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SigSpec
SigSpec (acronym of SIGnificance SPECtrum) is a statistical technique to provide the reliability of periodicities in a measured (noisy and not necessarily equidistant) time series. It relies on the amplitude spectrum obtained by the Discrete Fourier transform (DFT) and assigns a quantity called the ''spectral significance'' (frequently abbreviated by “''sig''”) to each amplitude. This quantity is a logarithmic measure of the probability that the given amplitude level would be seen in white noise, in the sense of a type I error. It represents the answer to the question, “What would be the chance to obtain an amplitude like the measured one or higher, if the analysed time series were random?” SigSpec may be considered a formal extension to the Lomb-Scargle periodogram, appropriately incorporating a time series to be averaged to zero before applying the DFT, which is done in many practical applications. When a zero-mean corrected dataset has to be statistically compared to a ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectral Density Estimation
In statistical signal processing, the goal of spectral density estimation (SDE) or simply spectral estimation is to estimate the spectral density (also known as the power spectral density) of a signal from a sequence of time samples of the signal. Intuitively speaking, the spectral density characterizes the frequency content of the signal. One purpose of estimating the spectral density is to detect any periodicities in the data, by observing peaks at the frequencies corresponding to these periodicities. Some SDE techniques assume that a signal is composed of a limited (usually small) number of generating frequencies plus noise and seek to find the location and intensity of the generated frequencies. Others make no assumption on the number of components and seek to estimate the whole generating spectrum. Overview Spectrum analysis, also referred to as frequency domain analysis or spectral density estimation, is the technical process of decomposing a complex signal into ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lomb-Scargle Periodogram
Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum, based on a least squares fit of sinusoids to data samples, similar to Fourier analysis. Fourier analysis, the most used spectral method in science, generally boosts long-periodic noise in long gapped records; LSSA mitigates such problems. Unlike with Fourier analysis, data need not be equally spaced to use LSSA. LSSA is also known as the Vaníček method or the Gauss-Vaniček method after Petr Vaníček, and as the Lomb method or the Lomb–Scargle periodogram, based on the contributions of Nicholas R. Lomb and, independently, Jeffrey D. Scargle. Historical background The close connections between Fourier analysis, the periodogram, and least-squares fitting of sinusoids have long been known. Most developments, however, are restricted to complete data sets of equally spaced samples. In 1963, Freek J. M. Barning of Mathematisch Centrum, Amsterdam, handled unequally spaced data by simila ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Series
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart). Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements. Time series ''analysis'' comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series ''forecasting' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is equal to one event per second. The period is the interval of time between events, so the period is the reciprocal of the frequency. For example, if a heart beats at a frequency of 120 times a minute (2 hertz), the period, —the interval at which the beats repeat—is half a second (60 seconds divided by 120 beats). Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light. Definitions and units For cyclical phenomena such as oscillations, waves, or for examples of simple harmonic motion, the term ''frequency'' is defined as the number of cycles or vibrations per unit of time. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Signal Processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. History According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the Bell System Technical Journal. The paper laid the groundwork for later development of information communication systems and the processing of signals fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monthly Notices Of The Royal Astronomical Society
''Monthly Notices of the Royal Astronomical Society'' (MNRAS) is a peer-reviewed scientific journal covering research in astronomy and astrophysics. It has been in continuous existence since 1827 and publishes letters and papers reporting original research in relevant fields. Despite the name, the journal is no longer monthly, nor does it carry the notices of the Royal Astronomical Society. History The first issue of MNRAS was published on 9 February 1827 as ''Monthly Notices of the Astronomical Society of London'' and it has been in continuous publication ever since. It took its current name from the second volume, after the Astronomical Society of London became the Royal Astronomical Society (RAS). Until 1960 it carried the monthly notices of the RAS, at which time these were transferred to the newly established ''Quarterly Journal of the Royal Astronomical Society'' (1960–1996) and then to its successor journal ''Astronomy & Geophysics'' (since 1997). Until 1965, MNRAS ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Footnotes
A note is a string of text placed at the bottom of a page in a book or document or at the end of a chapter, volume, or the whole text. The note can provide an author's comments on the main text or citations of a reference work in support of the text. Footnotes are notes at the foot of the page while endnotes are collected under a separate heading at the end of a chapter, volume, or entire work. Unlike footnotes, endnotes have the advantage of not affecting the layout of the main text, but may cause inconvenience to readers who have to move back and forth between the main text and the endnotes. In some editions of the Bible, notes are placed in a narrow column in the middle of each page between two columns of biblical text. Numbering and symbols In English, a footnote or endnote is normally flagged by a superscripted number immediately following that portion of the text the note references, each such footnote being numbered sequentially. Occasionally, a number between brack ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variable Star
A variable star is a star whose brightness as seen from Earth (its apparent magnitude) changes with time. This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as either: * Intrinsic variables, whose luminosity actually changes; for example, because the star periodically swells and shrinks. * Extrinsic variables, whose apparent changes in brightness are due to changes in the amount of their light that can reach Earth; for example, because the star has an orbiting companion that sometimes eclipses it. Many, possibly most, stars have at least some variation in luminosity: the energy output of the Sun, for example, varies by about 0.1% over an 11-year solar cycle. Discovery An ancient Egyptian calendar of lucky and unlucky days composed some 3,200 years ago may be the oldest preserved historical document of the discovery of a variable star, the eclipsing binary Algol. Of the modern astronomers, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asteroseismology
Asteroseismology or astroseismology is the study of oscillations in stars. Stars have many resonant modes and frequencies, and the path of sound waves passing through a star depends on the speed of sound, which in turn depends on local temperature and chemical composition. Because the resulting oscillation modes are sensitive to different parts of the star, they inform astronomers about the internal structure of the star, which is otherwise not directly possible from overall properties like brightness and surface temperature. Asteroseismology is closely related to helioseismology, the study of stellar pulsation specifically in the Sun. Though both are based on the same underlying physics, more and qualitatively different information is available for the Sun because its surface can be resolved. Theoretical background By linearly perturbing the equations defining the mechanical equilibrium of a star (i.e. mass conservation and hydrostatic equilibrium) and assuming that the pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Domain
Time domain refers to the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time. In the time domain, the signal or function's value is known for all real numbers, for the case of continuous time, or at various separate instants in the case of discrete time. An oscilloscope is a tool commonly used to visualize real-world signals in the time domain. A time-domain graph shows how a signal changes with time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies. Though most precisely referring to time in physics, the term ''time domain'' may occasionally informally refer to position in space when dealing with spatial frequencies, as a substitute for the more precise term ''spatial domain''. Origin of term The use of the contrasting terms ''time domain'' and ''frequency domain'' developed in U.S. communication engineering in the late 194 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dependent And Independent Variables
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, in turn, are not seen as depending on any other variable in the scope of the experiment in question. In this sense, some common independent variables are time, space, density, mass, fluid flow rate, and previous values of some observed value of interest (e.g. human population size) to predict future values (the dependent variable). Of the two, it is always the dependent variable whose variation is being studied, by altering inputs, also known as regressors in a statistical context. In an experiment, any variable that can be attributed a value without attributing a value to any other variable is called an in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by \sigma^2, s^2, \operatorname(X), V(X), or \mathbb(X). An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviation; for e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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