Construction of tight filter bank frames

In this paper, we present an explicit and numerically efficient formulae to construct a tight (paraunitary) FB frame from a given un-tight (non-paraunitary) FB frame. The derivation uses the well developed techniques from modern control theory, which results in the unified formulae for generic IIR and FIR FBs. These formulae involve only algebraic matrix manipulations and can be computed efficiently and reliably without the approximation required in the existing literature.