Abstract
This paper focuses on the construction and properties of spline dyadic wavelet that equals its reconstruction wavelet. A general construction method of finite spline dyadic low-pass and high-pass filters is given. It proves that finite spline dyadic low-pass filters are symmetric about 0 or 1/2, but there are no finite spline high-pass filters possessing symmetry with respect to 0 or 1/2. It further shows that there exist infinite spline high-pass filters possessing symmetry with respect to 0 or 1/2, which can be constructed. Their energy is concentrated and so finite symmetric spline dyadic wavelet filter that equals its reconstruction filter can be obtained approximately. Construction examples for quadratic and cubic spline dyadic wavelet filters are given.
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