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refinable

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Definitions of refinable in various dictionaries:

adj - subject to the payment of a fine

REFINABLE - In mathematics, in the area of wavelet analysis, a refinable function is a function which fulfils some kind of self-similarity. A function ...

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Possible Dictionary Clues
Capable of being refined
That may be refined.

Refinable description
In mathematics, in the area of wavelet analysis, a refinable function is a function which fulfils some kind of self-similarity. A function * * * * φ * * * {\displaystyle \varphi } * is called refinable with respect to the mask * * * * h * * * {\displaystyle h} * if* * * * φ * ( * x * ) * = * 2 * ⋅ * * ∑ * * k * = * 0 * * * N * − * 1 * * * * h * * k * * * ⋅ * φ * ( * 2 * ⋅ * x * − * k * ) * * * {\displaystyle \varphi (x)=2\cdot \sum _{k=0}^{N-1}h_{k}\cdot \varphi (2\cdot x-k)} * 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 * * * D * * * {\displaystyle D} * one can write more concisely: * * * * * φ * = * 2 * ⋅ * * D * * 1 * * / * * 2 * * * ( * h * ∗ * φ * ) * * * {\displaystyle \varphi =2\cdot D_{1/2}(h\varphi )} 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 * * * * φ * ↦ * 2 * ⋅ * * D * * 1 * * / * * 2 * * * ( * h * ∗ * φ * ) * * * {\displaystyle \varphi \mapsto 2\cdot D_{1/2}(h\varphi )} is linear. * A refinable function is an eigenfunction of that operator. * Its absolute value is not uniquely defined. * That is, if * * * * φ * * * {\displaystyle \varphi } * is a refinable function, * then for every * * * * c * * * {\displaystyle c} * the function * * * * c * ⋅ * φ * * * {\displaystyle c\cdot \varphi } * is refinable, too. * These functions play a fundamental role in wavelet theory as scaling functions.

Refinable description

In mathematics, in the area of wavelet analysis, a refinable function is a function which fulfils some kind of self-similarity. A function
*
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* {\displaystyle \varphi }
* is called refinable with respect to the mask
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* {\displaystyle h}
* if*
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* {\displaystyle \varphi (x)=2\cdot \sum _{k=0}^{N-1}h_{k}\cdot \varphi (2\cdot x-k)}
* 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
*
*
*
* D
*
*
* {\displaystyle D}
* one can write more concisely:
*
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*
* {\displaystyle \varphi =2\cdot D_{1/2}(h*\varphi )}
* 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
*
*
*
* φ
* ↦
* 2
* ⋅
*
* D
*
* 1
*
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*
*
* (
* h
* ∗
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* )
*
*
* {\displaystyle \varphi \mapsto 2\cdot D_{1/2}(h*\varphi )}
* is linear.
* A refinable function is an eigenfunction of that operator.
* Its absolute value is not uniquely defined.
* That is, if
*
*
*
* φ
*
*
* {\displaystyle \varphi }
* is a refinable function,
* then for every
*
*
*
* c
*
*
* {\displaystyle c}
* the function
*
*
*
* c
* ⋅
* φ
*
*
* {\displaystyle c\cdot \varphi }
* is refinable, too.
* These functions play a fundamental role in wavelet theory as scaling functions.

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