Complex wave digital networks using complex port references

Abstract

This paper presents a generalization of voltage wave digital filters to the complex domain by allowing complex refercnce impedances. The filters realized do not require the property of one-realness. All quantities'are now allowed to be complex giving new d e f~t i o n s for the adaptors, a new criterion for the interconnection of ports, and a new value of the reference impedance far 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 nalization of even-der classical filters with nal inputs and outputs is obtained with a complex one-port allpass network containing complex tweport adaptors, three-pon circulators and delays. The scattering maaix is highly structured and sparse giving maximum decoupling of the state variables.

Complex wave digital ladder filters using complex port references

“…Note that in each case both the real and the imaginary part of the appropriate port impedance was chosen to guarantee computability and to simplify the resulting structure. The complex transformer is defined in [4]. …”

Synthesis of complex lossless two‐ports

“…The polynomials will hereafter be referred to as the canonic polynomials. The lower asterisk is the para-conjugate (also called the Hurwitz conjugate) operator defined by are related by f f * + hh+= gg* ( 5 ) which is the analytic continuation of the Feldtkeller equation.…”