New Techniques for Rationalizing Orthogonal and Biorthogonal Wavelet Filter Coefficients

Most wavelet filters reported in the literature have irrational coefficients. Hardware implementation can be simpler if the filter coefficients are rational valued. In this paper, we present novel methods to rationalize both orthogonal and biorthogonal filter coefficients with perfect reconstruction and vanishing moments preservation. Rational orthogonal filter coefficients are obtained using lattice structures. Rational biorthogonal filter coefficients are obtained using the complementary filter technique in which one set of filter coefficients is expressed in terms of the other. The rationalized filters have characteristics that are very close to the original irrational filters. The techniques are simple yet general enough to be used for almost any filter bank unlike the techniques in previously reported works.