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Continuous Wavelets
In numerical analysis, continuous wavelets are functions used by the continuous wavelet transform. These functions are defined as analytical expressions, as functions either of time or of frequency. Most of the continuous wavelets are used for both wavelet decomposition and composition transforms. That is they are the continuous counterpart of orthogonal wavelets. The following continuous wavelets have been invented for various applications: * Poisson wavelet * Morlet wavelet * Modified Morlet wavelet * Mexican hat wavelet * Complex Mexican hat wavelet * Shannon wavelet * Meyer wavelet * Difference of Gaussians * Hermitian wavelet * Beta wavelet * Causal wavelet * μ wavelets * Cauchy wavelet * Addison wavelet See also *Wavelet A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the n ... ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Numerical Analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Meyer Wavelet
The Meyer wavelet is an orthogonal wavelet proposed by Yves Meyer. As a type of a continuous wavelet, it has been applied in a number of cases, such as in adaptive filters, fractal random fields, and multi-fault classification. The Meyer wavelet is infinitely differentiable with infinite support and defined in frequency domain in terms of function \nu as : \Psi(\omega) := \begin \frac \sin\left(\frac \nu \left(\frac -1\right)\right) e^ & \text 2 \pi /3<, \omega, < 4 \pi /3, \\ \frac \cos\left(\frac \nu \left(\frac-1\right)\right) e^ & \text 4 \pi /3<, \omega, < 8 \pi /3, \\ 0 & \text, \end where : There are many different ways for defining this auxiliary function, which yields variants of the Meyer wavelet. For instance, another standard implementation adopts : ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Wavelet
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of middle C and a short duration of roughly one tenth of a second. If this wavelet were to be convolved with a signal created from the recording of a melody, then the resulting signal would be useful for determining when the middle C note appeared in the song. Mathematically, a wavelet correlates with a signal if a portion of the signal is similar. Correlation is at the core of many practical wavelet applications. As a mathematical tool, wavelets can be used to extract information from many kinds of data, including audio signals and images. Sets of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Addison Wavelet
Addison may refer to: Places Canada * Addison, Ontario, a community United States * Addison, Alabama, a town * Addison, Illinois, a village * Addison, Kentucky, an unincorporated community * Addison, Maine, a town * Addison, Michigan, a village * Addison, New York, a town ** Addison (village), New York * Addison, Ohio * Addison, Pennsylvania, a borough * Addison, Tennessee, an unincorporated community in McMinn County * Addison, Texas, a town * Addison, Vermont, a town * Addison, West Virginia, the official name of the town commonly called Webster Springs * Addison, Wisconsin, a town ** Addison (community), Wisconsin, an unincorporated community * Addison County, Vermont * Addison Township (other), several places Transportation * Addison Avenue, a street in Notting Hill, London * Addison Road (other) * Addison Street, Chicago, Illinois, which runs by Wrigley Field * Addison Railroad (other) * Addison station (other) * Addison Motor Compan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Cauchy Wavelet
In mathematics, Cauchy wavelets are a family of continuous wavelets, used in the continuous wavelet transform. Definition The Cauchy wavelet of order p is defined as: \psi_p(t) = \frac\left ( \frac \right ) ^ where p > 0 and j = \sqrt therefore, its Fourier transform is defined as \hat(\xi) = \xi^e^I_. Sometimes it is defined as a function with its Fourier transform \hat(\xi) = \rho(\xi)\xi^e^I_ where \rho(\xi) \in L^(\mathbb) and \rho(\xi) = \rho(a\xi) for \xi \in \mathbb almost everywhere and \rho(\xi) \neq 0 for all \xi \in \mathbb. Also, it had used to be defined as \psi_p(t) = (\frac)^ in previous research of Cauchy wavelet. If we defined Cauchy wavelet in this way, we can observe that the Fourier transform of the Cauchy wavelet \int_^ \hat(\xi) \,d\xi = \int_^ \frac \xi^e^ \,d\xi = 2\pi Moreover, we can see that the maximum of the Fourier transform of the Cauchy wavelet of order p is happened at \xi = p and the Fourier transform of the Cauchy wavelet is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
μ Wavelet
Mu, or my (; uppercase Μ, lowercase μ; Ancient Greek , or μυ—both ), is the twelfth letter of the Greek alphabet, representing the voiced bilabial nasal . In the system of Greek numerals it has a value of 40. Mu was derived from the Egyptian hieroglyphic symbol for water, which had been simplified by the Phoenicians and named after their word for water, to become 𐤌 (mem). Letters that derive from mu include the Roman M and the Cyrillic М, though the lowercase resembles a small Latin U (u). Names Ancient Greek In Greek, the name of the letter was written and pronounced . Modern Greek In Modern Greek, the letter is spelled and pronounced . In polytonic orthography, it is written with an acute accent: . Use as symbol The lowercase letter mu (μ) is used as a special symbol in many academic fields. Uppercase mu is not used, because it appears identical to Latin M. Prefix for units of measurement "μ" is used as a unit prefix denoting a factor of 10� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Causal Wavelet
