TY - JOUR
T1 - Symmetric wavelet tight frames with two generators
AU - Selesnick, Ivan W.
AU - Abdelnour, A. Farras
N1 - Funding Information:
✩ Research supported by ONR Grant N00014-03-1-0217. * Corresponding author. E-mail addresses: [email protected] (I.W. Selesnick), [email protected] (A.F. Abdelnour).
PY - 2004/9
Y1 - 2004/9
N2 - 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. 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 h0(n) that is designed so as to ensure that both wavelets have at least a specified number of vanishing moments.
AB - 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. 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 h0(n) that is designed so as to ensure that both wavelets have at least a specified number of vanishing moments.
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U2 - 10.1016/j.acha.2004.05.003
DO - 10.1016/j.acha.2004.05.003
M3 - Article
AN - SCOPUS:4344709660
SN - 1063-5203
VL - 17
SP - 211
EP - 225
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
IS - 2 SPEC. ISS.
ER -