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It connects Hartley's result with Shannon's channel capacity theorem in a form that is equivalent to specifying the M in Hartley's line rate formula in terms of a signal-to-noise ratio, but achieving reliability through error-correction coding rather than through reliably distinguishable pulse levels.
This result was presented by Claude Shannon in 1948 and was based in part on earlier work and ideas of Harry Nyquist and Ralph Hartley. The Shannon limit or Shannon capacity of a communication channel refers to the maximum rate of error-free data that can theoretically be transferred over the channel if the link is subject to random data ...
The term Nyquist Sampling Theorem (capitalized thus) appeared as early as 1959 in a book from his former employer, Bell Labs, [22] and appeared again in 1963, [23] and not capitalized in 1965. [24] It had been called the Shannon Sampling Theorem as early as 1954, [25] but also just the sampling theorem by several other books in the early 1950s.
This relationship is described by the Shannon–Hartley theorem, which is a fundamental law of information theory. SNR can be calculated using different formulas depending on how the signal and noise are measured and defined.
For this calculation, it is conventional to define a normalized rate = / (), a bandwidth utilization parameter of bits per second per half hertz, or bits per dimension (a signal of bandwidth B can be encoded with dimensions, according to the Nyquist–Shannon sampling theorem). Making appropriate substitutions, the Shannon limit is:
This result is known as the Shannon–Hartley theorem. [11] When the SNR is large (SNR ≫ 0 dB), the capacity ¯ is logarithmic in power and approximately linear in bandwidth. This is called the bandwidth-limited regime.
Nyquist–Shannon sampling theorem; S. ... Shannon–Hartley theorem; Shannon's source coding theorem This page was last edited on 2 February 2012, at 17:02 (UTC ...
Shannon-Hartley theorem applies to continuous-time channel, so it not applicable to sampling over finite period T, besides it has nothing to do with Fat tail signals. I do not understand the remainder of your point about zero samples.