Characteristic Impedance of a Medium From Its Step Response: A Simple Second-Order Approximation

A second-order approximation is obtained which relates Z(t), the characteristic impedance of a one-dimensional scattering medium, to S(t), the time integral of the reflectance. Specifically z1/2(t) = z1/2(0) [1 - S(2t) + ¿2S2(2t)]. The simple form taken by the quadratic term seems not to have been explicitly recognized in the past.