On the Design of Biorthogonal Halfband Filterbanks With Almost Tight Rational Coefficients

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.