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Characterizations of Tight Frame Wavelets with Special Dilation Matrices

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  • Huang Yongdong
  • Zhu Fengjuan

Abstract

We study all generalized low-pass filters and tight frame wavelets with special dilation matrix (M-TFW), where M satisfies and generates the checkerboard lattice. Firstly, we study the pseudoscaling function, generalized low-pass filters and multiresolution analysis tight frame wavelets with dilation matrix (MRA M-TFW), and also give some important characterizations about them. Then, we characterize all M-TFW by showing precisely their corresponding dimension functions which are nonnegative integer valued. Finally, we also show that an M-TFW arises from our MRA construction if and only if the dimension of a particular linear space is either zero or one.

Suggested Citation

  • Huang Yongdong & Zhu Fengjuan, 2010. "Characterizations of Tight Frame Wavelets with Special Dilation Matrices," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-26, December.
    • Handle: RePEc:hin:jnlmpe:128294
    DOI: 10.1155/2010/128294
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