Conversions between parallel and hierarchic architecture analysis multirate filter banks

General conversion between equivalent parallel and hierarchic analysis multirate filter banks (MRBs) as well as sufficient conditions for existence and uniqueness of the conversions are derived. MRBs are used with arbitrary, rational number changes in sampling rate between successive outputs and arbitrary linear-time-invariant filtering for each output. Conversion consists of commuting sampling rate expanders, sampling rate compressors, and filters to turn one MRB into the form of the other. For a class of MRBs which the authors call well-formed the conversions between architectures are one to one