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High Quality Content by WIKIPEDIA articles! In mathematics, in the area of wavelet analysis, a refinable function is a function which fulfills some kind of self-similarity. A function varphi is called refinable with respect to the mask h if varphi(x)=2cdotsum_{k=0}^{N-1} h_kcdotvarphi(2cdot x-k). This condition is called refinement equation, dilation equation or two-scale equation. These functions play a fundamental role in wavelet theory as scaling functions.

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High Quality Content by WIKIPEDIA articles! In mathematics, in the area of wavelet analysis, a refinable function is a function which fulfills some kind of self-similarity. A function varphi is called refinable with respect to the mask h if varphi(x)=2cdotsum_{k=0}^{N-1} h_kcdotvarphi(2cdot x-k). This condition is called refinement equation, dilation equation or two-scale equation. These functions play a fundamental role in wavelet theory as scaling functions.