Nyquist-theorem

Nyquist theorem statement that a periodic signal must be... 

Nyquist criterion Nyquist theorem Nystan Nystarescent Nystatin... 

The noise thermometer is based on the temperature dependence of the mean square noise voltage V2 developed in a thermistor (Nyquist theorem, 1928) ... 

The SIN defined by Equation 7.6 for a given NMR resonance is proportional to the square of the nuclear precession frequency (mo, rad/s), the magnitude of the transverse magnetic field (Bi) induced in the RE coil per unit current (/), the number of spins per unit volume (Ns), the sample volume (Vs), and a scaling constant that accounts for magnetic field inhomogeneities. The SIN is inversely proportional to the noise generated in the RE receiver and by the sample (Vnoise) as defined by the Nyquist theorem,... 

Aliasing is a term for choosing slower digitization than required by the Nyquist-theorem to cover the full spectral window, while sign discrimination is accomplished by simultaneous acquisition of real and imaginary phase components (called also complex acquisition) [10, 12]. Sequential acquisition for sign discrimination (either TPPI, or the Redfield-Kunz... 

Figure 10.11—Optical arrangement of a Fourier transform IR spectrometer, a) A 90c Michelson interferometer including the details of the beam splitter (expanded view) b) optical diagram of a single beam spectrometer (based on a Nicolet model). A weak intensity HeNe laser (632.8 nm) is used as an internal standard to measure precisely the position of the moving mirror using an interference method (a simple sinusoidal interferogram caused by the laser is produced within the device). According to the Nyquist theorem, at least two points per period are needed to calculate the wavelength within the given spectrum.

It is only a small step from here to the equivalent statement, known as the Nyquist theorem, for current noise of thermal fluctuations in a circuit with resistance R.4... 

This concept is one of the most difficult to quantitate. There are some relatively explicit definitions of information content for electronic communications. (For example, the Nyquist theorem defines the minimum sampling rate required in order to preserve the maximum frequency information in a periodic signal. And, the relationships between digital encoding formats and information content of a data base can be quantitated.) However, for the general problem of evaluating the results of instrumental measurements of chemical systems, the definitions for information content of data are very clear. 

The FT requires a considerable amount of calculation, as the sampling velocity must be at least twice as great as the highest frequency that has to be measured (Nyquist theorem). The data flow to be treated is very large and needs appropriate computers. This inconvenience is impossible to overcome in the case of coupling with a chromatographic technique, unless we only want the spectra of a very limited number of components. 

Dwell time (DW) and spectral width (SW). The signal must be sampled at a rate at least twice the highest frequency (Nyquist theorem), such that DW s=l/(2SW). Thus, for SW = 5 kHz, a minimum DW is 100/rs. 

So, one important lesson is that the receiver circuit must be sampled often enough to make the pattern recognizable. The Nyquist theorem tells us that in order for a computer to determine the frequency (Av,) of each component of the wave function by this method, it must acquire at least two points... 

Note that this has nothing to do with the Fourier transform per se, but everything with the more general problem of representing continuous functions by discrete samples of such functions. The Nyquist theorem specifies that the underlying, continuous, repetitive function cannot be defined properly unless one samples it more than twice per its repeat period. 

Normally a FID is acquired using simultaneous quadrature detection, sequential quadrature detection is explained in section 2.3.1. The FID consists of the values of the X- and y-components of the magnetization measured at discrete intervals during the acquisition period T q. The time interval between two successive pairs of data points is called the dwell time For a given (chosen) spectral width SW [Hz], a total number of data points TD and acquisition time T q, the following relation is valid (Nyquist theorem) ... 

Nyquist theorem - An expression for the mean square thermal noise voltage across a resistor, given by RkTAf where R is the resistance, k the Boltzmann constant, T the temperature, and /y the frequency band within which the voltage is measured. 

The width of the time ehannels of the recorded photon distribution ean be made as small as 1 ps. The small time-bin width in conjunction with the high number of time ehannels available makes it possible to sample the signal shape adequately aeeording to the Nyquist theorem. Therefore standard deconvolution techniques [389] ean be used to determine fluorescence lifetimes much shorter than the IRF width and to resolve the eomponents of multiexponential decay functions. 

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