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An explanation of the Nyquist Theorem and its importance to Mu-Law Encoding in North American T-Carrier Telecommunications Systems June 2, 2009

Posted by HubTechInsider in Definitions, Fiber Optics, Mobile Software Applications, Telecommunications, VUI Voice User Interface, Wireless Applications.
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The Nyquist theorem established the principle of sampling continuous signals to convert them to digital signals. In communications theory, the Nyquist theorem is a formula stating that two samples per cycle is all that is needed to properly represent an analog signal digitally. The theorem simply states that the sampling rate must be double the highest frequency of the signal. So, for example, a 4KHz analog voice channel must be sampled 8000 times per second. The Nyquist Theorem is the mathematical underpinning of the Mu-Law encoding technique used in T-Carrier transmission systems. T-Carrier is used in North American telecommunications networks. In Europe, where E-carrier transmission systems are used, a similar but incompatible theorem, Shannon’s Law, is used in the European A-Law encoding technique. This is the reason why Mu-Law encoding is used in North America and A-Law encoding is used in Europe.

The author of the Nyquist Theorem was named Harry Nyquist. Harry worked in the research department at AT&T and later at Bell Telephone Laboratories. In 1924, he published a paper titled “Certain Factors Affecting Telegraph Speed”, which analyzed the correlation between the speed of the telegraph system and the number of signal values it used. Harry refined his paper in 1928, when he republished his work under the title “Certain Topics in Telegraph Transmission Theory”. It was in this paper that Harry expressed the Nyquist Theorem, which established the principle of using sampling to convert a continuous analog signal into a digital signal. Claude Shannon, the author of Shannon’s Law, cited both of Nyquist’s papers in the first paragraph of his classic paper “The Mathematical Theory of Communication”. Harry Nyquist is also known for his explanation of thermal noise, also sometimes known as “Nyquist noise” as well as AT&T’s 1924 version of a fax machine, called “telephotography”.

His remarkable career included advances in the improvement of long-distance telephone circuits, picture transmission systems, and television. Dr. Nyquist’s professional, technical, and scientific accomplishments are recognized worldwide. It has been claimed that Dr. Nyquist and Dr. Claude Shannon are responsible for virtually all the theoretical advances in modern telecommunications. He was credited with nearly 150 patents during his 37-year career. His accomplishments underscore the excellent preparation in engineering that he received at the University of North Dakota. In addition to Nyquist’s theoretical work, he was a prolific inventor and is credited with 138 patents relating to telecommunications.

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