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Explicit construction of framelets. (English) Zbl 0984.42022

In this paper the author studies sufficient conditions for generators of tight frames of dyadic multiwavelets in \(L^2 ({\mathbb R})\) (the author uses the term framelets). The condition is a matrix equation for low and high pass filters of the wavelets, \(m_0, m_1, \ldots, m_n\). This equation is further analyzed in case there are only two wavelets and the general form of the solution is provided. This result is used to prove that under additional assumptions on \(m_0\), there exist wavelets with filters which are trigonometric polynomials. For similar results see [C. K. Chui and W. He, Appl. Comput. Harmon. Anal. 8, No. 3, 293-319 (2000; Zbl 0948.42022)].

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems

Citations:

Zbl 0948.42022
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References:

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