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Allan Variance
The Allan variance (AVAR), also known as two-sample variance, is a measure of frequency stability in clock A clock or a timepiece is a device used to measure and indicate time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month and the ...s, oscillators and amplifiers. It is named after David W. Allan and expressed mathematically as \sigma_y^2(\tau). The Allan deviation (ADEV), also known as sigma-tau, is the square root of the Allan variance, \sigma_y(\tau). The ''M-sample variance'' is a measure of frequency stability using ''M'' samples, time ''T'' between measurements and observation time \tau. ''M''-sample variance is expressed as :\sigma_y^2(M, T, \tau). The Allan variance is intended to estimate stability due to noise processes and not that of systematic errors or imperfections such as frequency drift or temperature effects. The Allan variance and Al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
White Noise
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used, with this or similar meanings, in many scientific and technical disciplines, including physics, acoustical engineering, telecommunications, and statistical forecasting. White noise refers to a statistical model for signals and signal sources, rather than to any specific signal. White noise draws its name from white light, although light that appears white generally does not have a flat power spectral density over the visible band. In discrete time, white noise is a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean and finite variance; a single realization of white noise is a random shock. Depending on the context, one may also require that the samples be independent and have identical probability distribution (in other words independent and iden ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Average Fractional Frequency
In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, and 9 (summing to 25) is 5. Depending on the context, an average might be another statistic such as the median, or mode. For example, the average personal income is often given as the median—the number below which are 50% of personal incomes and above which are 50% of personal incomes—because the mean would be higher by including personal incomes from a few billionaires. For this reason, it is recommended to avoid using the word "average" when discussing measures of central tendency. General properties If all numbers in a list are the same number, then their average is also equal to this number. This property is shared by each of the many types of average. Another universal property is monotonicity: if two lists of numbers ''A'' and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root Mean Square
In mathematics and its applications, the root mean square of a set of numbers x_i (abbreviated as RMS, or rms and denoted in formulas as either x_\mathrm or \mathrm_x) is defined as the square root of the mean square (the arithmetic mean of the squares) of the set. The RMS is also known as the quadratic mean (denoted M_2) and is a particular case of the generalized mean. The RMS of a continuously varying function (denoted f_\mathrm) can be defined in terms of an integral of the squares of the instantaneous values during a cycle. For alternating electric current, RMS is equal to the value of the constant direct current that would produce the same power dissipation in a resistive load. In estimation theory, the root-mean-square deviation of an estimator is a measure of the imperfection of the fit of the estimator to the data. Definition The RMS value of a set of values (or a continuous-time waveform) is the square root of the arithmetic mean of the squares of the values, or th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Log–log Plot
In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form y=ax^k – appear as straight lines in a log–log graph, with the exponent corresponding to the slope, and the coefficient corresponding to the intercept. Thus these graphs are very useful for recognizing these relationships and estimating parameters. Any base can be used for the logarithm, though most commonly base 10 (common logs) are used. Relation with monomials Given a monomial equation y=ax^k, taking the logarithm of the equation (with any base) yields: \log y = k \log x + \log a. Setting X = \log x and Y = \log y, which corresponds to using a log–log graph, yields the equation: Y = mX + b where ''m'' = ''k'' is the slope of the line (gradient) and ''b'' = log ''a'' is the intercept on the (log ''y'')-axis, meaning w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency Deviation
Frequency deviation (f_) is used in FM radio to describe the difference between the minimum or maximum extent of a frequency modulated signal, and the nominal center or carrier frequency. The term is sometimes mistakenly used as synonymous with frequency drift, which is an unintended offset of an oscillator from its nominal frequency. The frequency deviation of a radio is of particular importance in relation to bandwidth, because less deviation means that more channels can fit into the same amount of frequency spectrum. The FM broadcasting range between 87.5 and 108 MHz uses a typical channel spacing of 100 or 200 kHz, with a maximum frequency deviation of +/-75 kHz, in some cases leaving a buffer above the highest and below the lowest frequency to reduce interaction with other channels. The most common FM transmitting applications use peak deviations of +/-75 kHz (100 or 200 kHz spacing), +/-5 kHz (15–25 kHz spacing), +/-2.5 kHz (3.75-12.5& ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leeson Effect
