WaveletA 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.
Scale parameterIn probability theory and statistics, a scale parameter is a special kind of numerical parameter of a parametric family of probability distributions. The larger the scale parameter, the more spread out the distribution. If a family of probability distributions is such that there is a parameter s (and other parameters θ) for which the cumulative distribution function satisfies then s is called a scale parameter, since its value determines the "scale" or statistical dispersion of the probability distribution.
Pseudo-differential operatorIn mathematical analysis a pseudo-differential operator is an extension of the concept of differential operator. Pseudo-differential operators are used extensively in the theory of partial differential equations and quantum field theory, e.g. in mathematical models that include ultrametric pseudo-differential equations in a non-Archimedean space. The study of pseudo-differential operators began in the mid 1960s with the work of Kohn, Nirenberg, Hörmander, Unterberger and Bokobza.
Discrete-time Fourier transformIn mathematics, the discrete-time Fourier transform (DTFT), also called the finite Fourier transform, is a form of Fourier analysis that is applicable to a sequence of values. The DTFT is often used to analyze samples of a continuous function. The term discrete-time refers to the fact that the transform operates on discrete data, often samples whose interval has units of time. From uniformly spaced samples it produces a function of frequency that is a periodic summation of the continuous Fourier transform of the original continuous function.
Computational geometryComputational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with a history stretching back to antiquity.
Unbounded operatorIn mathematics, more specifically functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables in quantum mechanics, and other cases. The term "unbounded operator" can be misleading, since "unbounded" should sometimes be understood as "not necessarily bounded"; "operator" should be understood as "linear operator" (as in the case of "bounded operator"); the domain of the operator is a linear subspace, not necessarily the whole space; this linear subspace is not necessarily closed; often (but not always) it is assumed to be dense; in the special case of a bounded operator, still, the domain is usually assumed to be the whole space.
Operator (physics)In physics, an operator is a function over a space of physical states onto another space of physical states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context). Because of this, they are useful tools in classical mechanics. Operators are even more important in quantum mechanics, where they form an intrinsic part of the formulation of the theory.
Location parameterIn statistics, a location parameter of a probability distribution is a scalar- or vector-valued parameter , which determines the "location" or shift of the distribution. In the literature of location parameter estimation, the probability distributions with such parameter are found to be formally defined in one of the following equivalent ways: either as having a probability density function or probability mass function ; or having a cumulative distribution function ; or being defined as resulting from the random variable transformation , where is a random variable with a certain, possibly unknown, distribution (See also #Additive_noise).
Computational scienceComputational science, also known as scientific computing, technical computing or scientific computation (SC), is a division of science that uses advanced computing capabilities to understand and solve complex physical problems. This includes Algorithms (numerical and non-numerical): mathematical models, computational models, and computer simulations developed to solve sciences (e.
SmoothingIn statistics and , to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine-scale structures/rapid phenomena. In smoothing, the data points of a signal are modified so individual points higher than the adjacent points (presumably because of noise) are reduced, and points that are lower than the adjacent points are increased leading to a smoother signal.
