Oversampled filter banks: optimal noise shaping, design freedom, and noise analysis

We show that oversampled filter banks (FBs) offer more design freedom and less noise sensitivity than critically sampled FBs. We provide a parameterization of all synthesis FBs satisfying perfect reconstruction for a given oversampled analysis and we derive bounds and expressions for the variance of the reconstruction error due to noisy subband signals. Finally we introduce noise shaping in oversampled FBs and calculate the optimal noise shaping system.