Noise reduction design of perfect reconstruction oversampled filter banks

This paper studies the noise reduction design problem for oversampled filter banks (FBs) with perfect reconstruction (PR) constraint. Both the optimal design and worst case design are considered, where the former method caters for the noise with known power spectral density (PSD) and the latter one for the noise with unknown PSD. Explicit formulae involving only algebraic Riccati equation and matrix manipulations are provided for the general (IIR or FIR) oversampled PR FBs.