Complex wave digital networks using complex port references

The authors generalize voltage wave digital filters to the complex domain by allowing complex reference impedances. The filters realized do not require the property of one-realness. All quantities are now allowed to be complex, giving new definitions for the adaptors, a new criterion for the interconnection of ports, and a new value of the reference impedance for the usual dynamic one-port elements. The theory developed reduces to the known theory of real wave digital filters if all quantities are real. The realization of even-order classical filters with real inputs and outputs is obtained with a complex one-port allpass network containing complex two-port adaptors, three-port circulators, and delays. The scattering matrix is highly structured and sparse, giving maximum decoupling of the state variables