Line frequency component

In microprocessor systems, the FFT signature is formed by breaking down the total frequency spectrum into unique components, or peaks. Each line or peak represents a specific frequency component that, in turn. 

Many electrical problems cause an increase in the amplitude of line frequency, typically 60 Hz, and its harmonics. Therefore, a narrowband should be established to monitor the 60, 120, and 180 Hz frequency components. 

The combination of bandwidth and lines of resolution selected for each machine-train must effect separation of the unique frequency components that represent a machine s operating dynamics. Resolution can be improved by reducing Fmax> increasing the lines of resolution, or a combination of both. 

Theoretically, a perfectly balanced machine that has no friction in the bearings would experience no vibration and would have a perfect vibration profile - a perfectly flat, horizontal line. However, there are no perfectly balanced machines in existence. All machine-trains exhibit some level of imbalance, which has a dominant frequency component at the fundamental mnning speed (lx) of each shaft. 

Figure 1 shows the Raman spectrum of Hb obtained with 406.7-and 413.1-nm excitation and the spectrum of monomeric, four-coordinate Ni protoporphyrin in aqueous micellar solution (9). Excitation at 413.1 nm is at resonance with the red component of the split Soret band of Ni-reconstituted hemoglobin at 406.7 nm the blue component of the Soret band is selectively probed. Comparison of the spectra shows that two sets of marker line frequencies exist. One set (labeled 4 in Figure 1) is enhanced by resonance with the blue Soret component the other set (labeled 5) is enhanced by excitation of the red Soret component. Thus, the shifts in the core-size lines in going from set 4 - 5 are -39 cm (i/-q at 1657 cm ), -20 cm cm ), and -34 cm 1 19 cm ). 

At this point it has been established that there are at least two basic mechanisms which contribute to the broad lines that are observed for the crystalline polymers. The residual zero frequency line broadening component can be analyzed in more detail. Specific attention can be given to factors which are a consequence of the chain-like character of the molecules. The local field at a given nucleus is the sum of the individual fields contributed by the neighboring magnetic nuclei. Segmental motions will induce a time dependence to the variables so that the individual contributions can be described by the equation (46)... 

Blass (1976a) and Blass and Halsey (1981) discuss data acquisition for a continuous scanning spectrometer in detail. The principal concept is that as a system scans a spectral line at some rate, the resulting time-varying signal will have a distribution of frequency components in the Fourier domain. 

The sampling theorem tells us that we must sample the signal at a rate equal to or greater than twice the highest-frequency component in the Fourier transform of the signal. For an actual spectrum of absorption lines, this maximum frequency depends on the selected scanning rate in a direct way. In addition, the bandpass of the electronics must be established in such a way that the maximum signal frequency will be minimally attenuated. 

In reality the individual lines obtained after the Fourier transformation are composed of both absorptive A(f) and dispersive D(f) components. This non-ideality arises because of a phase shift between the phase of the radiofrequency pulses and the phase of the receiver, PHCO, and because signal detection is not started immediately after the excitation pulse but after a short delay period A. Whereas the effect of the former is the same for all lines in a spectrum and can be corrected by a zero-order phase correction PHCO, the latter depends linearly on the line frequency and can be compensated for by a first-order phase correction PHCl. Both corrections use the separately stored real and imaginary parts of the spectrum to recalculate a pure absorptive spectrum. 

Fig. 4. (a) Time resolved changes of O-H stretching absorption in OH/OH (solid symbols) and OH/OD dimers (open circles) measured with parallel polarization of pump and probe and spectrally resolved detection of the probe at 2880 cm 1. Solid lines Calculated decay with time constants of 1 and 15 ps. (b) Oscillatory signal components from OH/OH (solid line) and OH/OD dimers (dotted line). The Fourier transforms shown in the inset display a major frequency component at 145 cm 1 in both cases. 

Each value of F corresponds to a different relative orientation of J and I and gives a slightly different energy. Thus each rotational level is split into 2/ + 1 (or 2J + 1 if 1 >J) components, and the microwave line frequencies... 

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. 

Even properly terminated lines can have reflections from impedance discontinuities along the line, and these reflections can degrade the signal rise time. Some of the transmitted signal is lost at each reflection point, and higher frequency components tend to be reflected (and thus attenuated) more than low-frequency components thus, the interconnection behaves like a low-pass filter and causes additional degradation of the signal rise time. 

The phase and amplitude spectrum of the laser pulse are tailored to create a wave packet with selected properties. The various eigenstates that comprise the wave packet are populated by different frequency components of the laser pulse, each with its specified amplitude and phase. For example, rovibrational wave packets of Li2 in the El E+ state were created, consisting of vibrational levels v = 12-16 and rotational levels J = 11, 19. The phases and amplitudes of the pump pulse shown in Fig. 20 were generated with a 128-pixel liquid crystal SLM. The pulse was tailored to optimize the ionization signal at a delay time of 7 ps. The phases used to maximize or minimize the ionization signal are shown by solid and dashed lines, respectively, and the intensities at the eigenfrequencies of the wave packet are indicated by circles. 

With cw, the increase of the recording time constant is not as efficient as expected because the low-frequency components of the noise are stronger and the reduction of the sweep speed increases line saturation. But with digital memory oscilloscopes and computers it is now possible to repeat the sweeps and average the different recordings. The improvement on a given line is obvious. The experiment is relatively easy to set up and it has been used for Stark effect studies 14).But the stability and reproducibility needed in the search of new lines, with broader sweeps, make this technique somewhat difficult to use and no suclt experiment seems so far to have been reported for nitrogen. 

FIG. 5. Oxygen-17 INDOR spectra of methanol enriched to 10mol obtained by monitoring the Me resonance in the proton spectrum. The frequency markers are in MHz and each trace is the result of 64 scans. Full line high frequency component of doublet monitored broken line low frequency component monitored. From ref 112. 

Let us assume that the rotational spectra of the torsional states v = 0 and v = 1 have been measured and assigned. The information available is sets of line frequencies p, splittings Ap, and an intensity ratio I0/Ix. From the frequencies v of the component lines of the multiplets, frequencies of fictitious unsplit lines are calculated by a weighted mean using formulas resulting from the Hamiltonian of Eq. (4). These lines are used to fit by a least squares method the rotational constants A> B, C or, implicitly, the effective principal moments of inertia / = fl2f2A, etc., of /fa, which are different from Ig [compare Eq. (8)]. Experience shows that for the two rotational spectra, v = 0 and v = 1, two different sets of rotational constants must be used. Here a limitation of the model... 

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