About: Refinable function

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In mathematics, in the area of wavelet analysis, a refinable function is a function which fulfils some kind of self-similarity. A function is called refinable with respect to the mask if This condition is called refinement equation, dilation equation or two-scale equation. Using the convolution (denoted by a star, *) of a function with a discrete mask and the dilation operator one can write more concisely: These functions play a fundamental role in wavelet theory as scaling functions.

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rdfs:label	Refinable function (en) Масштабирующая функция (ru)
rdfs:comment	В теории всплесков масштабирующей функцией называют функцию удовлетворяющую уравнению Это уравнение называют двухмасштабным соотношением или масштабирующим уравнением во временной области. Набор коэффициентов называется маской или фильтром. Обозначив и применив преобразование Фурье к обеим частям масштабирующего уравнения получим Это уравнение называют масштабирующим уравнением в частотной области. (ru) In mathematics, in the area of wavelet analysis, a refinable function is a function which fulfils some kind of self-similarity. A function is called refinable with respect to the mask if This condition is called refinement equation, dilation equation or two-scale equation. Using the convolution (denoted by a star, *) of a function with a discrete mask and the dilation operator one can write more concisely: These functions play a fundamental role in wavelet theory as scaling functions. (en)
dcterms:subject	Wavelets
Wikipage page ID	4557519 (xsd:integer)
Wikipage revision ID	1068894440 (xsd:integer)
Link from a Wikipage to another Wikipage	De Rham curve Iterated function systems Compact support Convolution Mathematics Eigenfunction Eigenvalue Eigenvector Boxcar function Logarithm Sobolev space Complex conjugate Subdivision surface B-spline Adjoint filter Laurent polynomial Self-similarity Fixed point (mathematics) Wavelets Discretization Wavelet Rational function Tensor product Truncated power function Triangular function Dirac delta function Distribution (mathematics) Positive number Spectral radius Indicator function Kronecker delta Natural number Transfer matrix Polynomial function Heaviside function Partial fraction Simultaneous linear equations
sameAs	Refinable function Refinable function Refinable function Refinable function Refinable function
dbp:wikiPageUsesTemplate	dbt:Reflist
has abstract	In mathematics, in the area of wavelet analysis, a refinable function is a function which fulfils some kind of self-similarity. A function is called refinable with respect to the mask if This condition is called refinement equation, dilation equation or two-scale equation. Using the convolution (denoted by a star, *) of a function with a discrete mask and the dilation operator one can write more concisely: It means that one obtains the function, again, if you convolve the function with a discrete mask and then scale it back.There is a similarity to iterated function systems and de Rham curves. The operator is linear.A refinable function is an eigenfunction of that operator.Its absolute value is not uniquely defined.That is, if is a refinable function,then for every the function is refinable, too. These functions play a fundamental role in wavelet theory as scaling functions. (en) В теории всплесков масштабирующей функцией называют функцию удовлетворяющую уравнению Это уравнение называют двухмасштабным соотношением или масштабирующим уравнением во временной области. Набор коэффициентов называется маской или фильтром. Обозначив и применив преобразование Фурье к обеим частям масштабирующего уравнения получим Это уравнение называют масштабирующим уравнением в частотной области. (ru)
prov:wasDerivedFrom	wikipedia-en:Refinable_function?oldid=1068894440&ns=0
page length (characters) of wiki page	12049 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Refinable_function
is Link from a Wikipage to another Wikipage of	Charles Anthony Micchelli De Rham curve Orthogonal wavelet Polyphase matrix Gerlind Plonka Wavelet Truncated power function Transfer matrix
is foaf:primaryTopic of	wikipedia-en:Refinable_function

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