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Pink Noise
Pink noise, noise, fractional noise or fractal noise is a signal (information theory), signal or process with a frequency spectrum such that the power spectral density (power per frequency interval) is inversely proportional to the frequency of the signal. In pink noise, each Octave (electronics), octave interval (halving or doubling in frequency) carries an equal amount of noise energy. Pink noise sounds like a waterfall. It is often used to tune loudspeaker systems in professional audio. Pink noise is one of the most commonly observed signals in biological systems. The name arises from the pink appearance of visible light with this power spectrum. This is in contrast with white noise which has equal intensity per frequency interval. Definition Within the scientific literature, the term "1/f noise" is sometimes used loosely to refer to any noise with a power spectral density of the form S(f) \propto \frac, where is frequency, and , with exponent usually close to 1. On ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Audio Normalization
Audio normalization is the application of a constant amount of gain to an audio recording to bring the amplitude to a target level (the norm). Because the same amount of gain is applied across the entire recording, the signal-to-noise ratio and relative dynamics are unchanged. Normalization is one of the functions commonly provided by a digital audio workstation. Two principal types of audio normalization exist. Peak normalization adjusts the recording based on the highest signal level present in the recording. Loudness normalization adjusts the recording based on perceived loudness. Normalization differs from dynamic range compression, which applies varying levels of gain over a recording to fit the level within a minimum and maximum range. Normalization adjusts the gain by a constant value across the entire recording. Peak normalization One type of normalization is peak normalization, wherein the gain is changed to bring the highest PCM sample value or analog signal peak ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Chi Distribution
In probability theory and statistics, the chi distribution is a continuous probability distribution over the non-negative real line. It is the distribution of the positive square root of a sum of squared independent Gaussian random variables. Equivalently, it is the distribution of the Euclidean distance between a multivariate Gaussian random variable and the origin. The chi distribution describes the positive square roots of a variable obeying a chi-squared distribution. If Z_1, \ldots, Z_k are k independent, normally distributed random variables with mean 0 and standard deviation 1, then the statistic :Y = \sqrt is distributed according to the chi distribution. The chi distribution has one positive integer parameter k, which specifies the degrees of freedom (i.e. the number of random variables Z_i). The most familiar examples are the Rayleigh distribution (chi distribution with two degrees of freedom) and the Maxwell–Boltzmann distribution of the molecular speeds in an id ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Octave
In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. 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'' (), ''8va bassa'' (, sometimes also ''8vb''), or simply ''8'' for the octave in the direction indicated by placing this mark above or below the staff. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Noise
Noise is sound, chiefly unwanted, unintentional, or harmful sound considered unpleasant, loud, or disruptive to mental or hearing faculties. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arises when the brain receives and perceives a sound. Acoustic noise is any sound in the acoustic domain, either deliberate (e.g., music or speech) or unintended. In contrast, noise in electronics may not be audible to the human ear and may require instruments for detection. In audio engineering, noise can refer to the unwanted residual electronic noise signal that gives rise to acoustic noise heard as a hiss. This signal noise is commonly measured using A-weighting or ITU-R 468 weighting. In experimental sciences, noise can refer to any random fluctuations of data that hinders perception of a signal. Measurement Sound is measured based on the amplitude and frequency of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Pink Noise Spectrum
Pink is a pale tint of red, the color of the pink flower. It was first used as a color name in the late 17th century. According to surveys in Europe and the United States, pink is the color most often associated with charm, politeness, sensitivity, tenderness, sweetness, childhood, femininity, and romance. A combination of pink and white is associated with innocence, whereas a combination of pink and black links to eroticism and seduction. In the 21st century, pink is seen as a symbol of femininity, though it has not always been seen this way. In the 1920s, light red, which is similar to pink, was seen as a color that reflected masculinity. In nature and culture File:Color icon pink v2.svg, Various shades of pink File:Dianthus.jpg, The color pink takes its name from the flowers called pinks, members of the genus ''Dianthus''. File:Rosa Queen Elizabeth1ZIXIETTE.jpg, In most European languages, pink is known as ''rose'' or ''rosa'', after the rose flower. File:Cherry b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Brownian 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 (electronics), octave (20 dB per Decade (log scale), decade) and, when heard, has a "damped" or "soft" quality compared to white noise, white and p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Fractional Derivative
Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator D D f(x) = \frac f(x)\,, and of the integration operator J The symbol J is commonly used instead of the intuitive I in order to avoid confusion with other concepts identified by similar glyphs, such as identities. J f(x) = \int_0^x f(s) \,ds\,, and developing a calculus for such operators generalizing the classical one. In this context, the term ''powers'' refers to iterative application of a linear operator D to a function that is, repeatedly composing D with itself, as in \begin D^n(f) &= (\underbrace_n)(f) \\ &= \underbrace_n (f)\cdots))). \end For example, one may ask for a meaningful interpretation of \sqrt = D^ as an analogue of the functional square root for the differentiation operator, that is, an expression for some linear operator that, when applied to any f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Benoit Mandelbrot
Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature. In 1936, at the age of 11, Mandelbrot and his family emigrated from Warsaw, Poland, to France. After World War II ended, Mandelbrot studied mathematics, graduating from universities in Paris and in the United States and receiving a master's degree in aeronautics from the California Institute of Technology. He spent most of his career in both the United States and France, having dual French and American citizenship. In 1958, he began a 35-year career ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
SIAM Review
Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific society devoted to applied mathematics, and roughly two-thirds of its membership resides within the United States. Founded in 1951, the organization began holding annual national meetings in 1954, and now hosts conferences, publishes books and scholarly journals, and engages in advocacy in issues of interest to its membership. Members include engineers, scientists, and mathematicians, both those employed in academia and those working in industry. The society supports educational institutions promoting applied mathematics. SIAM is one of the four member organizations of the Joint Policy Board for Mathematics. Membership Membership is open to both individuals and organizations. By the end of its first full year of operation, SIAM had 130 membe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Fractional Brownian Motion
In probability theory, fractional Brownian motion (fBm), also called a fractal Brownian motion, is a generalization of Brownian motion. Unlike classical Brownian motion, the increments of fBm need not be independent. fBm is a continuous-time Gaussian process B_H(t) on , T/math>, that starts at zero, has expectation zero for all t in , T/math>, and has the following covariance function: :E _H(t) B_H (s)\tfrac (, t, ^+, s, ^-, t-s, ^), where ''H'' is a real number in (0, 1), called the Hurst index or Hurst parameter associated with the fractional Brownian motion. The Hurst exponent describes the raggedness of the resultant motion, with a higher value leading to a smoother motion. It was introduced by . The value of ''H'' determines what kind of process the ''fBm'' is: * if ''H'' = 1/2 then the process is in fact a Brownian motion or Wiener process; * if ''H'' > 1/2 then the increments of the process are positively correlated; * if ''H'' < 1/2 then the increments of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Flicker Noise
Flicker noise is a type of electronic noise with a 1/''f'' power spectral density. It is therefore often referred to as 1/''f'' noise or pink noise, though these terms have wider definitions. It occurs in almost all electronic devices and can show up with a variety of other effects, such as impurities in a conductive channel, generation and recombination noise in a transistor due to base current, and so on. Properties 1/''f'' noise in current or voltage is usually related to a direct current, as resistance fluctuations are transformed to voltage or current fluctuations by Ohm's law. There is also a 1/''f'' component in resistors with no direct current through them, likely due to temperature fluctuations modulating the resistance. This effect is not present in manganin, as it has negligible temperature coefficient of resistance. In electronic devices, it shows up as a low-frequency phenomenon, as the higher frequencies are overshadowed by white noise from other sources. In o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dynamical System
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, fluid dynamics, the flow of water in a pipe, the Brownian motion, random motion of particles in the air, and population dynamics, the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real number, real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a Set (mathematics), set, without the need of a Differentiability, smooth space-time structure defined on it. At any given time, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
