Non-white Spectrum Research Articles

Errors-in-variables identification of dynamic systems excited by arbitrary non-white input

This work deals with the identification of dynamic systems from noisy input–output observations, where the noise-free input is not parameterized. The basic assumptions made are (1) the dynamic system can be modeled by a (discrete- or continuous-time) rational transfer function model, (2) the temporal input–output disturbances are mutually independent, identically distributed noises, and (3) the input power spectrum is non-white (not necessarily rational) and is modeled nonparametrically. The system identifiability is guaranteed by exploiting the non-white spectrum property of the noise-free input. A frequency domain identification strategy is developed to estimate consistently the plant model parameters and the input–output noise variances. The uncertainty bound of the estimates is calculated and compared to the Cramér–Rao lower bound. The efficiency of the proposed algorithm is illustrated on numerical examples.

QUANTUM FLUCTUATION DISSIPATION THEOREM REVISITED: REMARKS AND CONTRADICTIONS

The quantum fluctuation dissipation theorem (QFDT) in the Callen–Welton [ Phys. Rev.83 (1951) 34] form is critically revisited. We show that the role of the system eigenvalues is in general not correctly accounted for by the accepted form of the QFDT. As a consequence, a series of quantum results claimed in the literature, like the presence of zero point fluctuations, the violation of the quantum regression hypothesis, the non-white spectrum of the Langevin force, etc. emerge as a consequence of an incorrect application of the theorem. In this context the case of the single harmonic oscillator is illustrated as a typical example where the accepted form of the QFDT is proven to fail.

Method to distinguish possible chaos from colored noise and to determine embedding parameters.

We present a computational method to determine if an observed time series possesses structure statistically distinguishable from high-dimensional linearly correlated noise, possibly with a nonwhite spectrum. This method should be useful in identifying deterministic chaos in natural signals with broadband power spectra, and is capable of distinguishing between chaos and a random process that has the same power spectrum. The method compares nonlinear predictability of the given data to an ensemble of random control data sets. A nonparametric statistic is explored that permits a hypothesis testing approach. The algorithm can detect underlying deterministic chaos in a time series contaminated by additive random noise with identical power spectrum at signal to noise ratios as low as 3 dB. With less noise, this method can also be used to get good estimates of the parameters (the embedding dimension and the time delay) needed to perform the standard phase-space reconstruction of a chaotic time series.

Diffusion of a Quantum Particle in a Fluctuating Medium

Quantum motion of a particle in a fluctuating lattice is studied on the basis of a time-dependent Hamiltonian with site energies being randomly modulated by stochastic noises. The case of the two-state jump noise is studied in details. It is found that the particle moves diffusively on a long time scale. When the noise has a non-white spectrum, the diffusion constant is substantially enhanced in comparison with the white noise limit owing to the local coherence of the wavefunction of the particle. A numerical study is also carried out for one-dimensional cases. The analytical result is in rough agreement with the numerical calculation.

Two-user dispersive communication channels (Corresp.)

The optimum transmitters for maximum information throughput when two independent users share a dispersive channel are investigated. The channel is assumed to be linear and time invariant and is described by a 2 \times 2 matrix of transfer functions. The noise at each receiver is additive and Gaussian and may have a nonwhite spectrum. Assuming naive superposition (the interfering signal is treated as noise) it is shown that for many practical channels, frequency division multiplexing is optimum, and the structure of the optimum transmitters is obtained.

Effect on Stochastic Fluctuations of Possible Noise Sources in Non-Boiling Liquid Reactors

In an earlier paper, a stochastic model of a power reactor has been proposed by the present author on the premise that the coolant-flow through a core is usually accompanied by random variations in the flow-rate, which are eventually largely responsible for the internal reactivity fluctuations. In the present work, this model is extended to three different reactor systems: (a) where there exists a relaxation process corresponding to the effect of buoyant flow; (b) where a control or fuel element vibrates randomly, due to coolant flow-rate fluctuations; (c) where there are fluctuations in the inlet temperature with a non-white spectrum. The noise spectra are derived for various state quantities with use made of the Langevin procedure. The theory is illustrated by referring chiefly to the neutron noise spectra, and comparing with the results of observations. It is shown that the noise sources in question contribute significantly to the spectra, as compared with a low frequency component due to an inherent n...

Effect on Stochastic Fluctuations of Possible Noise Sources in Non-Boiling Liquid Reactors

In an earlier paper, a stochastic model of a power reactor has been proposed by the present author on the premise that the coolant-flow through a core is usually accompanied by random variations in the flow-rate, which are eventually largely responsible for the internal reactivity fluctuations. In the present work, this model is extended to three different reactor systems: (a) where there exists a relaxation process corresponding to the effect of buoyant flow; (b) where a control or fuel element vibrates randomly, due to coolant flow-rate fluctuations; (c) where there are fluctuations in the inlet temperature with a non-white spectrum. The noise spectra are derived for various state quantities with use made of the Langevin procedure. The theory is illustrated by referring chiefly to the neutron noise spectra, and comparing with the results of observations. It is shown that the noise sources in question contribute significantly to the spectra, as compared with a low frequency component due to an inherent noise source in the coolant flow. In particular, a strong resonance peak of the spectra arises from the coupling between the random mechanical vibrations and coolant the flow-rate fluctuations.

A general two-site solution for the chemical exchange produced dependence of T2 upon the carr-Purcell pulse separation

A general closed function for the t cp dependence of the transverse relaxation times of nuclei exchanging between two sites is described. Examination of the frequency and temperature dependence of this function demonstrates that, in contrast to T 2's determined from line widths, this spin echo method permits the evaluation of the populations of nuclei in the two sites. As a result, an unequivocal determination of all the exchange parameters becomes possible. Numerical examples are discussed for systems where the relaxation mechanism in the bound site is: (i) in the white spectrum approximation, and (ii) in the nonwhite spectrum approximation.

Spectra of earthquake time series

An earthquake time series consists of the (possibly weighted) number of events of a given class of earthquakes per unit time as a function of time. The spectrum of a single earthquake time series and the cross spectrum between different series determine the usefulness of past events in predicting future ones. The spectra of earthquakes might also shed light on the possible triggering of earthquakes by such things as tidal potential changes and other earthquakes.Much of the past work on earthquake time series has dealt with seeking significant periodicities in the data. In most cases [Davidson, 1938] significance tests have failed to take into account the correlation between events that result from the aftershock phenomena. In the spectral domain, nonrandom bunching of events due to aftershocks results in a nonwhite spectrum.