Condition for distortionless transmission line with a nonuniform characteristic impedance

The well-known condition for distortionless signal propagation on a dissipative transmission line with constant impedance is generalized to the case of nonuniform impedance. The result is based on a time-domain wave-splitting formulation of the Telegraphist´s equations. It is shown that an appropriate choice of the resistance and the conductance can eliminate the distortion caused by the varying characteristic impedance. A nonuniform transmission line that satisfies the given condition is distortionless in both directions, but reflectionless for signals propagating in one direction only