A systematic synthesis is presented to realize any digital filter into a power-wave digital filter. After three canonical matrix representations are introduced, a set of key concepts which comprises cascade interconnection of digital two-ports, pole localization, and computability is presented for the canonical cascade synthesis of lossless digital two-ports. The synthesis procedure consists of global decomposision and local decomposition. The procedure is so general as to give a unified solution to arbitrary frequency responses realization, and is so useful as to find new circuit structures. The synthesized circuits are of robustness and modularity. An illustrative example is included.