Causality is an influence by which one event, process, state, or object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the cause is at least partly responsible for the effect, and the effect is at least partly dependent on the cause. The cause of something may also be described as the reason for the event or process. In general, a process can have multiple causes,Compare: which are also said to be ''causal factors'' for it, and all lie in its past. An effect can in turn be a cause of, or causal factor for, many other effects, which all lie in its future. Some writers have held that causality is metaphysically prior to notions of time and space. Causality is an abstraction that indicates how the world progresses. As such it is a basic concept; it is more apt to be an explanation of other concepts of progression than something to be explained by other more fundamental concepts. The concept is like those of agency ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Beta Wavelet
Continuous wavelets of compact support alpha can be built, which are related to the beta distribution. The process is derived from probability distributions using blur derivative. These new wavelets have just one cycle, so they are termed unicycle wavelets. They can be viewed as a ''soft variety'' of Haar wavelets whose shape is fine-tuned by two parameters \alpha and \beta. Closed-form expressions for beta wavelets and scale functions as well as their spectra are derived. Their importance is due to the Central Limit Theorem by Gnedenko and Kolmogorov applied for compactly supported signals. Beta distribution The beta distribution is a continuous probability distribution defined over the interval 0\leq t\leq 1. It is characterised by a couple of parameters, namely \alpha and \beta according to: P(t)=\fract^\cdot (1-t)^,\quad 1\leq \alpha ,\beta \leq +\infty . The normalising factor is B(\alpha ,\beta )=\frac, where \Gamma (\cdot ) is the generalised factorial function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Hermitian Wavelet
Hermitian wavelets are a family of discrete and continuous wavelets used in the constant and discrete Hermite wavelet transforms. The n^\textrm Hermitian wavelet is defined as the normalized n^\textrm derivative of a Gaussian distribution for each positive n:\Psi_(x)=(2n)^c_\operatorname_\left(x\right)e^, where \operatorname_(x) denotes the n^\textrm probabilist's Hermite polynomial. Each normalization coefficient c_ is given by c_ = \left(n^\Gamma\left(n+\frac\right)\right)^ = \left(n^\sqrt2^(2n-1)!!\right)^\quad n\in\mathbb. The function \Psi\in L_(-\infty, \infty) is said to be an admissible Hermite wavelet if it satisfies the admissibility condition: C_\Psi = \sum_^ < \infty where are the terms of the Hermite transform of . In |
Difference Of Gaussians
In imaging science, difference of Gaussians (DoG) is a feature enhancement algorithm that involves the subtraction of one Gaussian blurred version of an original image from another, less blurred version of the original. In the simple case of grayscale images, the blurred images are obtained by convolving the original grayscale images with Gaussian kernels having differing width (standard deviations). Blurring an image using a Gaussian kernel suppresses only high-frequency spatial information. Subtracting one image from the other preserves spatial information that lies between the range of frequencies that are preserved in the two blurred images. Thus, the DoG is a spatial band-pass filter that attenuates frequencies in the original grayscale image that are far from the band center. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Shannon Wavelet
In functional analysis, the Shannon wavelet (or sinc wavelets) is a decomposition that is defined by signal analysis by ideal bandpass filters. Shannon wavelet may be either of real number, real or complex number, complex type. Shannon wavelet is not well-localized (noncompact) in the time domain, but its Fourier transform is band-limited (compact support). Hence Shannon wavelet has poor time localization but has good frequency localization. These characteristics are in stark contrast to those of the Haar wavelet. The Haar and sinc systems are Fourier duals of each other. Definition Sinc function is the starting point for the definition of the Shannon wavelet. Scaling function First, we define the scaling function to be the sinc function. \phi^(t) := \frac = \operatorname(t). And define the dilated and translated instances to be \phi^n_k(t) := 2^\phi^(2^n t-k) where the parameter n,k means the dilation and the translation for the wavelet respectively. Then we can deriv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Wavelet
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of middle C and a short duration of roughly one tenth of a second. If this wavelet were to be convolved with a signal created from the recording of a melody, then the resulting signal would be useful for determining when the middle C note appeared in the song. Mathematically, a wavelet correlates with a signal if a portion of the signal is similar. Correlation is at the core of many practical wavelet applications. As a mathematical tool, wavelets can be used to extract information from many kinds of data, including audio signals and images. Sets of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
