Two-channel 1D and 2D biorthonormal filter banks with causal stable IIR and linear phase FIR filters

A new class of two-channel biorthogonal filter banks is derived. The framework covers two useful subclasses: (i) causal stable IIR filter banks; (ii) linear phase FIR filter banks. Perfect reconstruction is structurally preserved and the structural complexity is very low. Filter banks of high frequency selectivity can be achieved by simply designing a single transfer function. Furthermore zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. We also map the proposed 1D framework into 2D. The mapping preserves: (i) perfect reconstruction; (ii) stability in the IIR case; (iii) linear phase in the FIR case; (iv) zeros at aliasing frequency and (v) frequency characteristic of the filters