Quantization is a process that maps a continous or discrete set of values into approximations that belong to a smaller set. Quantization is a lossy: some information about the original data is lost in the process. The key to a successful quantization is therefore the selection of an error criterion – such as entropy and signal-to-noise ratio – and the development of optimal quantizers for this criterion.

Quantization

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”.

Spectra of quantized signals

This paper introduces a new form of linear power amplifier for modulated radio-frequency waves. Plate circuit efficiencies of sixty to sixty-five per cent independent of modulation are obtained by means of the combined action of varying load distribution among the tubes and varying circuit impedance over the modulation cycle. The theory of operation is developed and detailed observations on the behavior of tubes in the new circuit are given in the paper. The use of stabilized feedback in connection with this circuit is discussed and significant measurements on a laboratory model of a fifty-kilowatt transmitter are shown.

A New High Efficiency Power Amplifier for Modulated Waves

Cyber-physical systems (CPSs) are the next generation of engineered systems in which computing, communication, and control technologies are tightly integrated. Research on CPSs is fundamentally important for engineered systems in many important application domains such as transportation, energy, and medical systems. We overview CPS research from both a historical point of view in terms of technologies developed for early generations of control systems, as well as recent results on CPSs in many relevant research domains such as networked control, hybrid systems, real-time computing, real-time networking, wireless sensor networks, security, and model-driven development. We outline the potential for CPSs in many societally important application domains.

http://cesg.tamu.edu/wp-content/uploads/2012/03/ps_files/12-02-10-CPS-Centennial.pdf

Cyber–Physical Systems: A Perspective at the Centennial

The class of codes discussed in this paper has the property that its error-correction capability is described in terms of correcting errors in specific digits of a code word even though other digits in the code may be decoded incorrectly. To each digit of the code words is assigned an error protection level f_{i} . Then, if f errors occur in the reception of a code word, all digits which have protection f_{i} greater than or equal to f will be decoded correctly even though the entire code word may not be decoded correctly. Methods for synthesizing these codes are described and illustrated by examples. One method of synthesis involves combining the parity check matrices of two or more ordinary random error-correcting codes to form the parity check matrix of the new code. A decoding algorithm based upon the decoding algorithms of the component codes is presented. A second method of code generation is described which follows from the observation that for a linear code, the columns of the parity check matrix corresponding to the check positions must span the column space of the matrix. Upper and lower bounds are derived for the number of check digits required for such codes. The lower bound is based upon counting the number of unique syndromes required for a specified error-correction capability. The upper bound is the result of a constructive procedure for forming the parity check matrices of these codes. Tables of numerical values for the upper and lower bounds are presented.

On linear unequal error protection codes

A radically new modulation technique for multichannel telephony has been developed which involves the conversion of speech waves into coded pulses. An 8-channel system employing pulse code modulation (PCM) and embodying these principles was produced. The method appears to have exceptional possibilities from the standpoint of freedom from interference, but its full significance in connection with future radio and wire transmission may take some time to reveal.

Pulse Code Modulation

This paper describes and explains the theory of the Feed-back principle and demonstrates how stability of amplification, reduction of modulation products, and certain other advantages follow when stabilized feed-back is applied to an amplifier. The underlying principle of design by means of which ``singing'' is avoided also is set Forth. The paper concludes with some examples of results obtained on amplifiers which have been built employing this new principle.

Stabilized Feed-Back Amplifiers

506,791. Two-way transmission. STANDARD TELEPHONES & CABLES, Ltd. (Western Electric Co., Inc.) Nov. 26, 1937, No. 32727. [A Specification was laid open to inspection under Sect. 91 of the Acts, June, 6, 1938.] [Class 40 (iv)] [Also in Group XL] A negative feedback amplifier using a, hybrid coil &c. bridge transformer input and output and so arranged as to obtain a prescribed value of impedance across one of the pairs of terminals of the hybrid coil is applicable to two way transmission systems. The Figure shows a system in which transmission control is effected by a network 77 1 in the feedback path. Separate amplifiers RE, RW are provided for east-west and west-east transmission respectively.

Wave translation system

This paper describes and explains the theory of the feed-back principle and demonstrates how stability of amplification reduction of modulation products, and certain other advantages follow when stabilized feedback is applied to an amplifier. The underlying principle of design by means of which "singing" is avoided also is set forth. The paper concludes with some examples of results obtained on amplifiers which have been built employing this new principle.

Stabilized feed-back amplifiers

A new 12-channel cable carrier system is described which is suitable for transcontinental communications. Important features are negative feed-back amplifiers of improved design, new arrangements for accurate equalization of the cable loss, and automatic thermistor regulators which continuously control the transmission of each system.

H. S. Black

Papers

Pulse Code Modulation

Stabilized Feed-Back Amplifiers

Wave translation system

Stabilized feed-back amplifiers

An Improved Cable Carrier System