spectra of Quantized Signals 



By W. R. BENNETT 



1. Discussion of Problem and Results Presented 



SIGNALS which are quantized both in time of occurrence and in magni- 

 tude are in fact cjuite old in the communications art. Printing tele- 

 graph is an outstanding example. Here, time is divided into equal divisions, 

 and the number of magnitudes to be distinguished in any one interval is 

 usually no more than two, corresponding to the closed or open positions of a 

 sending switch. It is only in recent years, however, that the development 

 of high speed electronic devices has progressed sufficiently to enable quan- 

 tizing techniques to be applied to rapidly changing signals such as pro- 

 duced by speech, music, or television. Quantizing of time, or time division, 

 has found application as a means of multiplexing telephone channels.^ 

 The method consists of connecting the different channels to the line in se- 

 quence by fast moving switches synchronized at the transmitting and re- 

 ceiving ends. In this way a transmission medium capable of handling a 

 much wider band of frequencies than required for one telephone channel can 

 be used simultaneously by a group of channels without mutual interference. 

 The plan is the same as that used in multiplex telegraphy. The difference 

 is that ordinary rotating machinery suffices at the relatively low speeds em- 

 ployed by the latter, while the high speeds needed for time division multi- 

 plex telephony can be realized only by practically inertialess electron 

 streams. Also the widths of frequency band required for multiplex tele- 

 phony are enormously greater than needed for the telegraph, and in fact 

 have become technically feasible only with the development of wide-band 

 radio and cable transmission systems. As far as any one channel is con- 

 cerned the result is the same as in telegraphy, namely that signals are re- 

 ceived at discrete or quantized times. In the limiting case when many 

 channels are sent the speech voltage from one channel is practically con- 

 stant during the brief switch closure and, in effect, we can send only one mag- 

 nitude for each contact or quantum of time. The more famihar word 

 "sampling" will be used here interchangeably with the rather formidable 

 term "quantizing of time". 



Quantizing the magnitude of speech signals is a fairly recent innovation. 

 Here we do not permit a selection from a continuous range of magnitudes 

 but only certain discrete ones. This means that the original speech signal 



446 



