Spectra of Quantized Signals

Signals which are quantized both in time of occurrence and in magnitude are in fact quite old in the communications art. Printing telegraph 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 quantizing techniques to be applied to rapidly changing signals such as produced by speech, music, or television. Quantizing of time, or time division, has found application as a means of multiplexing telephone channels. 1 The method consists of connecting the different channels to the line in sequence by fast moving switches synchronized at the transmitting and receiving 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 employed by the latter, while the high speeds needed for time division multiplex telephony can be realized only by practically inertialess electron streams. Also the widths of frequency band required for multiplex telephony 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 concerned the result is the same as in telegraphy, namely that signals are received at discrete or quantized times. In the limiting case when many channels are sent the speech voltage from one channel is practically constant during the brief switch closure and, in effect, we can send only one magnitude for each contact or quantum of time. The more familiar word “sampling” will be used here interchangeably with the rather formidable term “quantizing of time”.