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1 results

  • Conjugate Symmetric Complex Tight Wavelet Frames with Two Generators

  • Yanmei Xue, Ning Bi, Yuan Zhang
  • Journal:
    Numerical Mathematics: Theory, Methods and Applications / Volume 6 / Issue 2 / May 2013
    Published online by Cambridge University Press:
    28 May 2015, pp. 353-363
    Print publication:
    May 2013

  • Two algorithms for constructing a class of compactly supported conjugate symmetric complex tight wavelet frames ψ = {ψ1, ψ2} 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.