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Allan Variance
The Allan variance (AVAR), also known as two-sample variance, is a measure of frequency stability in clocks, 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 Allan deviation describe frequency stability. See also the section #Interpretation of value, Interpretation of value below. There are also different adaptations or alterations of Allan variance, notably the modified Allan variance MAVAR or MVAR, the total ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Noise
In signal processing, phase noise is the frequency-domain representation of random fluctuations in the phase of a waveform, corresponding to time-domain deviations from perfect periodicity (jitter). Generally speaking, radio-frequency engineers speak of the phase noise of an oscillator, whereas digital-system engineers work with the jitter of a clock. Definitions An ideal oscillator would generate a pure sine wave. In the frequency domain, this would be represented as a single pair of Dirac delta functions (positive and negative conjugates) at the oscillator's frequency; i.e., all the signal's power is at a single frequency. All real oscillators have phase modulated noise components. The phase noise components spread the power of a signal to adjacent frequencies, resulting in noise sidebands. Consider the following noise-free signal: :x(t)= A\cos(2 \pi f_0 t) Phase noise is added to this signal by adding a stochastic process represented by \phi(t) to the signal a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root Mean Square
In mathematics, the root mean square (abbrev. RMS, or rms) of a set of values is the square root of the set's mean square. Given a set x_i, its RMS is denoted as either x_\mathrm or \mathrm_x. The RMS is also known as the quadratic mean (denoted M_2), a special case of the generalized mean. The RMS of a continuous function is denoted f_\mathrm and can be defined in terms of an integral of the square of the function. In estimation theory, the root-mean-square deviation of an estimator measures how far the estimator strays from 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 the square of the function that defines the continuous waveform. In the case of a set of ''n'' values \, the RMS is : x_\text = \sqrt. The corresponding formula for a continuous function (or waveform) ''f''(''t'') defined over the interval T_1 \le t \le T_2 is : f_\text = \sqrt , and the R ... [...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. Exponentiation#Power_functions, 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 (Grade (slope), gradient) and ''b'' = log ''a'' is the ... [...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. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leeson Effect
Leeson is a surname. Notable people with the surname include: * Bill Leeson (born 1943), British filmmaker * Cecil Leeson (1902–1989), American musician * David Leeson (1957–2022), American photojournalist * Edward Leeson, British musician * George Mansfield Leeson, Canadian politician * John Leeson (born 1943), British actor * Joseph Leeson, 1st Earl of Milltown (1701–1783), Irish brewer *Lynn Hershman Leeson Lynn Hershman Leeson (née Lynn Lester Hershman; born June 17, 1941) is an American multimedia artist and filmmaker. Her work with technology and in media-based practices is credited with helping to legitimize digital art forms. Her interests inc ... (born 1941), American filmmaker * Michael J. Leeson (died 2016), American screenwriter * Nick Leeson (born 1967), derivatives trader for Barings Bank * Patrick Leeson (1915–1997), English cricketer * Peter Leeson (born 1979), American economist Other uses Leeson is an electric motor brand name under the Regal Rexnord C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Variance
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. 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. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase 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. (For a finite population, variance is the average of the squared deviations from the mean.) A useful property of the st ... [...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 processing), 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 hearing (sense), human ears, and as digital image, images they will have a visibly different texture (visual arts), 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 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 (physics), power within any equal interval of frequencies. That name was given by analogy with whi ... [...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_\text) = 10 \log_ \bigg \frac \bigg( \bigg(\frac\bigg)^2 + 1\bigg)\bigg(\frac + 1\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 the Boltzmann constant, is absolute temperature, 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 speaking it is the available power at the ... [...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 provid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bandwidth (signal Processing)
Bandwidth is the difference between the upper and lower Frequency, frequencies in a continuous Frequency band, band of frequencies. It is typically measured in unit of measurement, unit of hertz (symbol Hz). It may refer more specifically to two subcategories: ''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'' is equal to the upper cutoff frequency of a low-pass filter or baseband signal, which includes a zero 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 f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Systematic Bias
Systematic may refer to: Science * Short for systematic error * Systematic fault In engineering, a fault is a defect or problem in a system that causes it to fail or act abnormally. An example of this is the Windows fault screen, commonly referred to as the Blue Screen of Death (BSoD). The system actively monitors kernel-mod ... * Systematic bias, errors that are introduced by an inaccuracy inherent to the system Economy * Systematic trading, a way of defining trade goals, risk controls and rules that can make investment and trading decisions in a methodical way * Systematic Paris-Region: French business cluster devoted to complex systems Music * Systematic (band), American hard rock band * Systematic Chaos, a 2007 album by Dream Theater Others * Systematic SitaWare, a Danish software company; see See also * Systematics (other) * Systemic (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
