On frames with stable oversampled filter banks

This paper studies the frames corresponding to stable oversampled filter banks (FBs). For this class of frames, we present explicit and numerically efficient formulae to compute the tightest frame bounds, to obtain the dual frame and to construct a paraunitary FB for a given non-paraunitary FB. The derivation uses the well developed techniques from modern control theory, which results in the formulae that involve only algebraic matrix manipulation and can be performed efficiently and reliably without the approximation required in the existing methods.