Noise definition

Engel, Z. et al., 2001. Noise Definitions. In W. Karwolwski, ed. International Encyclopedia of Ergonomics and Human Factors. London Taylor Frands, pp. 1033-1046. 

In this figure the next definitions are used A - projection operator, B - pseudo-inverse operator for the image parameters a,( ), C - empirical posterior restoration of the FDD function w(a, ), E - optimal estimator. The projection operator A is non-observable due to the Kalman criteria [10] which is the main singularity for this problem. This leads to use the two step estimation procedure. First, the pseudo-inverse operator B has to be found among the regularization techniques in the class of linear filters. In the second step the optimal estimation d (n) for the pseudo-inverse image parameters d,(n) has to be done in the presence of transformed noise j(n). 

Minimum exposure times must be observed in order to reach the requisite S/N ratio. As per EN 1435 and EN 584-1, for the different ranges of utilization (energy, wall thickness), definite film elasses are prescribed. They are characterized by the minimum gradient-to-noise ratios. Based on this, one can calculate the minimum values for the S/N ratio based on the IP systems. The exposure time and the device parameter sensitivity and dynamics (latitude) must be adjusted accordingly, with an availability of an at least 12 bit system for the digitalization. 

One subtle, but major noise source is the output rectifier. The shape of the reverse recovery characteristic of the rectifiers has a direct affect on the noise generated within the supply. The abruptness or sharpness of the reverse recovery current waveform is often a major source of high-frequency noise. An abrupt recovery diode may need a snubber placed in parallel with it in order to lower its high-frequency spectral characteristics. A snubber will cost the designer in efficiency. Finding a soft recovery rectifier will definitely be an advantage in the design. 

Elevated Flares See Flares for a general definition. The elevated flare, by the use of steam injection and effective tip design, operates as a smokeless combustion device. Flaring generally is of low luminosity up to about 20 % of maximum flaring load. Steam injection tends to introduce a source of noise to the operation, and a compromise between smoke elimination and noise is usually necessary. When adequately elevated (by means of a stack) this type of flare displays the best dispersion characteristics for malodorous and toxic combustion products. Visual and noise pollution often creates nuisance problems. Capital and operating costs tend to be high, and an appreciable plant area can be rendered unavailable for plant operations and equipment because of excessive radiant heat. 

The continuous wave technique has a definite advantage over the other techniques a very narrow band of frequencies is needed to transmit the information. The pulse techniques, on the contrary, use a large band of frequencies, and the various noises, pump noises in particular, are more difficult to eliminate. 

The standard rates the offending noise according to its nature 5dB(A) is added where the noise has a definite continuous note and a further 5 dB(A) added for noise of an intermittent nature. The number of occasions that happen in an 8-hour period is then plotted on a graph and the correction for intermittency is derived. When these calculations have been performed, the noise level is compared to the background level. The standard states that where the noise exceeds the background by 5 dB or more, the nuisance is to be classed as marginal, and where the background is exceeded by lOdB(A) or more, complaints are to be expected. 

Thus, if we wish to compare the eigenvectors to one another, we can divide each one by equation [57] to normalize them. Malinowski named these normalized eigenvectors reduced eigenvectors, or REV". Figure 52 also contains a plot of the REV" for this isotropic data. We can see that they are all roughly equal to one another. If there had been actual information present along with the noise, the information content could not, itself, be isotropically distributed. (If the information were isotropically distributed, it would be, by definition, noise.) Thus, the information would be preferentially captured by the earliest... 

The limit of detection (LOD) (see Figure 2.6) is defined as the smallest quantity of an analyte that can be reliably detected. This is a subjective definition and to introduce some objectivity it is considered to be that amount of analyte which produces a signal that exceeds the noise by a certain factor. The factor used, usually between 2 and 10 [11], depends upon the analysis being carried out. Higher values are used for quantitative measurements in which the analyst is concerned with the ability to determine the analyte accurately and precisely. 

The simplest definition of sensitivity is the signal-to-noise ratio. One criterion for judging the sensitivity of an NMR spectrometer or an NMR experiment is to measure the height of a peak under standard conditions and to compare it with the noise level in the same spectrum. Resolution is the extent to which the line shape deviates from an ideal Lorentzian line. Resolution is generally determined by measuring the width of a signal at half-height, in hertz. 

