| Abstract: | When the scaling factor a = 2 is used to define scaling functions and wavelets, it is well known that any compactly supported orthonormal (o.n.) wavelet, which is symmetric or antisymmetric, is some integer translate and possible sign change of the Haar function. The objective of this paper is to exhibit the construction of compactly supported o.n. symmetric scaling functions with scaling factor a = 3 and the two corresponding compactly supported o.n. wavelets, one of which is symmetric and the other antisymmetric. Examples of low-order scaling functions and wavelets are given. Furthermore, decomposition and reconstruction algorithms are discussed. |
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