A NEW CLASS OF 2-CHANNEL BIORTHOGONAL FILTER BANKS AND WAVELET BASES

We propose a novel framework for a new class of two-channel biorthogon al filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks ii) linear phase FIR filter banks. There exis ts a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be a chieved by using the proposed framework with low complexity. The prope rties of such a class are discussed in detail. The design of the analy sis/synthesis systems reduces to the design of a single transfer funct ion. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily im posed, for the purpose of generating wavelets with regularity property . In the IIR case, two new classes of IIR maximally flat filters diffe rent from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biort hogonal systems are generated. We also provide a novel mapping of the proposed 1-D framework into 2-D. The mapping preserves the following: i) perfect reconstruction ii) stability in the IIR case iii) linear ph ase in the FIR case iv) zeros at aliasing frequency v) frequency chara cteristic of the filters.