Leeson is a surname. Notable people with the surname include: *Bill Leeson, British filmmaker *Cecil Leeson, American musician *David Leeson, American photojournalist *Edward Leeson, British musician *John Leeson, British actor *Joseph Leeson, 1st Earl of Milltown, Irish brewer *Lynn Hershman Leeson, American filmmaker * Michael J. Leeson, American screenwriter *Nick Leeson, derivatives trader for Barings Bank *Patrick Leeson, English cricketer *Peter Leeson, American economist Leeson is an electric motor brand name under the Regal Rexnord Corporation. See also * Zita Leeson Weinshienk (1833-2022), American judge *Leeson Street __NOTOC__ Leeson Street (; ) is a thoroughfare near central Dublin, Ireland. Location The street is divided into two parts by the Grand Canal: Lower Leeson Street, in Dublin 2 is to the north of the canal, linking to St Stephen's Green, with ..., a thoroughfare in south Dublin, Ireland * Leason, a surname and given name {{surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Variance
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. Standard deviation may be abbreviated SD, and is most commonly represented in mathematical texts and equations by the lower case Greek letter σ (sigma), for the population standard deviation, or the Latin letter '' s'', for the sample standard deviation. The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. The standard deviation of a popul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power-law Noise
In audio engineering, electronics, physics, and many other fields, the color of noise or noise spectrum refers to the power spectrum of a noise signal (a signal produced by a stochastic process). Different colors of noise have significantly different properties. For example, as audio signals they will sound different to human ears, and as images they will have a visibly different texture. Therefore, each application typically requires noise of a specific color. This sense of 'color' for noise signals is similar to the concept of timbre in music (which is also called "tone color"; however, the latter is almost always used for sound, and may consider very detailed features of the spectrum). The practice of naming kinds of noise after colors started with white noise, a signal whose spectrum has equal power within any equal interval of frequencies. That name was given by analogy with white light, which was (incorrectly) assumed to have such a flat power spectrum over the visibl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leeson's Equation
Leeson's equation is an empirical expression that describes an oscillator's phase noise spectrum. Leeson's expression for single-sideband (SSB) phase noise in dBc/Hz (decibels relative to output level per hertz) and augmented for flicker noise: :L(f_m) = 10 \log \bigg \frac \bigg( \bigg(\frac\bigg)^2 + 1\bigg)\bigg(\frac + 1\bigg)\bigg(\frac\bigg) \bigg/math> where is the output frequency, is the loaded quality factor, is the offset from the output frequency (Hz), is the corner frequency, is the noise factor of the amplifier, is Boltzmann's constant in joules/kelvin, is absolute temperature in kelvins, and is the available power at the sustaining amplifier input.https://www.ieee.li/pdf/essay/phase_noise_basics.pdf There is often misunderstanding around Leeson's equation, even in text books. In the 1966 paper, Leeson stated correctly that " is the signal level at the oscillator active element input" (often referred to as the power through the resonator now, strictly speaki ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Timebase
A time base generator (also timebase or time base) is a special type of function generator, an electronic circuit that generates a varying voltage to produce a particular waveform. Time base generators produce very high frequency sawtooth waves specifically designed to deflect the beam of a cathode ray tube (CRT) smoothly across the face of the tube and then return it to its starting position. Time bases are used by radar systems to determine range to a target, by comparing the current location along the time base to the time of arrival of radio echoes. Analog television systems using CRTs had two time bases, one for deflecting the beam horizontally in a rapid movement, and another pulling it down the screen 60 times per second. Oscilloscopes often have several time bases, but these may be more flexible function generators able to produce many waveforms as well as a simple time base. Description A cathode ray tube (CRT) consists of three primary parts, the electron gun that provide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bandwidth (signal Processing)
Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in hertz, and depending on context, may specifically refer to ''passband bandwidth'' or ''baseband bandwidth''. Passband bandwidth is the difference between the upper and lower cutoff frequencies of, for example, a band-pass filter, a communication channel, or a signal spectrum. Baseband bandwidth applies to a low-pass filter or baseband signal; the bandwidth is equal to its upper cutoff frequency. Bandwidth in hertz is a central concept in many fields, including electronics, information theory, digital communications, radio communications, signal processing, and spectroscopy and is one of the determinants of the capacity of a given communication channel. A key characteristic of bandwidth is that any band of a given width can carry the same amount of information, regardless of where that band is located in the frequency spectrum. For example, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
