Noise additive

There is some uncertainty connected with testing techniques, errors of characteristic measurements, and influence of fectors that carmot be taken into account for building up a model. As these factors cannot be evaluated a priori and their combination can bring unpredictable influence on the testing results it is possible to represent them as additional noise action [4], Such an approach allows to describe the material and testing as a united model — dynamic mathematical model. 

Here 0(l) is additional noise in current signal. The noise in reference signal is assumed to be compensated in the process of its averaging. 

The noise is expressed as noise density in units of V/(Hz), or integrated over a frequency range and given as volts rms. Typically, photoconductors are characterized by a g-r noise plateau from 10 to 10 Hz. Photovoltaic detectors exhibit similar behavior, but the 1/f knee may be less than 100 Hz and the high frequency noise roU off is deterrnined by the p—n junction impedance—capacitance product or the amplifier (AMP) circuit when operated in a transimpedance mode. Bolometers exhibit an additional noise, associated with thermal conductance. 

This equation describes not only the crystal growth, but with an additional noise term it also describes the evolution of the surface width and is called the Edward-Wilkinson model. An even better treatment has been performed by renormalization methods and other techniques [44,51-53]. 

SPC techniques are hardly affected by additive noise and multiplicative noise is absent. However, subtractive noise due to the collection efficiency and transmission of optics and the quantum efficiency of the detector do play a role. In addition, at high count rates, the efficiency goes down due to pileup effects. 

An analytical description of the photon-economy and additive noise could be carried out by the estimation of the Fisher-information matrix of the used estimators [34],... 

The vector nk describes the unknown additive measurement noise, which is assumed in accordance with Kalman filter theory to be a Gaussian random variable with zero mean and covariance matrix R. Instead of the additive noise term nj( in equation (20), the errors of the different measurement values are assumed to be statistically independent and identically Gaussian distributed, so... 

The functional relationships that characterize the real process behavior are never known exactly. A conventional way to account for the inaccuracies generated by approximations is to introduce additive noise, which in some sense reflects the expected degree of modeling errors, that is,... 

As predicted, the points next to the ends of the profile give unreliable (negative) estimates because the fluxes at the end points themselves become a substantial fraction of the fluxes in the neighborhood. In addition, noise in sections with rather flat gradients becomes a problem. More elaborated non-linear regression techniques should be used to handle this specific problem. Nevertheless, the profile between IS and SO/rm, where steep Ce variations are observed, shows evidence for substantial changes of the Off which seems to hint at much faster diffusion when this element is only in trace amounts in the apatite lattice, o... 

Figure 5-4. Log of the singular values for a 3 component chromatogram. Upper panel (+) for the data matrix Y with a noise level of lx lO3 and lower panel (x) for Y1 with additional noise of lxlO-L...

Neither of the CCD camera and IP has the ideal resolution of a single pixel, and in both detectors additional noises are introduced in the detection process. The recorded image can be generally expressed as... 

It is suitable, at this point, to repair our formulation of the problem in a realistic way that accounts explicitly for the nature of the additive noise n(x) ... 

Chapter 3. Consistency of solution 6+ x) with the observed data in the presence of additive noise of this type requires minimization of... 

Prior to deconvolution, the convolved spectrum was corrupted with additive noise to form rms signal-to-noise ratios of oo 1, 580 1,115 1, 60 1, and 30 1 for traces (c)-(g), respectively. The noise generated is similar to white noise (or detector noise) after passing through an amplification system with a negligible time constant. A typical spectrum would be recorded with the higher noise frequencies already attenuated, and thus our example may not represent a realistic situation. It should also be pointed out that the simulated noise differs from trace to trace in Fig. 3 only in amplitude and is thus not truly random. 

Under these prior conditions, the restoring algorithm given by Eqs. (59) and (60) becomes very close to one previously used by Frieden (1972). That one was also a maximum-entropy restoring algorithm in the presence of additive noise. We present some results of the latter method applied to spectral data. 

How do the form Qm of a prior object and the number z of degrees of freedom affect the estimate nm This was the problem (37) augmented by data constraints (50). Suppose in addition that the image data im suffer from Gaussian additive noise, so that Eq. (54) is true. Then the total estimator given by Eqs. (56) and (57) becomes... 

This equation is commonly characterized by the term additive noise , but a transformation of the variable y changes the additive noise into the multiplicative noise of (4.5), compare XVI. 1. 

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