Bandwidth criteria

Several classification schemes based on the comparison of observed to limiting bandwidths have been proposed for weakly coupled systems. When q da 0.2 (i.e., for a system that is 60% localized ). Equation (11) combined with Equation (31) predicts very narrow absorption bands. For larger values of ctda > higher order perturbation theory expressions are necessary. Obviously, bandwidth criteria alone are not sufficient for distinguishing a valence localized Q da <0.5) from a delocalized (aoA = 0-5) system. 

Coulomb correlation energy, U. The energy gain due to band formation is of the order of the bandwidth, W. Provided U can be calculated Table 1 can be used to examine the criterion UAV = 1 for Mott-localization ... 

The Fourier frequency bandpass of the spectrometer is determined by the diffraction limit. In view of this fact and the Nyquist criterion, the data in the aforementioned application were oversampled. Although the Nyquist sampling rate is sufficient to represent all information in the data, it is not sufficient to represent the estimates o(k) because of the bandwidth extension that results from information implicit in the physical-realizability constraints. Although it was not shown in the original publication, it is clear from the quality of the restoration, and by analogy with other similarly bounded methods, that Fourier bandwidth extrapolation does indeed occur. This is sometimes called superresolution. The source of the extrapolation should be apparent from the Fourier transform of Eq. (13) with r(x) specified by Eq. (14). 

For present purposes we will deem that a cluster partakes substantially of the metallic state if the electronic density of states (DOS) curve calculated for it compares well with that of the bulk metal. To compare well, the valence bandwidth must be approximately correct, as must the density of states at the Fermi level, and the general features, particularly the major peaks, in the DOS curves for cluster and bulk metal, must correspond. This criterion has a point of contact with experiment, because DOS curves can be compared with photoelectron emission spectra. 

Hush originally6 used a more complex criterion for bandwidth, Iv v[ma/1 [mvJ nax — 1/2, which reflects the fact that in theory, bands are only Gaussian when e/v is plotted versus v, but experimentalists never took to implementing this, and he later switched to the form usually quoted. The correction is rather minor, and the experimental bands are not exactly Gaussian plotted either way... 

From our data, obtained above for the temperatures —7°C, —30°C, and 100 K, we show in Fig. 38a that the bandwidth AvT ban(i decreases with cooling of ice. However, at very low temperature this parameter practically does not change with T. Our estimates show that at a given pressure the criterion (A36) roughly corresponds to the phase transition of ice Ih to other ice modification. 

Sampling Frequency. The sampling frequency selected for data acquisition obviously should be related to the bandwidth of the sampled waveform. From information theory, the criterion for adequate sampling is that the minimum sampling frequency Nyquist frequency) must be twice the bandwidth of the sampled waveform. Thus, for a 100-Hz signal, the sampling frequency must be at least 200 Hz to retain the information inherent in the waveform. 

Criterion Two Reduce the HOMO-LUMO energy gap and increase the bandwidths... 

The Nyquist criterion states that an input signal can be recovered if it is sampled at least two times the bandwidth of the signal. Sampling slower than the Nyquist... 

Before leaving the subject of pulse modulation formats, we discuss one more principle involved in choosing pulse shapes with bandwidth occupancy in mind, known as Nyquist s pulse-shaping criterion. The idea is to find pulse shapes p t), withbandlimited spectra, that have the zero intersymbol-interference... 

Raised-cosine spectra The spectrum of one family of pulses that obeys Nyquist s pulse-shaping criterion. Sampling Theorem One of several theorems, the most common of which is called the low-pass sampling theorem and says that a low-pass bandlimited signal of bandwidth W Hz may be represented in terms of samples taken periodically at a minimum rate of 2 W per second. 

The horizontal limitingresolution of a television system is usually determined by its electrical bandwidth. Assuming that the aperture response (a universal criterion for specifying picture definition and other aspects of imaging system performance) of the system components is adequate to make the black-and-white line pair (two television lines) visible, the equation for horizontal resolution Rh is, therefore... 

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