# sampling theorem

## sampling theorem

[′sam·pliŋ ‚thir·əm]
(communications)
The theorem that a signal that varies continuously with time is completely determined by its values at an infinite sequence of equally spaced times if the frequency of these sampling times is greater than twice the highest frequency component of the signal. Also known as Shannon's sampling theorem.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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However, a large amount of data will be produced when monitoring the composite structure real-time and online by the use of ultrasonic phased array technology with Nyquist sampling theorem, which not only needs complicated processing of the data but also needs higher requirements for the acquisition system to complete the data collection.
Compressive sampling (CS) has received extensive research attention in the past decade, as it allows sampling at a rate lower than that required by the Nyquist-Shannon sampling theorem. Besides, benefiting from its intrinsic simplicity, convenience and simultaneous encryption, and compression performance, CS also shows great potential in the information security field.
As stated in [17, Example 2], [S.sub.[delta],p] = [[summation].sup.[infinity].sub.n=-[infinity]][[delta].sub.np] is an impulse train and is useful in modelling the operation of sampling a continuous signal at sampling interval P and in establishing the link between analog and digital signals via the Sampling Theorem.
No matter which propagation method used, the numerical computation enforces the sampling theorem for both the complex fields and propagators, this in order to guarantee the correct propagation of the optical field (Goodman, 2005; Li & Picart, 2012).
The Nyquist-Shannon Sampling Theorem of Fourier transform theory allows access to the range of values of variables below the Heisenberg Uncertainty Principle limit under sampling measurement conditions, as demonstrated by the Brillouin zones formulation of solid state physics [13] [14, see p.21] [15, see p.
Nyquist sampling theorem is widely accepted as a means of representing band-limited signals by their digital samples.
Also, the Shannon-Nyquist sampling theorem establishes that for the perfect reconstruction of the signal it is necessary to take samples by using a rate of at least double the bandwidth [1].
In digital signal processing, the Nyquist sampling theorem indicates that the sampling rate must be twice as large as the bandwidth of the analog signal at least for acquiring the intact information of the signal.
Then by the optional sampling theorem, {[[??].sub.n]} and {[W.sup.[epsilon].sub.n]} have an identical law for any [epsilon] > 0.
To digitize such UWB radar signal, a very high sampling rate is required according to Shannon-Nyquist sampling theorem [1], namely, the received signals must be sampled at twice their baseband bandwidth.
It is worthwhile to highlight yet another aspect of our geometric sampling method: Shannon's Sampling theorem relates to bandlimited signals, that are, necessarily, unbounded in time or in spatial domain.

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