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Symmetric wavelet tight frames with two generators. (English) Zbl 1066.42027
Summary: This paper uses the UEP approach for the construction of wavelet tight frames with two (anti-) symmetric wavelets, and provides some results and examples that complement recent results by [Q. Jiang, Adv. Comput. Math. 18, No. 2–4, 247–268 (2003; Zbl 1020.42020)]. A description of a family of solutions when the lowpass scaling filter is of even-length is provided. When one wavelet is symmetric and the other is antisymmetric, the wavelet filters can be obtained by a simple procedure based on matching the roots of associated polynomials. The design examples in this paper begin with the construction of a lowpass filter \(h_0(n)\) that is designed so as to ensure that both wavelets have at least a specified number of vanishing moments.

MSC:
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
42C15 General harmonic expansions, frames
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