Interpolatory Subdivision and Wavelets on an Interval
نویسنده
چکیده
We consider a method of adapting Dubuc-Deslauriers sudivision, which is de ̄ned for bi-in ̄nite sequences, to accommodate sequences of ̄nite length. After deriving certain useful properties of the Dubuc-Deslauriers re ̄nable function on R, we de ̄ne a multi-scale ̄nite sequence of functions on a bounded interval, which are then proved to be re ̄nable. Using this fact, the resulting adapted interpolatory subdivision scheme for ̄nite sequences is then shown to be convergent. Corresponding interpolation wavelets on an interval are de ̄ned, and explicit formulations of the resulting decomposition and reconstruction algorithms are calculated.
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