Abstract
Various symmetric framelets and periodic framelets are widely utilized in data analysis due to their resilience to background noise, avoidance of linear phase distortion, and the stability of redundant representation. At present, the number of generators in known periodic framelets in high-dimensional space is infinite. It is natural to ask whether a periodic framelet exists with only one generator in high-dimensional space. In this study, for any given positive numbers, A and B, we will construct one symmetric framelet generator. This generator’s integer translate, dyadic dilation, and periodization can produce a periodic frame with optimal bounds A and B.
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