On the design and implementation of a class of multiplierless two-channel 1D and 2D nonseparable PR FIR filterbanks

This paper proposes a new design and implementation method for a class of multiplierless 2-channel 1D and 2D nonseparable perfect reconstruction (PR) filterbanks (FB). It is based on the structure proposed by S.M. Phoong et al. (see IEEE Trans. Sig. Proc., vol.43, p.649-64, 1995) and the use of multiplier blocks (MB). The latter technique allows one to further reduce the number of adders in implementing these multiplier-less FB by almost 50%, compared to the conventional method using sum of powers of two coefficients (SOPOT) alone. Furthermore, by generalizing the 1D to 2D transformation of Phoong et al., new 2D PR FBs with quincunx, hourglass, and parallelogram spectral support are obtained. These nonseparable FBs can be cascaded to realize new multiplierless PR directional FB for image processing and motion analysis. Design examples are given to demonstrate the usefulness of the proposed method.