Optimal design of oversampled filter banks with lattice structure

For an oversampled linear phase (LP) perfect reconstruction filter banks with lattice structure, the synthesis FB is not unique. However, existing methods to choose a synthesis FB for “optimal” noise reduction may destroy the linear phase and lattice structure property. This paper studies the noise reduction design problem for oversampled filter banks (FBs) preserving lattice structure. Both the optimal design and worst case design are considered, where the former caters for the noise with known power spectral density (PSD), and the latter for the noise with unknown PSD. Explicit formula for the former and LMI-based algorithms for the latter are provided.