Components high-frequency

Figure Bl.2.7. Time domain and frequency domain representations of several interferograms. (a) Single frequency, (b) two frequencies, one of which is 1.2 times greater than the other, (c) same as (b), except the high frequency component has only half the amplitude and (d) Gaussian distribution of frequencies.

You can add restraints to any molecular mechanics calculation (single point, optimization or dynamics). These might be NMR restraints, for example, or any situation where a length, angle, or torsion is known or pre-defined. Restraints with large force constants result in high frequency components in a molecular dynamics calculation and can result in instability under some circumstances. 

It is unusual to be able to And one capacitor to handle the entire ripple current of the supply. Typically one should consider paralleling two or more capacitors (n) of I/n the capacitance of the calculated capacitance. This will cut the ripple current into each capacitor by the number of paralleled capacitors. Each capacitor can then operate below its maximum ripple current rating. It is critical that the printed circuit board be laid out with symmetrical traced to each capacitor so that they truly share the current. A ceramic capacitor ( 0.I pF) should also be placed in parallel with the input capacitor(s) to accommodate the high frequency components of the ripple current. 

Straightforward application of OCT as described above often results in a quite complicated pulse shapes and may especially introduce some high frequency components, which are difficult to realize experimentally, into the pulse. It is thus highly desirable to find an optimized pulse with spectral components within a predefined frequency range. With this end in view the projected search direction is subjected to a spectral filter... 

In general, the high-frequency components are usually referred to as noise and the low-frequency component is called the ripple. Together they constitute the converter s Noise and Ripple (N R), which is also sometimes called by rather weird names such as PARD (I still don t see any need to remember what that stands for). 

We did it somehow, almost strangulating ourselves in the process. Now when I look back at this incident, I wonder why we didn t place a ceramic decoupling capacitor close to the switch, as shown in the lower half of the figure. The bulk capacitor could have successfully managed to provide the low-frequency current components, whereas the high-frequency capacitor could have really decreased the effective loop area in which the high-frequency components were circulating. 

When the return is received, it is demodulated to strip off the carrier frequency. Typically, the return is mixed with , that is multiplied by, cos 2irft and then low-pass filtered to eliminate the high frequency component of the mixed signal. This is the demodulation phase refered to earlier. 

According to [31], the following two methods could be used in order to relate the high-frequency components of the spectral density in Eqs. (9a-9c) ... 

This basic sampling theorem has profound implications. It says that any high-frequency components in the signal (for example, 60-cycle-per-second electrical noise) can necessitate very fast sampling, even if the basic process is quite slow. It is, therefore, always recommended that signals be analog-filtered before they are sampled. This eliminates the unimportant high-frequency components. 

Function approximation comes naturally with the Fourier transition. Since tiny details of a function in real space relate to high-frequency components in Fourier space, restricting to low-order components when transforming back to real space (low-pass filtering) effectively smoothes the function to any desirable degree. There are special function decomposition schemes, like spherical harmonics, which especially build on this ability [128]. 

This is critical for two reasons when considering the recent Fleming group results. First, they were not able to measure the high frequency components of the spectral density with definitive accuracy. Our results show that this does not matter. Second, they find some level of variation at low frequencies. Our results show that this might matter. The low frequency blips they see and we modeled... 

This may cause severe problons with differentiating noisy signals, the high frequency components of the nobe are amplified. In practice, differentiation has to be combined with a smoothing (low pass filtering) procedure. 

An important consequence of these relationships is that differentiation increases the amplitude of high-frequency components. It is well known that data-differentiation procedures often yield unsatisfactory results when applied to noisy data. In spectroscopy, peak positions are sometimes sought by looking for a vanishing first derivative. The spectral peaks contain predominantly low and middle frequencies, but the noise often contains high frequencies as well. A possible remedy to the problem is to fit a polynomial... 

Whatever its source, the electrical signal usually contains noise components having frequencies far higher than those found in the spectrum itself. Electrical filtering is then called for to remove these high-frequency components. 

The method employs a gradual increase in frequency beyond the data band limit. High-frequency components are not sought until the best values of low-frequency components are found. Because frequencies are not sought above the lowest needed to satisfy the data, the method is inherently smooth. Furthermore, Biraud s method appears to be the first to have simultaneously utilized both the constraint of positivity and that of finite extent with specific limits, the latter being inherent in the sampling. These facts are probably responsible for the impressiveness of the restoration in the original publication (Biraud, 1969), which is reproduced in Fig. 4. 

We assume that if many of the liquids of interest, such as propylene carbonate, were studied by higher frequency (measurement techniques, new, high frequency components would be discovered which would account at least partially for the short time scale dynamics we see in the solvation C(f) data. Indeed, the apparent observation of a single Debye time is inconsistent with theories of liquids that take into account dipole-dipole interactions (see Kivelson [109]). Furthermore, some of the liquids studied have extraordinarily large apparent infinite frequency dielectric constants (e.g., = 10... 

Delay Due to Resistive Losses. On electrically long, lossy lines, the signal rise time is degraded by dispersion in the interconnection. Dispersion delays and attenuates the high-frequency components of the signal more than the low-frequency components because of the frequency-depen-dent resistance of the interconnection. The rise time degradation contributes additional delay before the switching threshold is reached at the end of the line. 

To find an approximation to the optimal control function we collect all successful realizations (qfc(t),qfc(t), J esc(f)) that move it from the CA to 0fl. An approximate solution u(t) is then found as an ensemble average over the corresponding realizations of the random force l c c(t)) (the exact solution is u t) = lim/) o u t)). The results of this procedure are shown in the upper trace of Fig. 18. To remove the irrelevant high-frequency component left after averaging, we filtered through a zero-phase low-pass filter with frequency cutoff coc = 1.9. 

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