Abstract
A construction approach for the 3‐band tight wavelet frames by factorization of paraunitary matrix is developed. Several necessary constraints on the filter lengths and symmetric features of wavelet frames are investigated starting at the constructed paraunitary matrix. The matrix is a symmetric extension of the polyphase matrix corresponding to 3‐band tight wavelet frames. Further, the parameterizations of 3‐band tight wavelet frames with 3N + 1 filter lengths are established. Examples of framelets with symmetry/antisymmetry and Sobolev exponent are computed by appropriately choosing the parameters in the scheme.
Highlights
In the theory and applications of wavelets and wavelet frames, certain properties are always desirable
This paper deals with the construction of 3-band tight wavelet frames filters with prescribed properties using factorization and parameterizations of the paraunitary matrices
With the describing of unitary extension principle UEP in the polyphase representation, we firstly construct a paraunitary matrix based on the polyphase matrix corresponding to compactly supported wavelet frames with the least number generators
Summary
In the theory and applications of wavelets and wavelet frames, certain properties are always desirable. The main tools for construction and characterization of wavelet frames are the unitary extension principle UEP 16 and its versions generalized such as OEP and MEP 17. They give sufficient conditions for constructing MRA-based tight and dual wavelet frames. This paper deals with the construction of 3-band tight wavelet frames filters with prescribed properties using factorization and parameterizations of the paraunitary matrices. With the describing of unitary extension principle UEP in the polyphase representation, we firstly construct a paraunitary matrix based on the polyphase matrix corresponding to compactly supported wavelet frames with the least number generators. We use leng h K 1 to denote the filter length of h
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