Abstract
Abstract . We construct Daubechies' scaling function supported on [0, 3] from first principles and prove that it is continuous everywhere, left-differentiable at dyadic rationals and nowhere right-differentiable on dyadic rational on [0, 3). Furthermore, we prove that its integer translates are orthonormal and that its definite integral equals one. This scaling function is one of an infinite class of scaling functions introduced by Daubechies in [1] for the purpose of constructing orthonormal bases of compactly supported wavelets. The particular scaling function studied in this paper is distinguished from the others by the property that it is the simplest scaling function which can be used to construct a complete orthonormal wavelet basis of L 2 (R) whose primary wavelet is continuous.
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