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Harmonic Spline Series Representation of Scaling Functions

T. Blu, M. Unser

Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing X, San Diego CA, USA, August 4-8, 2003, vol. 5207, part I, pp. 120-124.



We present here an explicit time-domain representation of any compactly supported dyadic scaling function as a sum of harmonic splines. The leading term in the decomposition corresponds to the fractional splines, a recent, continuous-order generalization of the polynomial splines.


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