products between signal components and the sampling frequency scat- 

 tered fairly evenly over the audio spectrum. If the audio signal is a simple 

 sine wave, these many products may be identified individually; but for speech 

 or other complex signals they merge into an essentially flat band of noise that 

 sounds much like thermal noise. Since the level of this distortion is fixed by 

 the quantum size, an adequate number of steps must be provided for the lowest 



