nyquist's theorem and shannon's theorem

nyquist theorem vs shannon

both nyquist's theorem and shannon's theorem seem to tell tat if we want to a signal fm to be captured,we need to sample it at 2fm.
What difference do each have,or did both of them state the same thing.I do not know,obviously if both had said the same thing,we wouldn be reading both,

noisy channel nyquist theorem

The sampling theorem was implied by the work of Harry Nyquist in 1928 ("Certain topics in telegraph transmission theory"), in which he showed that up to 2B independent pulse samples could be sent through a system of bandwidth B; but he did not explicitly consider the problem of sampling and reconstruction of continuous signals. About the same time, Karl Küpfmüller showed a similar result[1], and discussed the sinc-function impulse response of a band-limiting filter, via its integral, the step response Integralsinus; this bandlimiting and reconstruction filter that is so central to the sampling theorem is sometimes referred to as a Küpfmüller filter (but seldom so in English).

The sampling theorem, essentially a dual of Nyquist's result, was proved by Claude E. Shannon in 1949 ("Communication in the presence of noise"). V. A. Kotelnikov published similar results in 1933 ("On the transmission capacity of the 'ether' and of cables in electrical communications", translation from the Russian), as did the mathematician E. T. Whittaker in 1915 ("Expansions of the Interpolation-Theory", "Theorie der Kardinalfunktionen"), J. M. Whittaker in 1935 ("Interpolatory function theory"), and Gabor in 1946 ("Theory of communication").

got it from
h**p://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem


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nyquist channel capacity

Hi
Shannon theory is in noisy channel but Nyquist doesnt regard noise.

state nyquist theorem

Nyquist's theorem states that the rate of sampling of a signal should be atleast 2fm for proper reconstruction at the receiver end,without considering the effect of noise.

Shannon's theorem is concerned with the rate of transmission of information over a noisy communication channel.It states that it is possible to transmit information with an arbitrarily small probabilty of error provided that the information rate(R) is less than or equal to the channel capacity(C).
Channel capacity is defined as the maximum information rate with which the probability of error is within tolerable limits.


Another variation to Shannon Theorem is the Shannon-Hartley theorem which applies to a channel in which the noise is Gaussian.


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In 1924, working at Bell Labs, Henry Nyquist, realized that the transmission capacity of a perfect channel is also finite. Nyquist discovered that it was not necessary to capture the entire analog signal to find the original signal, samples of the signal could be taken at various points to recover the original signal. Sampling is the process of converting a signal (for example, a function of continuous time or space) into a numeric sequence.

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Nyquist Theorem and Shanon Theorem

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Hi All,
1. There is no any proof that Nyquist stated any sampling theorem related to electrical signals. If disagree, please give paper, page, line, exact relevant quotation with proof.
2. Shannon gave two different version of a “ sampling theorem” and both of them, are wrong and irrelevant to the sampling theory and to electrical signals. Lack of any systematic approach to the question of “sampling electrical signals”. The two papers are not good reading.
3. Kotelnikov gave seven theorems and illustrated a very good systematic approach to the question, but did not answer directly the question of “sampling electrical signal”. His paper is a good reading.
I hope that help
Regards
Petre Petrov