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Red Noise
] In science, Brownian noise, also known as Brown noise or red noise, is the type of signal noise produced by Brownian motion, hence its alternative name of random walk noise. The term "Brown noise" does not come from brown, the color, but after Robert Brown (Scottish botanist from Montrose), Robert Brown, who documented the erratic motion for multiple types of inanimate particles in water. The term "red noise" comes from the "white noise"/"white light" analogy; red noise is strong in longer wavelengths, similar to the red end of the visible spectrum. Explanation The graphic representation of the sound signal mimics a Brownian pattern. Its spectral density is inversely proportional to ''f'' 2, meaning it has higher intensity at lower frequencies, even more so than pink noise. It decreases in intensity by 6 Decibel, dB per octave (20 dB per Decade (log scale), decade) and, when heard, has a "damped" or "soft" quality compared to white noise, white and pink noise. The sou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2D Brown Noise
D, or d, is the fourth Letter (alphabet), letter in the Latin alphabet, used in the English alphabet, modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is English alphabet#Letter names, ''dee'' (pronounced ), plural ''dees''. History The Semitic languages, Semitic letter Daleth, Dāleth may have developed from the logogram for a fish or a door. There are many different Egyptian hieroglyphs that might have inspired this. In Semitic, Ancient Greek and Latin, the letter represented ; in the Etruscan alphabet the letter was archaic, but still retained (see letter B). The equivalent Greek letter is Delta, Delta (letter), Δ. Architecture The Lower case, minuscule (lower-case) form of 'd' consists of a lower-story left Typeface anatomy#Strokes, bowl and a Typeface anatomy#Strokes, stem ascender. It most likely developed by gradual variations on the upper case, majuscule (capital) form 'D', and today now composed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octave
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music," the use of which is "common in most musical systems." The interval between the first and second harmonics of the harmonic series is an octave. In Western music notation, notes separated by an octave (or multiple octaves) have the same name and are of the same pitch class. To emphasize that it is one of the perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. Other interval qualities are also possible, though rare. The octave above or below an indicated note is sometimes abbreviated ''8a'' or ''8va'' ( it, all'ottava), ''8va bassa'' ( it, all'ottava bassa, sometimes also ''8vb''), or simply ''8'' for the octave in the direction indicated by pl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leaky Integrator
In mathematics, a leaky integrator equation is a specific differential equation, used to describe a component or system that takes the integral of an input, but gradually leaks a small amount of input over time. It appears commonly in hydraulics, electronics, and neuroscience where it can represent either a single neuron or a local population of neurons. This is equivalent to a 1st-order highpass filter with cutoff frequency far below the frequencies of interest. Equation The equation is of the form :dx/dt = -Ax + C where C is the input and A is the rate of the 'leak'. General solution The equation is a nonhomogeneous first-order linear differential equation In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form :a_0(x)y + a_1(x)y' + a_2(x)y'' \cdots + a_n(x)y^ = b .... For constant C its solution is :x(t) = ke^ + \frac where k is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sample (signal)
In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of "samples". A sample is a value of the signal at a point in time and/or space; this definition differs from the usage in statistics, which refers to a set of such values. A sampler is a subsystem or operation that extracts samples from a continuous signal. A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points. The original signal can be reconstructed from a sequence of samples, up to the Nyquist limit, by passing the sequence of samples through a type of low-pass filter called a reconstruction filter. Theory Functions of space, time, or any other dimension can be sampled, and similarly in two or more dimensions. For functions that vary with time, let ''S''(''t'') be a continuous function (or "signal") to be sampled, and let sa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Data
Digital data, in information theory and information systems, is information represented as a string of discrete symbols each of which can take on one of only a finite number of values from some alphabet, such as letters or digits. An example is a text document, which consists of a string of alphanumeric characters . The most common form of digital data in modern information systems is '' binary data'', which is represented by a string of binary digits (bits) each of which can have one of two values, either 0 or 1. Digital data can be contrasted with ''analog data'', which is represented by a value from a continuous range of real numbers. Analog data is transmitted by an analog signal, which not only takes on continuous values, but can vary continuously with time, a continuous real-valued function of time. An example is the air pressure variation in a sound wave. The word ''digital'' comes from the same source as the words digit and ''digitus'' (the Latin word for '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be interpreted as the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are positive while areas below are negative. Integrals also refer to the concept ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called ''analysis''. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term ''Fourier transform'' refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude ( absolute value) of the complex value represents the amplitude of a constituent complex sinusoid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectral Density
The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range. The statistical average of a certain signal or sort of signal (including noise) as analyzed in terms of its frequency content, is called its spectrum. When the energy of the signal is concentrated around a finite time interval, especially if its total energy is finite, one may compute the energy spectral density. More commonly used is the power spectral density (or simply power spectrum), which applies to signals existing over ''all'' time, or over a time period large enough (especially in relation to the duration of a measurement) that it could as well have been over an infinite time interval. The power spectral density (PSD) then refers to the spectral energy distribution that would b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiener Process
In mathematics, the Wiener process is a real-valued continuous-time stochastic process named in honor of American mathematician Norbert Wiener for his investigations on the mathematical properties of the one-dimensional Brownian motion. It is often also called Brownian motion due to its historical connection with the physical process of the same name originally observed by Scottish botanist Robert Brown. It is one of the best known Lévy processes ( càdlàg stochastic processes with stationary independent increments) and occurs frequently in pure and applied mathematics, economics, quantitative finance, evolutionary biology, and physics. The Wiener process plays an important role in both pure and applied mathematics. In pure mathematics, the Wiener process gave rise to the study of continuous time martingales. It is a key process in terms of which more complicated stochastic processes can be described. As such, it plays a vital role in stochastic calculus, diffusion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Colors Of 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] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decade (log Scale)
One decade (symbol dec) is a unit for measuring ratios on a logarithmic scale, with one decade corresponding to a ratio of 10 between two numbers. Example: Scientific notation When a real number like .007 is denoted alternatively by 7. × 10—3 then it is said that the number is represented in scientific notation. More generally, to write a number in the form ''a'' × 10''b'', where 1 < ''a'' < 10 and ''b'' is an , is to express it in , and ''a'' is called the ''significand'' or the ''mantissa'', and ''b'' is its |
