Related papers: Red noise-based false alarm thresholds for astroph…
Periodograms are common tools used to search for periodic signals in unevenly spaced time series. The significance of periodogram peaks is often assessed using false alarm probability (FAP), which in most studies assumes uncorrelated noise…
In ultra-fast astronomical observations featuring fast transients on sub-$\mu$s time scales, the conventional Signal-to-Noise Ratio (SNR) threshold, often fixed at $5\sigma$, becomes inadequate as observational window timescales shorten,…
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…
Identifying frequencies with low signal-to-noise ratios in time series of stellar photometry and spectroscopy, and measuring their amplitude ratios and peak widths accurately, are critical goals for asteroseismology. These are also…
{\sc SigSpec} computes the spectral significance levels for the DFT amplitude spectrum of a time series at arbitrarily given sampling. It is based on the analytical solution for the Probability Density Function (PDF) of an amplitude level,…
In this work, time series analysis techniques are used to analyze sequential, equispaced mass measurements of a Si density artifact, collected from an electromechanical transducer. Specifically, techniques such as Power Spectral Density,…
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…
We propose a new method to reduce the frequency noise of a Local Oscillator (LO) to the level of white phase noise by maintaining (not destroying by projective measurement) the coherence of the ensemble pseudo-spin of atoms over many…
Accurate pulsar astrometric estimates play an essential role in almost all high-precision pulsar timing experiments. Traditional pulsar timing techniques refine these estimates by including them as free parameters when fitting a model to…
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 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…
We carry out a comparative analysis of the performance of three algorithms widely used to identify significant periodicities in radial-velocity (RV) datasets: the Generalised Lomb-Scargle Periodogram (GLS), its modified version based on…
Gravity modes in main-sequence stars have traditionally been studied using a prewhitening approach, which iteratively identifies modes in the Fourier domain and subsequently tunes their frequencies, amplitudes, and phases through…
Astrophysical time series often contain periodic signals. The large and growing volume of time series data from photometric surveys demands computationally efficient methods for detecting and characterizing such signals. The most efficient…
Many speech and music analysis and processing schemes rely on an estimate of the fundamental frequency $f_0$ of periodic signal components. Most established schemes apply rather unspecific signal models such as sinusoidal models to the…
The term "false-alarm probability" denotes the probability that at least one out of M independent power values in a prescribed search band of a power spectrum computed from a white-noise time series is expected to be as large as or larger…
LLM hallucination, i.e. generating factually incorrect yet seemingly convincing answers, is currently a major threat to the trustworthiness and reliability of LLMs. The first step towards solving this complicated problem is to measure it.…
We estimate the probability that random noise, of several plausible standard distributions, creates a false alarm that a periodicity (or log-periodicity) is found in a time series. We investigate general situations with non-Gaussian…
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…
Radio Frequency Interference (RFI) increasingly contaminates the radio astronomy spectrum, often exceeding astronomical signal amplitudes by 50-70 dB. Reliable detection and mitigation are therefore essential for studies of faint transient…