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refinabl

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There are 8 letters in REFINABL ( A¹B³E¹F⁴I¹L¹N¹R¹ )

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AIL AIN AIR ALB ALE ANE ANI ARB ARE ARF BAL BAN BAR BEL BEN BIN BRA EAR ELF ERA ERN FAB FAN FAR FEN FER FIB FIE FIL FIN FIR IRE LAB LAR LEA LEI LIB LIE LIN NAB NAE NEB NIB NIL RAI RAN REB REF REI RIA RIB RIF RIN

2 letters out of REFINABL

AB AE AI AL AN AR BA BE BI EF EL EN ER FA FE IF IN LA LI NA NE RE

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Definitions of refinabl in various dictionaries:

REFINABL - 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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Refinabl might refer to
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.

Refinabl might refer to

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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* is called refinable with respect to the mask
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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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*
*
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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
*
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* c
*
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* {\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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