The transient response of tapered transmission lines

Tapered transmission lines are frequently used in communications engineering to transform voltages and impedances. Much has been done in the steady-state analysis
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of these devices. The need remains, however, for a theory of the optimum taper based upon transient considerations because of intrinsic limitations of any steady-state theory. Steady-state treatments are sufficient for a-c applications, but are difficult to apply meaningfully to transient phenomena. Very little has been done in the realm of tapered-transmission line transient analysis. An analysis for exponential tapers has appeared in the literature,
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but there has been no attempt to find the optimum taper from transient considerations.