Symmetric Wavelet Tight Frames with Two Generators

Ivan Selesnick and A. Farras Abdelnour


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 anti-symmetric, 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.

Preprint: Symmetric Wavelet Tight Frames with Two Generators. Applied and Computational Harmonic Analysis, 17(2):211-225, 2004.

Reproducing the design example in the paper: DesignExampleDoc.pdf.

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