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Fbsp Wavelet
In applied mathematics, fbsp wavelets are frequency B-spline wavelets. ''fbsp m-fb-fc'' These frequency B-spline wavelets are complex wavelets whose spectrum are spline. : fbsp^(t) := .\operatorname^m \left( \frac \right). e^ where sinc function that appears in Shannon sampling theorem. * ''m'' > 1 is the order of the spline * fb is a bandwidth parameter * fc is the wavelet center frequency Clearly, Shannon wavelet (sinc wavelet) is a particular case of fbsp. References * S.G. Mallat, ''A Wavelet Tour of Signal Processing'', Academic Press, 1999, * C.S. Burrus, R.A. Gopinath, H. Guo, ''Introduction to Wavelets and Wavelet Transforms: A Primer'', Prentice-Hall, 1988, . * O. Cho, M-J. Lai, A Class of Compactly Supported Orthonormal B-Spline Wavelets in: ''Splines and Wavelets'', Athens 2005, G Chen and M-J Lai Editors pp. 123–151. * M. Unser, Ten Good Reasons for Using Spline Wavelets, ''Proc. SPIE'', Vol.3169, Wavelets Applications in Signal and Image P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Fbsp Wavelet
Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each other * Complex (psychology), a core pattern of emotions etc. in the personal unconscious organized around a common theme such as power or status Complex may also refer to: Arts, entertainment and media * Complex (English band), formed in 1968, and their 1971 album ''Complex'' * Complex (band), a Japanese rock band * ''Complex'' (album), by Montaigne, 2019, and its title track * ''Complex'' (EP), by Rifle Sport, 1985 * "Complex" (song), by Gary Numan, 1979 * Complex Networks, publisher of magazine ''Complex'', now online Biology * Protein–ligand complex, a complex of a protein bound with a ligand * Exosome complex, a multi-protein intracellular complex * Protein complex, a group of two or more associated polypeptide chains * Specie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spline Wavelet
In the mathematical theory of wavelets, a spline wavelet is a wavelet constructed using a spline function. There are different types of spline wavelets. The interpolatory spline wavelets introduced by C.K. Chui and J.Z. Wang are based on a certain spline interpolation formula. Though these wavelets are orthogonal, they do not have compact supports. There is a certain class of wavelets, unique in some sense, constructed using B-splines and having compact supports. Even though these wavelets are not orthogonal they have some special properties that have made them quite popular. The terminology ''spline wavelet'' is sometimes used to refer to the wavelets in this class of spline wavelets. These special wavelets are also called B-spline wavelets and cardinal B-spline wavelets. The Battle-Lemarie wavelets are also wavelets constructed using spline functions. Cardinal B-splines Let ''n'' be a fixed non-negative integer. Let ''C''''n'' denote the set of all real-valued functions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spline (mathematics)
In mathematics, a spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees. In the computer science subfields of computer-aided design and computer graphics, the term ''spline'' more frequently refers to a piecewise polynomial ( parametric) curve. Splines are popular curves in these subfields because of the simplicity of their construction, their ease and accuracy of evaluation, and their capacity to approximate complex shapes through curve fitting and interactive curve design. The term spline comes from the flexible spline devices used by shipbuilders and draftsmen to draw smooth shapes. Introduction The term "spline" is used to refer to a wide class of functions that are used in applications requiring data interpolation and/or smoothing. The data ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sinc Function
In mathematics, physics and engineering, the sinc function, denoted by , has two forms, normalized and unnormalized.. In mathematics, the historical unnormalized sinc function is defined for by \operatornamex = \frac. Alternatively, the unnormalized sinc function is often called the sampling function, indicated as Sa(''x''). In digital signal processing and information theory, the normalized sinc function is commonly defined for by \operatornamex = \frac. In either case, the value at is defined to be the limiting value \operatorname0 := \lim_\frac = 1 for all real . The normalization causes the definite integral of the function over the real numbers to equal 1 (whereas the same integral of the unnormalized sinc function has a value of ). As a further useful property, the zeros of the normalized sinc function are the nonzero integer values of . The normalized sinc function is the Fourier transform of the rectangular function with no scaling. It is used in the concep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shannon Sampling Theorem
Shannon may refer to: People * Shannon (given name) * Shannon (surname) * Shannon (American singer), stage name of singer Shannon Brenda Greene (born 1958) * Shannon (South Korean singer), British-South Korean singer and actress Shannon Arrum Williams (born 1998) * Shannon, intermittent stage name of English singer-songwriter Marty Wilde (born 1939) * Claude Shannon (1916-2001) was American mathematician, electrical engineer, and cryptographer known as a "father of information theory" Places Australia * Shannon, Tasmania, a locality * Hundred of Shannon, a cadastral unit in South Australia * Shannon, a former name for the area named Calomba, South Australia since 1916 * Shannon River (Western Australia) Canada * Shannon, New Brunswick, a community * Shannon, Quebec, a city * Shannon Bay, former name of Darrell Bay, British Columbia * Shannon Falls, a waterfall in British Columbia Ireland * River Shannon, the longest river in Ireland ** Shannon Cave, a subterranean section of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 Shnnon 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 funcition 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 intances 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 derive th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
