Abstract
A new method is introduced for the exact decomposition of a linear <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> th-order periodically time-varying digital filter into a set of independent, linear time-invariant, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> 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.
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