Cross-correlations

The calculation of characteristic values causes a high amount of values which contain redundant informations. Due to this the forth partial step will be to reduce this amount of values using extraction methods. This can be realized with statistical methods like cross correlation analysis. 

Signal processing in mechanical impedance analysis (MIA) pulse flaw detectors by means of cross correlation function (CCF) is described. Calculations are carried out for two types of signals, used in operation with single contact and twin contact probes. It is shown that thi.s processing can increase the sensitivity and signal to noise ratio. 

In this report problem of information processing in MIA pulse flaw detectors by means of cross correlation function is considered. Such processing promises to increase the sensitivity and to reduce the noises, mainly the frictional ones. 

Figure Al.6.14. Schematic diagram showing the promotion of the initial wavepacket to the excited electronic state, followed by free evolution. Cross-correlation fiinctions with the excited vibrational states of the ground-state surface (shown in the inset) detennine the resonance Raman amplitude to those final states (adapted from [14].

The cross-correlation effects between the DD and CSA interactions also influence the transverse relaxation and lead to the phenomenon known as differential line broadening in a doublet [40], cf Figure Bl.13.8. There is a recent experiment, designed for protein studies, that I wish to mention at tire end of this section. It has been proposed by Pervushin etal [4T], is called TROSY (transverse relaxation optimized spectroscopy) and... 

Werbelow L G 1996 Relaxation processes cross correlation and interference terms Encyclopedia of Nuclear Magnetic Resonance ed D M Grant and R K Harris (Chichester Wiley) pp 4072-8... 

The instrument response fiinction (IRF) for the fluorescence upconversion experiment, then, caimot be shorter than the intensity cross-correlation fiinction, which can be obtained usmg an mstniment like that shown in figure B2.1.4... 

Narevicius E, Neuhauser D, Korsch H J and Moiseyev M 1997 Resonances from short time complex-scaled cross- correlation probability amplitudes by the filter-diagonalization method Chem. Phys. Lett. 276 250... 

Cross Correlation. Considerable research has been devoted to correlation techniques where a tracer is not used. In these methods, some characteristic pattern in the flow, either natural or induced, is computer-identified at some point or plane in the flow. It is detected again at a measurable time later at a position slightly downstream. The correlation signal can be electrical, optical, or acoustical. This technique is used commercially to measure paper pulp flow and pneumatically conveyed soHds. 

The practice of estabHshing empirical equations has provided useflil information, but also exhibits some deficiencies. Eor example, a single spray parameter, such as may not be the only parameter that characterizes the performance of a spray system. The effect of cross-correlations or interactions between variables has received scant attention. Using the approach of varying one parameter at a time to develop correlations cannot completely reveal the tme physics of compHcated spray phenomena. Hence, methods employing the statistical design of experiments must be utilized to investigate multiple factors simultaneously. 

A time cross-correlation function between dynamic variables A (it) and B(t) is defined in a similar way ... 

In the case where x and y are the same, C (r) is called an autocorrelation function, if they are different, it is called a cross-correlation function. For an autocorrelation function, the initial value at t = to is 1, and it approaches 0 as t oo. How fast it approaches 0 is measured by the relaxation time. The Fourier transforms of such correlation functions are often related to experimentally observed spectra, the far infrared spectrum of a solvent, for example, is the Foiuier transform of the dipole autocorrelation function. ... 

Lam, R.B. "On the Relationship of Least Squares to Cross-correlation Quantitative Spectral Analysis", Appl. Spec. 1983 (37) 567-569. 

McLeman<7, ) used a method which was really a pre-cursor of the cross-correlation technique. He injected a pulse of air into the conveying line as a result of which there was a very short period during which the walls at any particular point were not subject to... 

Figure 4. The fringe contrasts measure the resemblance (cross-correlation) of the two mixed fields, (right).

As stated in the previous section, the major reactant feed was chosen as the manipulated variable. In the trial this feed was subjected to a pseudo-random binary sequence (PRBS) signal in an open loop operation of the process. The results of the trial, plotted in Fig. 2, show a strong -- but delayed -- cross-correlation between the manipulated feed rate and the reactor temperature. Using techniques described by Box and Jenkins (2), a transfer function relating the manipulated variable to the control variable of interest can be developed. The general form of this transfer function is... 

The relaxation data for the anomeric protons of the polysaccharides (see Table II) lack utility, inasmuch as the / ,(ns) values are identical within experimental error. Obviously, the distribution of correlation times associated with backbone and side-chain motions, complex patterns of intramolecular interaction, and significant cross-relaxation and cross-correlation effects dramatically lessen the diagnostic potential of these relaxation rates. 

We also calculated the cross-correlations of the position fluctuations in the Xj- and %2-directions at each distance, which method has been utilized for analyzing the... 

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