New Class of Two-Channel Biorthogonal Filter Banks and Wavelet Bases

摘要

We propose a novel framework for a new class of two-channel biorthogonal filterbanks. The framework covers two useful subclasses: (1) causal stable IIR filter banks; (2) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IRR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. We also provide a novel mapping of the proposed one dimensional (iD) framework into two dimensional (2D). The mapping preserves: (1) perfect reconstruction; (2) stability in the IIR case; (3) linear phase in the FIR case; (4) zeros at aliasing frequency; (5) frequency characteristic of the filters.