Amplitude distribution

Figure 1 Amplitude distribution of AE signals from model glass epoxy specimens...

In statistical terms, a perceptual improvement is therefore obtained if the amplitude distribution in the filtered signal (image) is more concentrated around zero than in the raw data (contrast enhancement). A more concentrated amplitude distribution generally means smaller entropy. Thus, from an operator perception point of view, interesting results should be obtained if the raw data can be filtered to yield low entropy amplitude distributions. However, one should note that the entropy can be minimized by means of a (pathological) filter which always outputs zero or another constant value. Thus, appropriate restrictions must be imposed on the filter construction process. 

We first supposed that the field radiated into the piece by the transducer is known, thanks to the Champ-Sons model. Then, the main approximation used consists in making far field assumptions in the beam defect interaction area. In the case of a focused transducer we assume that the incident wavefronts on the defect are plane. This is equivalent to say that the defect is located in or near the transducer focal area and that a defect located outside this zone does not cause a significant echo. In the case of planar contact transducer, the incident wavefronts on the defect are assumed to be spherical The incident field on the defect is therefore approximated by the product of a spatial function gfp,0,z)describing the amplitude distribution in the beam and a time-delayed waveform < ) ft) representing the plane or spherical propagation in the beam. The incident field on the defect can therefore be approximated for ... 

Hogg. W.K., Miller, R., Rabech, G. and Ryder, D.M., The relationship of partial discharge amplitude distribution with electrie damage at different levels of voltage and frequency, IEEE Symposium on Electrical Insulation, USA, June (1984). 

As is clear from the previous discussion, the long-time power law behavior of the heat capacity is determined by the slow two-level systems corresponding to the higher barrier end of the tunneling amplitude distribution, argued to be of the form shown in Eq. (24). If one assumes that this distribution is valid for the... 

The theoretical approach is based on the solution to the mixed type linear/nonlinear generalized Schrodinger equation for spatiotemporal envelope of electrical field with account of transverse spatial derivatives and the transverse profile of refractive index. In the quasi-static approximation, this equation is reduced to the linear/nonlinear Schrodinger equation for spatiotemporal pulse envelope with temporal coordinate given as a parameter. Then the excitation problem can be formulated for a set of stationary light beams with initial amplitude distribution corresponding to temporal envelope of the initial pulse. 

One must be aware of the limits of this technique. Since the assessment of Z depends on frequency shifts of two modes, any minimal shift leads to errors due to substantial mechanical or thermal stresses. It is not necessary to mention that under such circumstances the Z match technique, too, leads to similar errors. Nevertheless, the automatic Z value determination of the Z match technique is somewhat more reliable regarding occurrence of errors because the amplitude distribution of the (102) mode is asymmetric over the active crystal surface and that of the (100) mode is symmetric. 

In this case m = 1 (t is simply a dummy variable of integration). If A is the wavelength, aT the radius of the transducer, L the distance from the transducer, and r the cylindrical radial coordinate at that distance, then u = 2nLaT/Xr. Since jinc(0) = 5, the amplitude distribution is A + 2A0 )m.c 2nLai/ r), where Ao is the amplitude on the axis at distance L. Whether the Fraunhofer approximation is valid is determined by the dimensionless distance spi which is defined as... 

Because low amplitude RF burst waveforms do not significantly modify the z-mode amplitudes of ions, the intensities would be expected to reflect the z-mode amplitude distribution just before excitation. This gives us one means of checking the above hypothesis by allowing the z-mode amplitudes to relax via ion-molecule collisions, the relative peak intensities should change. Indeed, at long delay, the high frequency peak increases at the expense of the low frequency peak. 

This ideal FM spectrum can be Fourier transformed into the frequency domain to give a spectrum of equally spaced modes with a Bessel function amplitude distribution. These equally spaced modes can be used for comparing optical frequencies by heterodyning a reference laser, unknown laser and FM laser on a nonlinear detector. Three beats can be observed ie the beats between the reference laser and one of the modes of the FM laser, the beats between the unknown laser and one of the modes of the FM laser and the mode spacing of the FM laser. The separation between the reference and unknown laser can hence be deduced. 

A different interpretation is favoured for the chromium on polyimide data by Jordan et al. [21], who propose that initial attack of chromium and charge transfer occurs on the carbonyl moiety. Since the charge transferred from the metal is distributed over the planar PMDA moiety of the polyimide, the core level spectra by themselves will not allow a distinction between the two models proposed. However, a careful analysis of the shake up features in the Cls, Ols and Nls core hole spectra might reveal the initial binding site when the amplitude distributions of the LUMO s and HOMO S in the system relative to the created core hole are considered. 

Figure 2.22 Typical time-harmonic excitations used on the surface for receptivity studies (a) Strip excitation (b) Gaussian amplitude distribution and (c) Simultaneous blowing and suction...

The main flaw of the noise obtained by filtered maximal sequences is that the amplitude distributions are usually afliwjted by a skewness. This problem has been faced by Tomlison and Galvin. Their method of eliminating this effect does not seem to be suitable for our purposes, since we need to get completely rid of skewness. Furthermore, for our work program to be pursued, the cutoff frequency of the low-pass filter has to be selectable in a wide interval of values (as a function of X). 

Figure 2. Comparison between the amplitude distribution of noise in (A) the presence of skewness and (a) in the sence of skewness, reqtectively. The solid curve indicates the theoretical Gaussian curve.

As the fracture propagates, the elastic energy released due to the micro-fractures occurring within the sample can be measured. This ultrasonic emission due to micro-fracture aftershock relaxation has recently been measured for various laboratory samples. Petri et al (1994) measured the ultrasonic emission amplitude distribution in a large number of stressed solid samples under different experimental conditions. A power law decay for the cumulative energy release distribution n Er) with the released energy amplitude Er was observed in all cases n Er) E (see Fig. 3.21). This is indeed very similar to the Guttenberg-Richter law for the frequency distribution of earthquakes, as discussed briefly in Chapter 1, and will be discussed in detail in the next chapter. 

Figure 3.1. Fourier relationship between an rf pulse of duration Tp and the amplitude distribution A(v) of the frequency components present.

SPREAD saturation pulses with reduced amplitude distribution SPRITE single-point ramped imaging with Ti enhancement SQUID superconducting quantum-interference device... 

Fig. 3A, B Tonic release of anandamide presynaptically facilitates glutamatergic synaptic transmission in substantia nigra by activating TRPVl receptors. A Anandamide AEA, 30 pM) increases the rate (leftward shift in the cumulative distribution ofthe inter-event interval), but has no effect on the amplitude distribution of spontaneous EPSCs (sEPSCs). B The TRPVl antagonist iodoresiniferatoxin (IRTX, 300 nM) decreases the rate (rightward shift in the cumulative distribution of the inter-event interval), but has no effect on the amplitude distribution of sEPSCs. Insets show raw traces of sEPSCs before (control) and during AEA and IRTX. (Modified from Marinelli et al. 2003, by permission)...

The resulting value (A(fjj, x)) is related to that part of the frequency band which predominantly contributes to the spectral sum, i.e. to the arithmetic mean frequency (f j) of the spectral amplitude distribution within the i band. Subsequently, for a continuously moving window a series of attenuation coefficients (ot(f j)) is computed from the natural logarithm of the spectral ratio of the attenuated and reference signal... 

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