Communications in the Presence of Noise in Proceedings of the IRE [The Institute of Radio Engineers] 37, No. 1, January 1949, pp. 10-21

New York: Institute of Radio Engineers, 1949. 1st Edition. TRUE FIRST EDITION IN ORIGINAL PRINTED WRAPS OF CLAUDE SHANNON'S MATHEMATICAL PROOF & REFINEMENT OF NYQUIST'S SAMPLING THEOREM (now Nyquist-Shannon), "THE BACKBONE OF MODERN COMMUNICATIONS" (Gran, Numerical Computing, 136). Following this publication, the paper appeared in Bell Telephone's Technical Publications. Shannon's paper, a manuscript first written in 1940 but held from publication until after WWII ended, "set the foundation of information theory. [It] is a masterpiece both in terms of achievement and conciseness. It is undoubtedly one of the theoretical works that has had the greatest impact on modern electrical engineering" (Unser, Sampling, 1). Note that we offer the Nyquist paper separately.

An American mathematician and engineer, Claude Shannon is most often connected to the sampling theorem which bears his name. "Shannon is considered the father of information theory, which laid the foundation for digital communications and source compression, and ultimately, the information society as we know it" (Vetterli, Signal Processing, 498).

The Nyquist-Shannon theorem is the principle by which engineers are able to digitize analog signals. In order that the analog-to-digital conversion produces a faithful reproduction of the original signal, slices - called samples - of the analog waves must be taken often, with the number taken per second known as the sampling rate. The samples are bridges that allow engineers to span analog signals (continuous) and digital signals (discrete). 

While working at Bell Labs in 1924, Harry Nyquist's work centered upon the obvious need to improve the speed with which data transmission was carried over the wires. Toward this end, Nyquist made two significant distinctions, one related to signal shaping and the second to the choice of codes (Norman). "The first is concerned with the best shape to be impressed on the transmitting medium so as to permit greater speed without undue interference either in the circuit under consideration or in those adjacent, while the latter deals with the choice of codes which will permit of transmitting a maximum amount of intelligence with a given number signal elements" (Nyquist, "Certain Factors..." BSTJ 3, 1924, p. 324).

Nyquist's 1924 paper established the principles by which continuous signals could be converted into digital signals. "According to the Sampling Theorem, an analog signal must be sampled... at twice the frequency of its highest-frequency component to be converted into an adequate representation of the signal in digital form. Thus, the "Nyquist frequency" is the highest frequency that can be accurately sampled. It represents one-half of the sampling frequency. Adhering to the Nyquist Sampling Theorem ensures no lost data upon reconstruction in the analog domain" (Maliniak, Electronic Design, Oct. 20, 2005). 

Shannon's paper presented the first formal proof of the concepts the Nyquist theorem proposed. In order to convert an analog signal into a sequence of numbers, Shannon devised a geometric proof of the theorem that establishes the famous formula W log (1 + S) for the capacity of a channel with bandwidth W, additive thermal (i.e., Gaussian) noise, and signal-to-noise ratio S" (History of Science: The Wenner Collection). With this, he was able to show that if the interval between the intensity measurements is less than half the period of the highest frequency in the signal, it will then be possible to faithfully reconstruct the original signal from the digital values recorded (Shannon, 1949). CONDITION AND DETAILS: New York: Institute of Radio Engineers. 4to. No institutional stamps. Original printed wrappers with some rubbing at the front wrap and spine (see photos). The interior is pristine. Very good condition. Housed in an archival quality custom clamshell case, gilt-lettered at the spine.