Almost tight rational coefficients biorthogonal wavelet filters

Wavelet filters with rational coefficients can be implemented efficiently in digital hardware using simple register shifts and adders. In this letter, a technique to construct biorthogonal filters with rational coefficients is presented. The filters have linear phase and also have very similar characteristics to orthogonal filters, while the latter cannot have linear phase. The frame bound ratio of the filters is very close to unity, i.e., almost tight. The filters are constructed via the lifting scheme with four lifting steps. The perfect reconstruction and the no-dc-leakage properties are preserved with these rational coefficients filters.