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  [14, see p.
Nyquist sampling theorem
is widely accepted as a means of representing band-limited signals by their digital samples.
Therefore, to some extent, compressed sensing is considered as a sampling technology similar to Shannon's sampling theorem
Huawei's FTN technology breaks the limit of the Nyquist sampling theorem
, which defines a maximum transmission speed for a fixed channel bandwidth.
To digitize such UWB radar signal, a very high sampling rate is required according to Shannon-Nyquist sampling theorem
, namely, the received signals must be sampled at twice their baseband bandwidth.
In this way, the sampling theorem
is broken, cause the signal s(t) cannot correctly be sampled with the sampling frequency [f.
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.
The Nyquist sampling theorem
differentiates samplers from digitizers.
The handbook's chapter titles include "Fourier Transforms in Probablility, Random Variables, and Stochastic Processes" and "Generalizations of the Sampling Theorem
If the interested domain for the vibration signals is 0-200Hz, this means we have to used a sampling rate of minimum 400Hz, taking into account the Shannon sampling theorem
Because a DDS device works with sampled data, designers must take into account the Nyquist sampling theorem