Noise averaging

QUANTUM AND CLASSICAL DYNAMICS OF NONINTEGRABLE SYSTEMS 143 where l(t) is a Gaussian white-noise source with noise average... 

One of the main limitations of NMR spectroscopy is its inherent lack of sensitivity. As a result, the CW method is unsuitable for recording spectra from nuclei of low natural abundance or even from abundant nuclei in solutions of very low concentration. One way of improving the signal-to-noise (S/N) ratio is to record several spectra from a sample and add them together. The noise averages... 

The temperature jump equipment comprised a Hartley Measurements, joule heating temperature jump assembly with both oscilloscope output and a Varian trace superposition noise averaging facility for increasing signal to noise ratio, also equipped with an analogue to digital (paper tape) converter for data storage. The relaxation effect was monitored by fast kinetic spectrophoto-... 

The adaptive estimation of the pseudo-inverse parameters a n) consists of the blocks C and E (Fig. 1) if the transformed noise ( ) has unknown properties. Bloek C performes the restoration of the posterior PDD function w a,n) from the data a (n) + (n). It includes methods and algorithms for the PDD function restoration from empirical data [8] which are based on empirical averaging. Beeause the noise is assumed to be a stationary process with zero mean value and the image parameters are constant, the PDD function w(a,n) converges, at least, to the real distribution. The posterior PDD funetion is used to built a back loop to block B and as a direct input for the estimator E. For the given estimation criteria f(a,d) an optimal estimation a (n) can be found from the expression... 

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. 

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... 

If there are no reactions, the conservation of the total quantity of each species dictates that the time dependence of is given by minus the divergence of the flux ps vs), where (vs) is the drift velocity of the species s. The latter is proportional to the average force acting locally on species s, which is the thermodynamic force, equal to minus the gradient of the thermodynamic potential. In the local coupling approximation the mobility appears as a proportionality constant M. For spontaneous processes near equilibrium it is important that a noise term T] t) is retained [146]. Thus dynamic equations of the form... 

Effect of signal averaging on a spectrum s signal-to-noise ratio (a) spectrum for a single scan ... 

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