Volume 6, Issue 2
Conjugate Symmetric Complex Tight Wavelet Frames with Two Generators

Yanmei Xue, Ning Bi & Yuan Zhang

Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 353-363.

Published online: 2013-06

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  • Abstract

Two algorithms for constructing a class of compactly supported conjugate symmetric complex tight wavelet frames $\Psi$={$\psi_1$, $\psi_2$} are derived. Firstly, a necessary and sufficient condition for constructing the conjugate symmetric complex tight wavelet frames is established. Secondly, based on a given conjugate symmetric low pass filter, a description of a family of complex wavelet frame solutions is provided when the low pass filter is of even length. When one wavelet is conjugate symmetric and the other is conjugate antisymmetric, the two wavelet filters can be obtained by matching the roots of associated polynomials. Finally, two examples are given to illustrate how to use our method to construct conjugate symmetric complex tight wavelet frames which have some vanishing moments.

  • Keywords

Complex tight wavelet frame, conjugate symmetry, vanishing moments.

  • AMS Subject Headings

42C15, 94A12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-6-353, author = {}, title = {Conjugate Symmetric Complex Tight Wavelet Frames with Two Generators}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2013}, volume = {6}, number = {2}, pages = {353--363}, abstract = {

Two algorithms for constructing a class of compactly supported conjugate symmetric complex tight wavelet frames $\Psi$={$\psi_1$, $\psi_2$} are derived. Firstly, a necessary and sufficient condition for constructing the conjugate symmetric complex tight wavelet frames is established. Secondly, based on a given conjugate symmetric low pass filter, a description of a family of complex wavelet frame solutions is provided when the low pass filter is of even length. When one wavelet is conjugate symmetric and the other is conjugate antisymmetric, the two wavelet filters can be obtained by matching the roots of associated polynomials. Finally, two examples are given to illustrate how to use our method to construct conjugate symmetric complex tight wavelet frames which have some vanishing moments.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.y11016}, url = {http://global-sci.org/intro/article_detail/nmtma/5908.html} }
TY - JOUR T1 - Conjugate Symmetric Complex Tight Wavelet Frames with Two Generators JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 353 EP - 363 PY - 2013 DA - 2013/06 SN - 6 DO - http://doi.org/10.4208/nmtma.2013.y11016 UR - https://global-sci.org/intro/article_detail/nmtma/5908.html KW - Complex tight wavelet frame, conjugate symmetry, vanishing moments. AB -

Two algorithms for constructing a class of compactly supported conjugate symmetric complex tight wavelet frames $\Psi$={$\psi_1$, $\psi_2$} are derived. Firstly, a necessary and sufficient condition for constructing the conjugate symmetric complex tight wavelet frames is established. Secondly, based on a given conjugate symmetric low pass filter, a description of a family of complex wavelet frame solutions is provided when the low pass filter is of even length. When one wavelet is conjugate symmetric and the other is conjugate antisymmetric, the two wavelet filters can be obtained by matching the roots of associated polynomials. Finally, two examples are given to illustrate how to use our method to construct conjugate symmetric complex tight wavelet frames which have some vanishing moments.

Yanmei Xue, Ning Bi & Yuan Zhang. (2020). Conjugate Symmetric Complex Tight Wavelet Frames with Two Generators. Numerical Mathematics: Theory, Methods and Applications. 6 (2). 353-363. doi:10.4208/nmtma.2013.y11016
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