Noise coefficient

The inherent properties of the fire-resistant mastic may be exploited for many other applications. On the basis of low thermal conductivity, the mastic forms a suitable coating on metal sheet buildings which prevents condensation, reduces noise coefficient, and retards radiated heat. Another property which is sometimes important is that the mastic does not support mildew. For this and other reasons, the mastic has been applied on the interior of concrete storage granaries to prevent the grain from mildewing in the area adjacent to the concrete walls. 

To calculate complex amplitudes and noise functions we insert the solution (138) to (144) and (145), perform the averages using (135), and evaluate the resulting integrals [127,135,141]. The amplitudes and noise coefficients at given z depend on the initial values J -(0), 5,(0), Cj(0) and mean numbers of chaotic phonons (nVj). Usually the input modes are not correlated, hence Djk(0) =... 

SD is the standard deviation in a standard ROI k is the electronic noise coefficient... 

For these coefficients, respectively use wavelet packet de-noise limit method to process these coefficients and get de-noising coefficients ... 

Thus the average velocity decays exponentially to zero on a time scale detennined by the friction coefficient and the mass of the particle. This average behaviour is not very interesting, because it corresponds to tlie average of a quantity that may take values in all directions, due to the noise and friction, and so the decay of the average value tells us little about the details of the motion of the Brownian particle. A more interesting... 

The sound absorption of materials is frequency dependent most materials absorb more or less sound at some frequencies than at others. Sound absorption is usually measured in laboratories in 18 one-third octave frequency bands with center frequencies ranging from 100 to 5000 H2, but it is common practice to pubflsh only the data for the six octave band center frequencies from 125 to 4000 H2. SuppHers of acoustical products frequently report the noise reduction coefficient (NRC) for their materials. The NRC is the arithmetic mean of the absorption coefficients in the 250, 500, 1000, and 2000 H2 bands, rounded to the nearest multiple of 0.05. 

In this relation a(r, t) is the experimentally observed signal, s represents random noise, axi r) represents the time invariant systematic noise and aRi(f) the radial invariant systematic noise Schuck [42] and Dam and Schuck [43] describe how this systematic noise is ehminated. x is the normahsed concentration at r and t for a given sedimenting species of sedimentation coefficient 5 and translational diffusion coefficient D it is normalised to the initial loading concentration so it is dimensionless. 

The relationship between the noise and atmospheric covariances is also evident in Eq. 17. If the noise on the measurements is large the N term dominates the inverse which means only the large eigenvalues of C contribute to the inverse. Consequently only the low order modes are compensated and a smooth reconstruction results. When the data is very noisy then 1 and hence a tend to zero. If the data is very noisy, then no estimate of the basis coefficients is made. 

If in the ideal case the noise on the measurements is zero, such that N = 0, then the measurements are explained exactly and the basis coefficients are assigned by their relative probability, which is determined by C. 

Figure 1. The coefficient of tilt, 0,2, with increasing noise covariance, N.

Figure 2.2. Examples of correlations with high and low coefficients of determination. Data were simulated for combinations of various levels of noise (a = 1,5, 25, top to bottom) and sample size (n - 10, 20, 40, left to right). The residual standard deviation follows the noise level (for example, 0.9, 5.7, 24.7, from top to bottom). Note that the coefficient 0.9990 in the top left panel is on the low side for many analytical calibrations where the points so exactly fit the theoretical line that > 0.999 even for low n and small calibration ranges.

Note that a number of complicating factors have been left out for clarity For instance, in the EMF equation, activities instead of concentrations should be used. Activities are related to concentrations by a multiplicative activity coefficient that itself is sensitive to the concentrations of all ions in the solution. The reference electrode necessary to close the circuit also generates a (diffusion) potential that is a complex function of activities and ion mobilities. Furthermore, the slope S of the electrode function is an experimentally determined parameter subject to error. The essential point, though, is that the DVM-clipped voltages appear in the exponent and that cheap equipment extracts a heavy price in terms of accuracy and precision (viz. quantization noise such an instrument typically displays the result in a 1 mV, 0.1 mV, 0.01 mV, or 0.001 mV format a two-decimal instrument clips a 345.678. .. mV result to 345.67 mV, that is it does not round up ... 78 to ... 8 ). 

PROS REJECT jcls Section 3.6, Fig. 1.29 In a production environment there are often several superimposed processes that yield measurement series like that depicted in the lower panel there is drift that unexpectedly changes slope, there is bias and measurement noise, and there are operators who take corrective action. The model includes the probability of drift occurring and a feed-back loop that permits both positive and negative coefficients. The operators can be ordered to react if a single value exceeds a set limit, or only if 2, 3, or more successive values do so. The program calculates the two-sided (asymmetric) total probability of a value being OOS and depicts this in the upper panel on a log(p) scale. The red horizontal is the upper limit on the total risk as set in cell B20. 

Fig. 14. Esxtracting distinguishing features from noise pulse signal. Wavelet coefficients in shaded regions represent stable extrema, (a) Wavelet decomposition of noisy pulse signal (b) wavelet decomposition of pulse signal. (Reprinted from Bakshi and Stephanopoulos, Representation of process trends. Part III. Computers and Chemical Engineering, 18(4), p. 267, Copyright (1994), with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.)...

The combination of PCA and LDA is often applied, in particular for ill-posed data (data where the number of variables exceeds the number of objects), e.g. Ref. [46], One first extracts a certain number of principal components, deleting the higher-order ones and thereby reducing to some degree the noise and then carries out the LDA. One should however be careful not to eliminate too many PCs, since in this way information important for the discrimination might be lost. A method in which both are merged in one step and which sometimes yields better results than the two-step procedure is reflected discriminant analysis. The Fourier transform is also sometimes used [14], and this is also the case for the wavelet transform (see Chapter 40) [13,16]. In that case, the information is included in the first few Fourier coefficients or in a restricted number of wavelet coefficients. 

The phase spectrum 0(n) is defined as 0(n) = arctan(A(n)/B(n)). One can prove that for a symmetrical peak the ratio of the real and imaginary coefficients is constant, which means that all cosine and sine functions are in phase. It is important to note that the Fourier coefficients A(n) and B(n) can be regenerated from the power spectrum P(n) using the phase information. Phase information can be applied to distinguish frequencies corresponding to the signal and noise, because the phases of the noise frequencies randomly oscillate. 

Ideally, any procedure for signal enhancement should be preceded by a characterization of the noise and the deterministic part of the signal. Spectrum (a) in Fig. 40.18 is the power spectrum of white noise which contains all frequencies with approximately the same power. Examples of white noise are shot noise in photomultiplier tubes and thermal noise occurring in resistors. In spectrum (b), the power (and thus the magnitude of the Fourier coefficients) is inversely proportional to the frequency (amplitude 1/v). This type of noise is often called 1//... 

---