The complete parametrization of orthogonal hexagonally symmetric low-pass filters with $$\sqrt{3}$$ refinement is presented for several cases of coefficient supports. Given a symmetric low-pass filter, a method that allows to construct hexagonally symmetric tight wavelet frames is suggested. Also, a framework for the construction of orthogonal hexagonally symmetric wavelets is presented.

中文翻译：

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具有 $$\sqrt{3}$$ 细化的六边形对称正交滤波器

对于几种系数支持情况，提出了具有 $$\sqrt{3}$$ 细化的正交六边形对称低通滤波器的完整参数化。给定一个对称低通滤波器，提出了一种允许构造六边形对称紧小波框架的方法。此外，还提出了用于构造正交六边形对称小波的框架。