Parallel MD recursive digital filtering using 1D vector recursive filters

It is shown that a parallel MD (multidimensional) recursive digital filter algorithm can be derived from a given sequential MD recursive filter algorithm, where no additional arithmetic operations occur if appropriate recursion directions are used for processing MD data. The derived parallel filter is expressible as a 1-D vector system whose coefficient matrices are directly related to the coefficients of the original sequential system. The stability of this 1-D vector system leads to the result that the original sequential system possesses the practical BIBO (bounded input, bounded output) property