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Compactly Supported Tight and Sibling Frames Based on Generalized Bernstein Polynomials

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  • Ting Cheng
  • Xiaoyuan Yang

Abstract

We obtain a family of refinable functions based on generalized Bernstein polynomials to provide derived properties. The convergence of cascade algorithms associated with the new masks is proved, which guarantees the existence of refinable functions. Then, we analyze the symmetry, regularity, and approximation order of the refinable functions, which are of importance. Tight and sibling frames are constructed and interorthogonality of sibling frames is demonstrated. Finally, we give numerical examples to explicitly illustrate the construction of the proposed approach.

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  • Ting Cheng & Xiaoyuan Yang, 2016. "Compactly Supported Tight and Sibling Frames Based on Generalized Bernstein Polynomials," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-13, June.
    • Handle: RePEc:hin:jnlmpe:2463673
    DOI: 10.1155/2016/2463673
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