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ata  chip  communication  datasheet  mhz  módulos  pages revision  parte parte  rate  sampling theorem  sampling  theorem  transceiver 
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Preview: Victor Rocha

Victor Rocha

Updated: 2014-10-04T21:22:05.527-07:00


Texto PDS


1Fifty years ago the publications of Claude E, Shannon brought the sampling theorem to the broad attention oi communication engineers. This article demonstrates how practicians, theoreticians, and mathematicians discovered the implications of the sampling theorem almost independent of one another.In 1948 and 1949, Claude E. Shannon published the two revolutionary papers in which he founded the information theory [1, 2]. In [1] the sampling theorem is formulated as “Theorem 13”:Lei f(t) contam no frequencies over W. ThenIt was not until these papers were published that the theorem known as “Shannon’s sampling theorem” became common propriety among communication engineers, although Shannon himself writes in [2] thatThis is a fact which is common knowledge in the communication art.A few times further on, however, he adds:But in spire of its evident importance [it] seems not to have appeared explicitly in the literature of communication theory.The following analysis takes the above statement as its starting point. It will become apparent that mathematicians, practicians, and theoreticians in communication engineering carne across the implications of the sampling theorem almost independent of one another, and that the Links between them did not emerge until later stages of this development.THE PRACTICIANSIn communication engineering, the first experiments with time-division multiplexing (TDM) in telephony led to the questions of how and how often it is necessary lo sample a continuous-time signal.The attempt to transmit more than one signal simultaneously over a single wire began shortly after the early commercial successes with telegraphy in the 1840s. The first proposals for TDM using synchronously rotating commutators derive from F. C. Bakewell (1848), A. V. Newton (1851). and M. B. Farmer (1853). Technically more accomplished methods were then developed by B. Meyer (1870), J. M. E. Baudot (to 1874), as well as P. Lacour and P. B. Delany (1878) [ 4]. It is significant not only that methods were used in which complete telegraphic signals from different transmitters were placed in chronological order (e.g., Baudot), but that certain systems were also equipped with fast rotating commutators which were able to transmit at least two samples of each elementary signal (egg., Delany). This technique makes additional synchronization between transmitterand sampler unnecessary. One of these fast rotating commutators, the “distributor” of the telegraphy system by F. J. Patten (around 1891), was used for the first demonstration of TDM of telephone signals. The inventor’s name was Willard M. Miner. He had his method patented in 1903 following many years of preliminary experiments [5]. Figures 1 and 2 from [6] show the circuit diagram and the “Patten Distributor” which was used. Miner determined the required sampling rate experimentally [6]:It will be understood, then, that the apparatus devised by Mr. Miner, while in its general form the same as that heretofore used for multiplex telegraphy — or telephony for that matter — such apparatus is run at a much greater speed so as to bring the frequency of the closures of connection upon the several! Branches or sub-circuits up lo a rate approximating in greater or less degree the rate of the vibrations of the overtones characterizing speech. A rate of closure of 1,000 or 2,000 per second will nor answer the purpose, but as the rate increase and passes beyond 3,000, improved results become apparent, and are marked-ly better when a rate of 3,500 or 3,600 per second is reached; the best results being obtained with a rate of about 4,300 per second.Miner thus assumed that the sampling rate would coincide approximately with the upper frequency components of speech. In actuality, his telephone apparatus will have had a cutoff frequency of barely more than 2 kHz, which fulfills the requirements of the sampling theorem.Since a theoretical clarification of the sampling process was not forthcoming, pronouncements concerning the sampling rate in publications as well as patent appl[...]

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