Nyquist rate

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Related to Nyquist rate: sampling rate, Nyquist interval

Nyquist rate

[′nī‚kwist ‚rāt]
The maximum rate at which code elements can be unambiguously resolved in a communications channel with a limited range of frequencies; equal to twice the frequency range.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

Nyquist theorem

The concept behind digitizing sound. Working at Bell Labs, Harry Nyquist discovered that it was not necessary to capture the entire analog waveform, and samples of the wave could be taken at various points. He also found that in order to have enough information in the sample pool to reconstruct the original waveform, the sampling rate must be at least twice the signal bandwidth.

The Basis for PCM
These realizations became the foundation for using pulse code modulation (PCM) to convert analog sound to digital in North America and Japan. A typical 4 kHz voice signal is sampled 8,000 times a second, with each sample converted into an 8-bit number, resulting in a 64 Kbps data stream (a single DS0 channel). See sampling and PCM.

The Human Ear
It was believed that people could not hear a frequency greater than 20 kHz (20,000 cycles per second). However, this number was always an approximation and has been challenged since the first music CDs came on the market in the mid-1980s. To deliver 20 kHz to the human ear, analog waves are sampled at 44.1 kHz for a regular music CD. Next-generation audio takes samples more frequently (see SACD and DVD-Audio.
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Three operating scenarios from Section 1 are compared: (1) the onboard classification, (2) the CS signal streaming, and (3) the streaming of uncompressed Nyquist rate signal.
In the CS streaming scenario, range of the CS compression rates was chosen to yield comparable classification performance with respect to Nyquist rate signal acquisition.
The geometric approach is endowed with an inherent advantage in that the sampling points are associated with relevant geometric features (via curvature) and are not imposed arbitrarily at equal intervals determined by the Nyquist rate. To be more precise, each code word is represented, according to the proposed geometric approach, by a (sampling) point in some [R.sup.N], belonging to the given geometric signal.
Moreover, it should be stressed again that the geometric approach, based on curvature radii, inherently produces a sparse, with respect to the Nyquist rate, adaptive sampling (see [1]), lending itself to interesting benefits, insofar as various applications are concerned.
As stated previously, the sparsity in this context may come from the inability of the ADC to acquire signals at a Nyquist rate. The time samples t are thus acquired at a sub-Nyquist rate which may result in a sparse vector.
The example f(z) = [[OMEGA].sub.m](z) sin [sigma] z, with f(x) = O([x.sup.m]), [absolute value of x] [right arrow] [infinity], x [member of] R shows that the asymptotic f(x) = o([x.sup.m]), [absolute value of x] [right arrow] [infinity], x [member of] R is crucial for exact interpolating recovery in [E.sub.[sigma]] by using samples at Nyquist rate and at most m additional Hermite type of data.
The echo signals of each subpulse are demodulated to baseband and then sampled at the Nyquist rate [F.sub.S].
Although uniform sampling at the Nyquist rate for low-pass signals is quite straightforward, the extensions to bandpass and multi-band signals are not trivial.
But these algorithms are mostly based on data independent matched filter (MF) theorem which requires a large number of uniform samples to obey the Nyquist rate. In addition, the focussing of LASAR data based on MF-based methods is usually analogous to SINC function and limited by the "Rayleigh" resolution, and generates a value of -13.4 dB sidelobe fuzzy [16, 17].
Key words and phrases: Nyquist-Landau density, Nyquist rate, multidimensional sampling theorems, bandlimited functions
It is well known that any finite missing samples of a band-limited signal can be recovered when the signal is oversampled at a rate higher than the minimum Nyquist rate. This paper handles the problem of recovering any finite missing samples when a band-limited signal is oversampled through two channels.
For time-domain applications, the six-pole BesseI LIR filters divide the sample rate by 4, 10,20, or 40, producing Nyquist rates of 250 kHz, 100 kHz, 50 kHz, and 25 kHz, respectively.