Related papers: On the Statistical Properties of Cospectra
The cross spectrum encodes the correlated variability between two time signals. In recent years, the cross spectrum has been used to study astronomical sources, particularly in the field of X-ray timing. In the literature, it has been…
The light curves from a variety of celestial objects display aperiodic variations, often giving rise to red-noise components in their power spectra. Searching for a narrow power spectrum peak resulting from a periodic modulation over the…
Pulse profiles probe the emission geometry of accreting X-ray pulsars, but their observed shapes may depend on instrumental response and observational setup. The pulsed fraction spectrum provides a compact spectro-timing observable that can…
Aperiodic variability is a characteristic feature of young stars, massive stars, and active galactic nuclei. With the recent proliferation of time domain surveys, it is increasingly essential to develop methods to quantify and analyze…
The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has recently reported strong statistical evidence for a common-spectrum red-noise process for all pulsars, as seen in their 12.5-yr analysis for an isotropic…
This article addresses the measurement of the power spectrum of red noise processes at the lowest frequencies, where the minimum acquisition time is so long that it is impossible to average on a sequence of data record. Therefore, averaging…
A statistical framework is presented for the study of the orthogonally polarized modes of radio pulsar emission via the covariances between the Stokes parameters. To accommodate the typically heavy-tailed distributions of single-pulse radio…
Analysis of pulsar timing data have provided evidence for a stochastic gravitational wave background in the nHz frequency band. The most plausible source of such a background is the superposition of signals from millions of supermassive…
Many astrophysical sources, especially compact accreting sources, show strong, random brightness fluctuations with broad power spectra in addition to periodic or quasi-periodic oscillations (QPOs) that have narrower spectra. The random…
As the hunt for an Earth-like exoplanets has intensified in recent years, so has the effort to characterise and model the stellar signals that can hide or mimic small planetary signals. Stellar variability arises from a number of sources,…
Dead time affects many of the instruments used in X-ray astronomy, by producing a strong distortion in power density spectra. This can make it difficult to model the aperiodic variability of the source or look for quasi-periodic…
We explore the use of the bispectrum for understanding quasiperiodic oscillations. The bispectrum is a statistic which probes the relations between the relative phases of the Fourier spectrum at different frequencies. The use of the…
In this paper, we report on the hard X-ray observation of the X-ray pulsar 1E 1145.1-6141 performed with the Nuclear Spectroscopic Telescope Array mission (NuSTAR). The coherent pulsation of the source with a period of…
The periodogram is a popular tool that tests whether a signal consists only of noise or if it also includes other components. The main issue of this method is to define a critical detection threshold that allows identification of a…
We demonstrate a simple method for testing the significance of peaks in the periodogram of red noise data. The procedure was designed to test for spurious periodicities in X-ray light curves of active galaxies, but can be used quite…
Combination frequencies are not solutions of the perturbed stellar structure equations. In dense power spectra from a light curve of a given multi-periodic pulsating star, they can compromise the mode identification in an asteroseismic…
This paper summarises two recently developed techniques in power spectral analysis and their application to a sample of X-ray light curves of accreting collapsed objects in active galactic nuclei and X-ray binaries. The first technique is…
The study of X-ray time-lag spectra in active galactic nuclei (AGN) is currently an active research area, since it has the potential to illuminate the physics and geometry of the innermost region (i.e. close to the putative super-massive…
It is well known that if the power spectral density of a continuous time stationary stochastic process does not have a compact support, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum…
Most biological signals are non-Gaussian, reflecting their origins in highly nonlinear physiological systems. A versatile set of techniques for studying non-Gaussian signals relies on the spectral representations of higher moments, known as…