Design of computationally efficient FIR filters for sampling rate alteration and multiband filtering with arbitrary passbands and time response

A general method is presented for designing computationally efficient FIR filters for sampling rate alteration and multiband filtering with arbitrary frequency response and time response. These filters are constructed by cascading subfilters whose delays are integer powers of the unit delay. The non-linear approximation problem is solved using the dual simplex algorithm enabling simultaneous use of multiple sets of constraints including the time response constraints. The basic algorithm is derived from the general framework for minimax solution of overdetermined systems of non-linear equations.