Wavelet filters with rational coefficients are efficiently implemented by using simple adders and register shifts in digital hardware. In this brief, a new halfband polynomial with rational coefficients (RC-HBP) is proposed to design biorthogonal filterbanks. The Bernoulli polynomial is used to construct RC-HBP. This new class of RC-HBP is used in modified $L-$ step lifting scheme to construct the biorthogonal filters with rational coefficients. The predict and update steps of lifting are designed from RC-HBP. The filters are constructed using three and four lifting steps. The properties of the proposed filters are measured and the result shows that the proposed wavelet filters give better symmetry, regularity and almost unity frame bound ratio, i.e., almost tight as compared to the existing methods. The proposed design method is illustrated with different examples.

中文翻译：

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近有理系数双正交半带滤波器组的设计

通过在数字硬件中使用简单的加法器和寄存器移位，可以有效地实现具有有理系数的小波滤波器。在这个简介中，提出了一种新的具有有理系数的半带多项式 (RC-HBP) 来设计双正交滤波器组。伯努利多项式用于构造 RC-HBP。这种新的 RC-HBP 类用于改进的 $L-$ 步进提升方案，以构造具有有理系数的双正交滤波器。提升的预测和更新步骤是从 RC-HBP 设计的。过滤器是使用三个和四个提升步骤构建的。对所提出的滤波器的性质进行了测量，结果表明所提出的小波滤波器具有更好的对称性、规则性和几乎统一的框界比，即与现有方法相比几乎是紧的。