Noise function

A signal function y(z), which is mostly treated as a time-dependent function, /(f), can be regarded as consisting of the original true signal function yt rue (S ) which is superposed by a noise function n(t) see Fig. 2.15i... 

Orientation angle, or polar spherical coordinate. Brownian noise function, (7.96). 

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) =... 

Figure 12.4 Relation of Noise Function to Relative Standard Deviation...

Now carry out the regression command/TAR /AR /DR with B10..F31 as the Independent variable, and G10-G31 as the Dependent variable. You will note that the X coefficients obtained fi om the regression analysis match the coefficients exactly. This is, of course, ideal. Try it again, this time multiplying the A j by a suitable noise function (see Chapter 12), e.g., with P = 0.01. 

A random absolute error can be achieved by multiplying the expected random absolute error, e.g., 0.0002g in mass measurement by the noise function using P = 1. The expected relative error, in this case 1%, arising from uncertainties in purity, is obtained by multiplying the mass by the noise function where P=0.02. (See Figure 12.4) Hence W, the randomized mass is... 

As a result of the calculations A s.oand 10 at (5), (6) we defined that the given noises have a weak influence at the signal/noise function value so it is possible to neglect them in the expression (3). 

FIGURE 2 The graphics of the signal/noise function dependence fiom the earth surface energy illuniination for insects with different vision types a) monochrome, b) dichrome, c) trichromatic. 

As a calculation result there are signal/noise function values, which are within 0.003 and 1, which can be seemed as insufficient for effective providing of the insects behavior monitoring process (Fig. 5). 

FIGURE 5 The dependence graphics from the altitude h of the signal/noise function for the insects with different vision types a) trichromatic, b) monochrome, c) dichrome and for the electromagnetic emission selective sources (H- halogen tube, X- xenon lamp, T- tungsten lamp at T= 1500K, x=4m, N ). 

The graphics analysis at the Fig. 6 shows that there is a dependence of the signal/noise function from the distance between the monitoring signal source and the monitoring object. 

While evaluating the dependence of the signal/noise function (Fig. 7) created with natural and artificial optical emission source (halogen tube), we observed the different surfaces weight coefficients combinations in (Table 1.)... 

From the graphics analysis at the Fig. 7, it follows that for all natural surfaces weight coefficients sets there is the dependence of the signal/ noise function maximum value from the electromagnetic emission selective source altitude above the Earth surface. Signal/noise fimction reaches its maximum at the altitude = 4i, than it has a steady decreasing character. Also for all vision types there is a vivid dependence from the random set of the natural surfaces weight coefficients. 

It was stated that the natural surfaces spectral characteristics weight coefficients changes lead to the signal/noise function values... 

Biocybernetical system Earth axis azimuth angle Halogen tube Insect s visual organ Signal/noise function... 

Finally, there is the possibility to simulate an experimental curve (spectrum) by a mathematical algorithm, e.g., by a polynomial, a Fourier transform expression, or the superposition of Gaussian or other suitable distribution curves (cf. Sec. 2.3.4, Eq. (2-41) (2-47)). In this case, one must keep in mind that for simulation of real spectra it is also necessary to add a noise function, produced by a random generator, to the PC-computed curve. Otherwise, it is not possible to transfer the results of the investigations to real signals produced by any apparatus. Of course, it is much easier to get useful derivatives from undisturbed curves than from real spectra containing noise. 

At the Fig. 3 there are the graphics of the signal/noise function dependence from the earth surface energy illumination in different seasons and at a different daytime (in this case winter is not observed as it doesn t correspond with the insects vital active phase). 

From the curve analyses we can notice that the signal/noise function changes greatly depending on the season and on the daytime and reaches its maximum at night and then decays quickly and at t = 12- period reaches its minimum. 

From the graphics analysis (Figs. 6, and 7) it follows that in all cases there is a dependence of the signal/noise function maximum value from the altitude of the electromagnetic emission selective source above the Earth surface what defines its optimal value for the insects with different vision t) es. For the insects with monochrome vision type there is... 

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