What is Nyquist's Information in Discrete Measurements?

In summary, Nyquist's information in discrete measurements is a measure of the maximum data rate that can be reliably transmitted within a given bandwidth, and it is based on the concept of sending two distinct values per cycle in order to reconstruct the original data.
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What is a Nyquist's information in discrete measurements?

We perform a measurement of some physical object, giving a result value in interval [0,1] in some units. The value has a gaussian statistical error of some known [itex]\sigma[/itex] (by order of magnitude comparable to 1).
We do lots ([itex]\rightarrow \infty[/itex]) of such measurements of various real objects, our only a priori knowledge is that true values have some unknown distribution bounded within [0,1].

What is a maximal average information (in Shannon-Nyquist meaning) carried by such measurement? Intuition tells me that Nyquist's law should apply here (with some proportionality factor maybe).

Had anyone read (or even better: written...) any article on such topics? I would be really grateful for a reference!
 
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Nyquist's information in discrete measurements is a measure of the amount of data that can be reliably transmitted within a given bandwidth. It states that the maximum data rate (in bits per second) is equal to twice the bandwidth of the channel (in hertz). This is because two distinct values must be sent per cycle in order to reconstruct the original data.
 

What is Nyquist's Information in Discrete Measurements?

Nyquist's Information in Discrete Measurements is a concept in signal processing that relates to the minimum sampling rate required to accurately represent a continuous signal in a digital form. It was developed by Harry Nyquist in the 1920s and is essential in digital communication and data acquisition systems.

What is the Nyquist-Shannon Sampling Theorem?

The Nyquist-Shannon Sampling Theorem is a fundamental result in signal processing that states that in order to accurately reconstruct a continuous signal from its digital samples, the sampling rate must be at least twice the highest frequency component of the signal. This theorem is based on Nyquist's work and was further developed by Claude Shannon in the 1940s.

What is the relationship between Nyquist's Information and aliasing?

Aliasing is a phenomenon that occurs when a signal is improperly sampled, resulting in incorrect representation of the original signal. Nyquist's Information states that in order to avoid aliasing, the sampling rate must be at least double the highest frequency in the signal. If this condition is not met, aliasing will occur and the reconstructed signal will be distorted.

Why is Nyquist's Information important in data acquisition systems?

Data acquisition systems are used to convert analog signals into digital form for processing and analysis. Nyquist's Information is crucial in these systems because it dictates the minimum sampling rate required to accurately represent the original signal. If the sampling rate is too low, the resulting data will not be a faithful representation of the original signal.

How does Nyquist's Information affect digital communications?

In digital communication systems, information is transmitted in the form of discrete signals. Nyquist's Information is important in these systems because it determines the maximum data rate that can be achieved without introducing errors. If the sampling rate is too low, the transmitted signal will be distorted and the receiver will not be able to accurately decode the information.

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