Given a space G, let g (x) be the closest model in G to the real function, fix). As it is shown in Appendbc 1, if /e G and the L°° error measure [Eq. (4)] is used, the real function is also the best function in G, g = f, independently of the statistics of the noise and as long as the noise is symmetrically bounded. In contrast, for the measure [Eq. (3)], the real function is not the best model in G if the noise is not zero-mean. This is a very important observation considering the fact that in many applications (e.g., process control), the data are corrupted by non-zero-mean (load) disturbances, in which cases, the error measure will fail to retrieve the real function even with infinite data. On the other hand, as it is also explained in Appendix 1, if f G (which is the most probable case), closeness of the real and best functions, fix) and g (x), respectively, is guaranteed only in the metric that is used in the definition of lig). That is, if lig) is given by Eq. (3), g ix) can be close to fix) only in the L -sense and similarly for the L definition of lig). As is clear,... 

This observation is the first part of the cancellation puzzle [20, 21, 27, 29]. We know from Section lll.B that we should be able to solve it directly by applying Eq. (19), which will separate out the contributions to the DCS made by the 1-TS and 2-TS reaction paths. That this is true is shown by Fig. 9(b). It is apparent that the main backward concentration of the scattering comes entirely from the 1-TS paths. This is not a surprise, since, by definition, the direct abstraction mechanism mentioned only involves one TS. What is perhaps surprising is that the small lumps in the forward direction, which might have been mistaken for numerical noise, are in fact the products of the 2-TS paths. Since the 1-TS and 2-TS paths scatter their products into completely different regions of space, there is no interference between the amplitudes f (0) and hence no GP effects. 

It is important to note that the matrix effects, interferences, and variability in method efficiency are to be factored in when determining the MDL. If this was not done then only the background noise (see Figure 2, peak 13) would be considered in the definition of the MDL. In real-life samples there is a good possibility that matrix component peaks would either co-elute or elute at retention times close to... 

In Eq. (13), the vector q denotes a set of mass-weighted coordinates in a configuration space of arbitrary dimension N, U(q) is the potential of mean force governing the reaction, T is a symmetric positive-definite friction matrix, and , (/) is a stochastic force that is assumed to represent white noise that is Gaussian distributed with zero mean. The subscript a in Eq. (13) is used to label a particular noise sequence For any given a, there are infinitely many... 

The definition (21) of the TS trajectory in white noise can be rewritten as follows [40]. For a function /(f) with the Fourier transform... 

The constant matrices i- act as projection operators onto the different eigenspaces. They are given in Ref. 38. The solution Eq. (30) is entirely analogous to Eq. (20) in the white noise case. To obtain a trajectory that remains in the vicinity of the barrier for all times, we again have to set caj = 0 and identify Eq. (31) as the TS trajectory. It satisfies the condition of the general definition in that it provides, at fixed time, a random ensemble of trajectories that is stationary in time, and at fixed noise sequence a a trajectory that spends most of its time close to the barrier. 

Signal-to-noise ratio characterizes recorded signals and signal functions with regard of their quality, i.e., their precision. Unfortunately, the signal-to-noise is not uniformly used in analytical chemistry. In addition to the definitions given in Eqs. (7.1) and (7.2), there exist another one, related to the peak-to-peak noise Npp ... 

It is difficult to comprehend why this measure has not been applied in analytical chemistry. Instead of this, in the last decades the signal-to-noise ratio has increasingly been used. Signal-to-noise ratio, see Eq. (7.1), is the measure that corresponds to r in the signal domain. In principle, quantities like S/N (Eq. (7.1)) and / (Eq. (7.7)) could represent measures of precision, but they have an unfavourable range of definition, namely range[r = range[S/N] = 0... oo. 

Now that we have completed our expository interlude, we continue our derivation along the same lines we did previously. The next step, as it was for the constant-noise case, is to derive the absorbance noise for Poisson-distributed detector noise as we previously did for constant detector noise. As we did above in the derivation of transmittance noise, we start by repeating the definition and the previously derived expressions for absorbance [3],... 

The guidelines provide variant descriptions of the meaning of the term linearity . One definition is, ... ability (within a given range) to obtain test results which are directly proportional to the concentration (amount) of analyte in the sample [12], This is an extremely strict definition, one which in practice would be unattainable when noise and error are taken into account. Figure 63-la schematically illustrates the problem. While there is a line that meets the criterion that test results are directly proportional to the concentration of analyte in the sample , none of the data points fall on that line, therefore in the strictest sense of the phrase, none of the data representing the test results can be said to be proportional to the analyte concentration. In the face of nonlinearity of response, there are systematic departures from the line as well as random departures, but in neither case is any data point strictly proportional to the concentration. 

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