Non-linear distortion

Separation of linear from non-linear distortions. Linear distortions of the input signal are less objectionable than non-linear distortions. 

CCITT86sgl2con46, 1986] CCITT86sgl2con46 (1986). Objective evaluation of non-linear distortion effects on voice transmission quality. ITU-T Study Group 12. Contribution 46. 

An audio recording may be subject to various forms of non-linear distortion, some of which are listed below ... 

Laser-induced US spectroscopy has been used to study the effect of microcracks in rock specimens on non-linear distortion of the elastic pulse shape [57]. 

The first non-linear polarizability is a tensor of rank 3 and possesses non-vanishing elements only in the case of molecules without a centre of symmetry. This Born distortion tensor was resorted to by Piekara for explaining the non-linear dielectric behaviour of nitrobenzene. In the case of axially symmetric molecules, the tensor of the first non-linear distortion (hyperpolarizability ) can be written as follows ... 

In the middle of domains, the overlayers are well ordered, with a lattice parameter very close to that of metallic A1 (expansion of 4 % with respect to the registered state), and a small rotation (-1.4° with respect to the R state) with the epitaxial relationships (111)A1//(0001)A1203 and [Tl0]Al//(R1.4°)[1120]Al2O3. In the domain walls, large expansion and rotation, and even loss of honeycomb network topology were found. The observed structure was interpreted in the spirit of rotational epitaxy with non-linear distortions. 

E. V. Gheem, R. Pintelon, J. Vereecken, J. Schoukens, A. Hubin, P. Verboven, and O. Blajiev, "Electrochemical Impedance Spectroscopy in the Presence of Non-Linear Distortions and Non-Stationary Behavior I. Theory and Validation," Electrochimica Acta, 49 (2006) 4753-4762. 

Non-linear distortions in a measured image can be of following type positioning, straightness, squareness, and rotational errors (Fig. 10.8). 

Combination frequencies n. Two vibrations of arbitrary frequencies fi and when applied simultaneously to a non-linear (distorting) device will excite it to a motion containing not only the original frequencies, but also members of a set of combination frequencies given by fc = mf + nfi, where m and n are integers. A resonator sharply tuned to any one of these frequencies, which may be produced in the non-linear device will resound to it with an amphtude depending on the type of non-linearity. The superheterodyne radio receiver depends on this phenomenon. 

Arfib, D. (1979). Digital synthesis of complex spectra by means of multiphcation of non-linear distorted sound waves. Journal of the Audio Engineering Society, 27, 757-768. 

I When the system voltage is linear (an ideal condition that would seldom exist) but the load is non-linear The current will be distorted and become non-sinusoidal. The actual current /, (r.m.s.) (equation (23.2)) will become higher than could be measured by an ammeter or any other measuring instrument, at the fundamental frequency. Figure 23.13 illustrates the difference between the apparent current, measured by an instrument, and the actual current, where / = active component of the current... 

The second component is caused by the different harmonic quantities present in the system when the supply voltage is non-linear or the load is nonlinear or both. This adds to the fundamental current, /,- and raises it to Since the active power component remains the same, it reduces the p.f of the system and raises the line losses. The factor /f/Zh is termed the distortion factor. In other words, it defines the purity of the sinusoidal wave shape. 

A distribution network 33 kV, three-phase 50 Hz feeding an industrial belt with a number of medium-sized factories some with non-linear loads and some with static drives and some with both. It was observed that while the lines were apparently running reasonably loaded, the active power supplied was much below the capacity of the network. Accordingly, a harmonic study of the network was conducted and it was found that despite localized p.f. control by most factories, the p.f. of the network itself was well below the optimum level and the voltage was also distorted by more than was permissible. To improve this network to an acceptable level, we have considered the following load conditions, as were revealed through the analysis. 

Steady-state voltage regulation Acceptable transitent voltage variation Non-linearity characteristics of load current Percentage distortion in voltage Frequency tolerance Power factor of load Inmsh upon switch-on... 

