Delayed-rational Green's-function-based method of transmission lines and the Heaviside condition

In electronics as well as in communications, it is highly desirable to be able to transmit a signal that is preserved from any distortions that is due to the lossy nature of the medium in which the signal travels, normally a transmission line. In this paper, we exploit the connections between the delayed Green's-function-based method from the authors and the well-known distortionless Heaviside condition. It is found that, in the method, an important results was already present but its importance not yet understood. In particular, we prove that we are able to identify the distortionless transmission line associated to a generic transmission line. We consider only 1-conductor transmission lines, with frequency-independent per-unit-length parameters. The multiconductor transmission-line case will be addressed in future works.