Mathematical Analysis of Random Noise-Conclusion

Dynamic reliability analysis of nonlinear structures using a Duffing-system-based equivalent nonlinear system method

An attempt is made to give a coherent, elementary account of the ways in which fluctuation theory has been applied to some of the simpler types of physical measurement. Uncertainties in measurements involving suspended systems are discussed on the basis of simple correlation function arguments, and consideration is given to the methods of measurement appropriate when there are various practical limitations on the parameters of the suspended system. There follows an elementary development of the mathematical and physical considerations usually employed in treating fluctuations in linear measuring instruments: remarks on the status of the random force method as applied to equilibrium systems are included. The circumstances under which there is an absolute limit to the attainable accuracy are discussed. It is shown that, in the case of measurements with a suspended system, feedback may enable these limits to be attained with a convenient measurement procedure. An account is given of various approaches to the calculation of the limits of accuracy in measurements with radiation detectors. Finally some elementary results are established concerning the optimum characteristics of an instrument used to follow a varying signal in the presence of noise.

http://iopscience.iop.org/article/10.1088/0034-4885/16/1/307/pdf

Fluctuation theory in physical measurements

/pdf/the-expected-number-of-zeros-of-continuous-stationary-38nv3p141f.pdf

The expected number of zeros of continuous stationary Gaussian processes

The ensemble distribution is derived for the number of photons n counted in a short time interval by a photodetector which is illuminated by a partially polarized beam of thermal light. It is shown to be of the form expected for n bosons distributed between 2/(1 + P) cells of phase space, where P is the degree of polarization. This number also has a simple classical analogue as the statistical degrees of freedom of light waves with a Gaussian amplitude distribution, and it is completely determined by the ratio of the eigenvalues of the usual 2 × 2 coherence matrix. It is suggested that no comparable simple conclusions will normally hold for non-thermal light, as, for example, from an optical maser.

https://iopscience.iop.org/article/10.1088/0370-1328/81/6/316/pdf

Mathematical Analysis of Random Noise-Conclusion

Citations

Dynamic reliability analysis of nonlinear structures using a Duffing-system-based equivalent nonlinear system method

Fluctuation theory in physical measurements

The expected number of zeros of continuous stationary Gaussian processes

Intensity Fluctuations of Partially Polarized Light

Time-variant reliability analysis using the parallel subset simulation

Related Papers (5)

Mathematical analysis of random noise

Stationary and Related Stochastic Processes

On the statistical distribution of the heights of sea waves

Probability, random variables and stochastic processes

Statistical properties of a sine wave plus random noise