The "add-to-memory" signal averaging method currently available to us distorts fluorescence intensity versus time plots when the fluorescence intensity is a non-linear function of incident laser energy and the laser energy varies from shot to shot. For this reason we have not attempted detailed kinetic modelling of the observed fluorescence intensity decay curves recorded at high 532 nm laser fluence. 

Because of the assumption that linear relations exist between shear stress and shear rate (equation 3.4) and between distortion and stress (equation 3.128), both of these models, namely the Maxwell and Voigt models, and all other such models involving combinations of springs and dashpots, are restricted to small strains and small strain rates. Accordingly, the equations describing these models are known as line viscoelastic equations. Several theoretical and semi-theoretical approaches are available to account for non-linear viscoelastic effects, and reference should be made to specialist works 14-16 for further details. 

Tor the purpose of this brief account we will provide only a notional definition of optical aberrations. In an optical system, the angular coordinates of incident rays are transformed according to sequential applications of Descarte s law from one optical surface to the next. Aberrations are essentially the non-linear terms of the transformation, the angular coordinates of emerging rays not being strictly proportional to those of the incident ones -thereby generating distorted and/or blurred images. 

Finite-element techniques can cope with large, highly non-linear deformations, making it possible to model soft tissues such as skin. When relatively large areas of skin are replaced during plastic surgery, there is a problem that excessive distortion of the apphed skin will prevent adequate adhesion. Finite-element models can be used to determine, either by rapid trial-and-error modelhng or by mathematical optimisation, the best way of... 

The concerns we have expressed are bound to get even more acute if the problem under study demands that we are able to adequately describe distortion effects induced in the electron distribution by external fields. The evaluation of linear (and, still more, non linear) response funetions [1] by perturbation theory then forces one to take care also of the nonoccupied portion of the complete orbital spectrum, which is entrusted with the role of representing the polarization caused by the external fields in the unperturbed electron distribution [4], ... 

A note of caution should be sounded here. Whilst the curves shown in Figure 6.5 are characteristic of many charged dispersions it should be recalled that once we apply a sinusoid to a non-linear system the response need not be a sinusoid. As the strain is increased into the nonlinear region, the waveform passing through the sample becomes progressively distorted. The instrumental analysis in this case involves... 

Figure 1. Translation, rotation, and vibration of a diatomic molecule. Every molecule has three translational degrees of freedom corresponding to motion of the center of mass of the molecule in the three Cartesian directions (left side). Diatomic and linear molecules also have two rotational degrees of freedom, about rotational axes perpendicular to the bond (center). Non-linear molecules have three rotational degrees of freedom. Vibrations involve no net momentum or angular momentum, instead corresponding to distortions of the internal structure of the molecule (right side). Diatomic molecules have one vibration, polyatomic linear molecules have 3V-5 vibrations, and nonlinear molecules have 3V-6 vibrations. Equilibrium stable isotope fractionations are driven mainly by the effects of isotopic substitution on vibrational frequencies.

Image distortion Stability Non-linear difficult to correct Mostly linear easier to correct... 

Polarization is one of the reasons for the asymmetrical form of the water molecule, and also may be partially responsible for the non-linearity of H2S molecules. Polarization would lead to the pyramidal shape observed for the molecules NH3 and PH3, but it is very doubtful whether it can be held responsible for the asymmetrical form of molecules such as PC13 and SOa. In these molecules, the central ion is positive, if it is assumed that the bonds in these compounds are ionic, and since positive ions have not a large polarizability, the distortion of the molecule can scarcely be due to polarization effects. Indeed, we cannot continue to consider these compounds as purely ionic in character, but will find it necessary to explain their asymmetry on the basis of the homopolar bond (see Section 53). Even in hydrogen compounds such as H20 and NH3 we shall find we have to take into account their partial homopolar structure in order to arrive at a really satisfactory explanation of their structures. 

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