Coloured noise

Fig. 40.32. Deconvolution (result in solid line) of a Gaussian peak (dashed line) for peak broadening ((M i/,)prf/(H vi)G = 1). (a) Without noise, (b) With coloured noise (A((0,1%), Tx = 1.5) inverse filter in combination with a low-pass filter, (c) With coloured noise (A (0,1 %), Ta = 1.5) inverse filter without low-pass filter.

A point that has not been investigated is the possibility of considering u(k) a coloured noise instead of white noise, and therefore a non diagonal E. For example, the choice of a tridiagonal Ey would imply the assumption of u(k) a random walk process. On the one hand, by imposing a correlation among successive values of u(k), the flexibility of the output is reduced, and for example a delta function could not be recuperated. On the other hand, smoother outputs and better solutions could be obtained if good "a priori" estimations of the real autocorrelations of u(k) could be provided. 

Koo et al., 1989] Koo, B., Gibson, J. D., and Gray, S. D. (1989). Filtering of coloured noise for speech enhancement and coding. Proc. IEEE Int. Conf. Acoust., Speech and Signal Proc, pages 349-352. 

Assume the SISO model (2.25) where is coloured noise and follows an ARMA process with lag polynomials < (B) and 0 B). Without loss of generality fi is assumed to be zero and (2.25) changes to... 

L. Arnold, W. Horsthemke, and R. Lefever, White and Coloured Noise and Transition Phenomena in Nonlinear Systems, Z. Physik. B 29, 367-373 (1978). 

Noise-induced transition the effect of coloured noise... 

An often-used coloured noise is the Ornstein-Uhlenbeck process its expectation E[ j] = 0 vanishes, and its correlation function is exponential ... 

What is more interesting, at least from the theoretical point of view is that oscillatory behaviour might emerge as a result of the interaction between the system and the external noise applied. This phenomenon was earlier described in a radio-engineering context (Kuznetsov et ai, 1965). Studying the role of multiplicative coloured noise for the catalytic oxidation of CO on a platinum surface, de la Rubia et ai (1982) demonstrated that a limit cycle is induced by external noise. Similarly, Treutlein Schulten (1985) found noise induced limit cycles in the Bonhoffer-van der Pol model of neural pulses (see further Lefever Turner (1984)). 

Coloured noise, narrow band noise and periodic impulsive noise are usually modeled as background noise because they remain stationary from seconds to even hours. Periodic impulsive noise synchronous to the mains and asynchronous impulsive noise may cause bit or burst errors over the transmission, although they are time variant. A complete theoretical analysis on shown noises in Figure 2 can be found on [5, 6,11,12,13]. 

The control requirements for the previously described coloured noise, narrow band noise, periodic impnilsive noise and asynchronous impulsive noise, can be separately analyzed in two different scenarios. 

A Tuned Mass Damper (TMD) is one of the simplest and the most rehable passive device for vibration control in a wide range of applications, and for this reason many optimization criteria have been proposed for this specific device. Essentially, a TMD consists in an additional mass connected to a main system by a spring and a damper. The main system, excited by a base acceleration, is modelled as a stochastic stationary coloured noise and introducing the global space state vector ... 

Fig. 8 shows a simple model of an offshore platform. The distribution of the hydromechanic force excited at a frequency of 1,2 r.p.s. is presented in Fig. 9. The frequency response function of the tip-deflection for various distances of the sloping beach is recorded in Fig. 10. Evolutionary pov/er spectral densities are shown in Figs. 11, 12 for white and coloured noise excitation, respectively, switched on at time zero.

Fig.12 Evolution of the power spectral density of tip deflection after switching on a coloured noise g round acceleration process. Kanai-Tajimi filter parameters are C =0.6, w =2.7. Ref. /8/.

Colour Plate 3 Absorbance noise as a function of transmittance, for the exact solution (upper curve equation 42-32) and the approximate solution (lower curve equation 42-33). The noise-to-signal ratio, i.e., AE/Et was set to 0.01. (see Figure 42-2, p. 237)... 

Colour Plate 5 Family of curves of multiplication factor as a function of Et, for different values of the parameter sigma (the noise standard deviation), for Normally distributed error. Values of sigma range from 0.1 to 1.0 for the ten curves shown, (see Figure 43-6, p. 251)... 

Colour Plate 8 Comparison of empirically determined transmittance noise value with those determined according to the low-noise approximations of equation 44-19 and equation 44-52b. (see Figure 44-8a, p. 264)... 

Colour Plate 9 Transmittance noise as a function of reference S/N ratio, at various values of sample transmittance. Blue curve T = 1. Green curve T = 0.5. Red curve T = 0.1. (see Figure 44-9a-l, p. 265)... 

Colour Plate 11 Transmittance noise as a function of transmittance, for different values of reference energy S/N ratio (recall that, since the standard deviation of the noise equal unity, the set value of the reference energy equals the S/N ratio), (see Figure 44-10a, p. 266)... 

Colour Plate 12 Comparison of computed absorbance noise to the theoretical value (according to equation 44-32), as a function of S/N ratio, for constant transmittance (set to unity), (see Figure 44-lla-l, p. 267)... 

Colour Plate 18 Relative absorbance noise for Poisson-distributed data, determined by numerical computation using equation 51-77. Figure 51-29b is an ordinate expansion of Figure 51-29a. (see Figure 51-29, p. 320)... 

Digital noise-reduction Videonoise is related to tape quality, camera resolution and light conditions. In a video picture, pixels will change their colour ran-... 

The name pyrotechnic is derived from the Greek words pyr (fire) and techne (an art), which describes the effect observed from a burning pyrotechnic composition. These effects include the production of coloured smoke, noise, and the emission of bright-coloured light. Pyrotech-... 

This method provided a simple and fast procedure to identify the presence of a nucleic acid sequence with good sensitivity. On average, the liposomes entrapped several thousand dye molecules, which provided intrinsic amplification of individual binding events. A qualitative measure of nucleic acid hybridization by visualization of the colour on the dip stick was intrinsically provided and quantitative measurements were also possible by use of a reflectometer. This approach resulted in a limit of detection of 1 fmol and a dynamic range of over two orders of magnitude. Maximum signal-to-noise was obtained with 0.2 mol% of probe sequence immobilized on the liposomes. 

Genuine chemical methods were preceded by techniques such as the touchstone,26 and also by the direct investigation of the material or object by the use of the senses. A material could be felt, it could be tasted, its colour could be observed, it could be smelt, and the noise it could be induced to make could be listened to. The use of such methods of organoleptic analysis in the work of the Georgian King, Vakhtang VI (1675-1737) have been described.27 Probably the first demand for a quantitative analytical method arose from a desire to estimate the purity of samples of gold. While... 

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