A general realization scheme of periodically time-varying digital filters

A new method is introduced for the exact decomposition of a linear
M
th-order periodically time-varying digital filter into a set of independent, linear time-invariant,
M
th-order digital filters, each one of which is a single-input, multiple-output system plus a set of parallel blocks of multiply-in, add-out type of operations. It is shown that the adopted vector decomposition approach yields a general realization scheme that exhibits high parallelism as well as great regularity. The application of the vector decomposition method to the realization of linear time-invariant digital filters is also examined as a special case of the general one.