A class of rational coefficients biorthogonal Hilbert-pairs

Two filter banks whose corresponding wavelets are related via the Hilbert transform are said to form a Hilbert-pair. A simple technique for designing biorthogonal Hilbert-pairs is the common-factor technique. The technique yields approximately linear-phase filters but with irrational coefficients in general. This paper proposes a technique to rationalize the coefficients while preserving the perfect reconstruction and vanishing moment properties of the filters. The rational coefficient filters can be implemented efficiently without any multipliers using simple shifts and adds. The characteristic and analytic qualities of the rationalized filters are comparable with that of the original irrational filters.