## Certain Topics in Telegraph Transmission Theory in Bell Telephone Laboratories, August 1928, pp. 1-79 [NYQUIST'S SAMPLING THEOREM IN ORIGINAL WRAPPERS]

American Institute of Electrical Engineers, 1928. 1st Edition. FIRST EDITION OF NYQUIST’S SAMPLING THEOREM, the process of converting a signal, here that of a telegraph, into a numerical sequence. ORIGINAL WRAPPERS. The sampling theorem, later refined by Claude Shannon and now known as 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. In essence, the samples are bridges that allow engineers to span analog signals (or continuous-time signals) and digital signals (or discrete-time signals).

In 1924 and while working at Bell Telephone Laboratories, Harry Nyquist’s work centered upon trying “to improve the speed of data transmission over telegraph wires, Nyquist isolated two key factors - signal shaping and choice of codes” (Origins of Cyberspace 163, p. 154). “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 affecting telegraph speed,” in Bell System Technical Journal 3, 1924, p. 324). We offer the 1924 paper separately.

Building upon and refining his earlier work, Nyquist’s 1928 paper offered here 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).

In 1949 Claude Shannon, also of Bell Labs, wrote a paper entitled “Communication in the presence of noise” where he presented the first formal proof of the general concept presented by Nyquist. The conditions specified by Nyquist for recovering the original signal from samples of the signal are now known as the Nyquist Sampling Theorem, or as the Nyquist-Shannon Sampling Theorem” (Hecht, ‘The Nyquist Sampling Theorem’, 1).

“Numerous experts say that Nyquist stated the Sampling Theorem, and Shannon later mathematically proved it… Both Nyquist and Shannon are considered “founding fathers of digital communications… [and] products like cell phones, audio CDs, and iPods are all based on the broad-shouldered foundation of the [sampling] theorem” (Maliniak).

Both Nyquist’s 1924 paper and his 1928 paper (along with one by Hartley also published in 1928) are cited in the first paragraph of Shannon’s classic essay of 1948, “The Mathematical Theory of Communication” wherein their seminal role in the development of information theory is acknowledged. Item #1418

CONDITION & DETAILS: American Institute of Electrical Engineers. [9 x 6 inches; 225 x 150mm]. pp. 1-79. Complete issue. Bound in original paper wraps in pristine condition save for a small spot at the inner margin of the front wrap. Three holes punched in the left margin are well outside of the area of text. In fine condition, it is housed in a custom pamphlet case, gilt-lettered at the spine.

Price: \$1,500.00

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