Related papers: Understanding the Lomb-Scargle Periodogram
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…
The least-squares (or Lomb-Scargle) periodogram is a powerful tool which is used routinely in many branches of astronomy to search for periodicities in observational data. The problem of assessing statistical significance of candidate…
The Lomb-Scargle periodogram is a common tool in the frequency analysis of unequally spaced data equivalent to least-squares fitting of sine waves. We give an analytic solution for the generalisation to a full sine wave fit, including an…
Detection of a signal hidden by noise within a time series is an important problem in many astronomical searches, i.e. for light curves containing the contributions of periodic/semi-periodic components due to rotating objects and all other…
This paper introduces the multiband periodogram, a general extension of the well-known Lomb-Scargle approach for detecting periodic signals in time-domain data. In addition to advantages of the Lomb-Scargle method such as treatment of…
Accurate time series analysis is essential for studying variable astronomical sources, where detecting periodicities and characterizing power spectral density (PSD) are crucial. The Lomb-Scargle periodogram, commonly used in astronomy for…
We consider the problem of estimating the period of an unknown periodic function observed in additive noise sampled at irregularly spaced time instants in a semiparametric setting. To solve this problem, we propose a novel estimator based…
The detection of signals hidden in noise is one of the oldest and common problems in astronomy. Various solutions have been proposed in the past such as the parametric approaches based on the least-squares fit of theoretical templates or…
We address the problem of assessing the statistical significance of candidate periodicities found using the so-called `multi-harmonic' periodogram, which is being used for detection of non-sinusoidal signals, and is based on the…
We consider the estimation of a common period for a set of functions sampled at irregular intervals. The problem arises in astronomy, where the functions represent a star's brightness observed over time through different photometric…
Context. Frequency analyses are very important in astronomy today, not least in the ever-growing field of exoplanets, where short-period signals in stellar radial velocity data are investigated. Periodograms are the main (and powerful)…
Multiple-frequency periodograms -- based on time series models consisting of two or more independent sinusoids -- have long been discussed. What is new here is the presentation of a practical, simple-to-use computational framework…
Period estimation is one of the central topics in astronomical time series analysis, where data is often unevenly sampled. Especially challenging are studies of stellar magnetic cycles, as there the periods looked for are of the order of…
This paper introduces an extension of the linear least-squares (or Lomb-Scargle) periodogram for the case when the model of the signal to be detected is non-sinusoidal and depends on unknown parameters in a non-linear manner. The attention…
This paper introduces a novel periodogram-like function, called the expectile periodogram, for modeling spectral features of time series and detecting hidden periodicities. The expectile periodogram is constructed from trigonometric…
The need to unravel modulations hidden in noisy time series of experimental data is a well known problem, traditionally attacked through a variety of methods, among which a popular tool is the so called Lomb-Scargle periodogram. Recently,…
Time series with missing or irregularly sampled data are a persistent challenge in machine learning. Many methods operate on the frequency-domain, relying on the Fast Fourier Transform (FFT) which assumes uniform sampling, therefore…
Astronomical time series often have non-uniform sampling in time, or irregular cadences, with long gaps separating clusters of observations. Some of these data sets are also explicitly non-Gaussian with respect to the expected model fit, or…
One of the central problems in massive Internet of Things (IoT) deployments is the monitoring of the status of a massive number of links. The problem is aggravated by the irregularity of the traffic transmitted over the link, as the traffic…
The detection of periodic signals in irregularly-sampled time series is a problem commonly encountered in astronomy. Traditional tools used for periodic searches, such as the periodogram, have poorly defined statistical properties under…