Nonstationary Power Spectrum Research Articles

Non-stationary variability in accreting compact objects

Accreting compact objects show variations in source flux over a broad range of timescales and in all wavebands. The light curves typically show a lognormal distribution of flux and a linear relation between flux and rms. It has been demonstrated that an exponential transform of an underlying (and unobserved) Gaussian stochastic process provides a very good description of the light curves with these observed properties. Recently, a non-stationary power spectrum was observed on fast timescales (~ days) in the active galaxy, IRAS 13224--3809, as well as a non-lognormal flux distribution and non-linear rms-flux relation. Here, we investigate the affects of piecewise non-stationary power spectra on the resultant flux distribution and rms-flux relation. We demonstrate that the simple "exponentiation" model successfully reproduces the observed quantities, even when the light curves are non-stationary. We also demonstrate how non-lognormal flux distributions and rms-flux relations inconsistent with a linear model can be erroneously produced from poorly sampled PSDs. This is of particular importance for AGN surveys where very long baselines are required to sample the PSD down to low enough frequencies.

Nonstationary Probabilistic Seismic Response Analysis of Nonlinear Soil Profile under Bidirectional Dynamic Loading

In this paper, according to the characteristics of near-fault earthquakes, combined with the strong ground motion attenuation law in China, the nonstationary power spectrum of bidirectional ground motion input is obtained through random vibration analysis. By introducing the pseudo excitation algorithm, the evolutionary power spectral density (PSD) of acceleration at the engineering bedrock is handled as the nonstationary pseudo input, and the Hardin-Drnevich hyperbolic model is utilized to take into account the nonlinearity of soil layer. On this basis, finite element method in the time domain and frequency domain are used for seismic response analysis of soil profile. Values including various time-varying power spectral density of the dynamic response, time varying RMS and time-dependent reliability at different threshold can be obtained by calculating, which provides a basis for the analysis of the foundation dynamic reliability assessment.

Searching for the trigger of the active galactic nucleus quasi-periodic oscillation: 8 years of RE J1034+396

RE J1034+396 is one of the most extreme Narrow-line Seyfert 1s detected thus far, showing the only quasi-periodic oscillation (QPO) reliably detected in an Active Galactic Nucleus (AGN). Comparison with similar spectral and timing properties observed in the black hole X-ray binary (BHB) GRS 1915+105 suggests that RE J1034+396 is a super-Eddington accretor. A more complete understanding of the behaviour of RE J1034+396 can therefore lead to a unification of the accretion physics between such extreme AGN and super-Eddington BHBs. Here we report on our latest XMM-Newton observations of RE J1034+396, which no longer show the QPO, indicating that this source shows a non-stationary power-spectrum. We use spectral and temporal analysis across all five XMM-Newton observations of the source to probe the evolution of the object. The combination of the shape of the fractional variability with energy and the inferred velocity of absorbing material in the line-of-sight rules out an absorption-only method of creating the QPO. Instead the periodically changing absorption may be produced by the QPO causing a change in ionization state. We extend our analysis by including the covariance spectra which give much better signal to noise than an rms spectrum. These reveal a new aspect of the QPO, which is that there is also a small contribution from a soft component which is hotter than the soft excess seen in the mean spectrum. Folding the lightcurve on the QPO period shows that this component lags behind the hard X-rays. If this is due to re-processing then the lag corresponding to a light travel time across 30 R_g. Some of the remaining observations have similar energy spectra and covariance spectra, but none of them show a significant QPO, so we conclude that none of these features are the trigger for the appearance of the QPO in this object.

Time–frequency analysis and instantaneous frequency estimation using two-sided linear prediction

This paper presents a new time–frequency distribution which uses a time-dependent two-sided linear predictor model. The current sample is estimated as a weighted sum of the past and future values. The two-sided linear prediction approach yields a smaller prediction error than that obtained by using the usual one-sided linear predictor model. To estimate the time-dependent coefficients of the two-sided linear predictor, these are expanded as a linear combination of a set of time functions basis which leads to an ensemble of equations of the type of Yule-Walker equations. The nonstationary power spectrum estimate is used as a time–frequency distribution to characterize the signal jointly in the time domain and the frequency domain. We show that two-sided prediction-based time–frequency distribution can discriminate two close components in the time–frequency plane that neither Choi-Williams distribution nor one-sided prediction-based time–frequency distribution are capable of resolving. Also, the proposed time–frequency distribution is used to estimate the instantaneous frequency. Examples show that the proposed approach outperforms the usual technique based on the nonstationary autoregressive model.

Initial transient detection in simulations using the second-order cumulant spectrum

Procedures for detecting an initial transient in simulation output data are developed. The tests use the second-order cumulant spectrum which differs from the power spectrum in that the stationarity constraint is not required for the former. The second-order cumulant spectrum can be interpreted as the nonstationary power spectrum and is an orthogonal decomposition of the variance of a nonstationary process. The null hypothesis is that the simulation output data series is a covariance stationary process. Equivalently, all estimates of the second-order cumulant spectrum in the region which excludes the estimates of the power spectrum will have an expected value of zero. The test procedures are designed to detect initialization bias in the estimation of the mean and the variance. These procedures can be extended to detect bias in the moments of cumulants of ordern, wheren>2. Results are presented from the application of the test to simulated processes with superimposed mean and variance transients and anM/M/1 queue example.

Dynamics of the electroencephalogram during performance of a mental task.

Dynamics of the EEG activity — during the performance of a mental task — was investigated by the nonstationary power spectrum method. The performance of the mental arithmetic is associated with suppression of the alpha wave. The suppression of the alpha wave is not as marked as the alpha blocking accompanying opening of the eyes. Alpha wave suppression during the mental task was nonsymmetric around the center frequency of the alpha wave, and lower frequency components were suppressed more than high frequency components. An explanation of these observations is proposed in terms of decrease in the periods of alpha prevalence during performance of mental tasks.

A nonstationary analysis of the electroencephalogram.

A statistical technique is described which allows description of the statistical characteristics of nonstationary electroencephalograms (EEG's). The EEG is investigated in terms of its nonstationary power spectrum. The instantaneous power spectra of certain transition processes in the EEG (the evolution and blocking of the alpha wave) are calculated and described on the time-frequency plane.

Nonstationary power spectrum analysis of the photic alpha blocking.

The dynamics of the EEG activity under light stimulation was investigated in terms of the nonstationary power spectrum method. The alpha wave was blocked by light stimulation, however the blocking was temporary, and the alpha activity recovered to that of the resting state even though under light. Moreover the alpha rhythm was also blocked by light off. The frequencies of the preand post-blocked activity were different. The frequency of the post-blocked wave shifted gradually downward and became stable after 3–4 sec.