Digital signal propagation in dispersive media

In this article, the propagation of digital and analog signals through media which, in general, are both dissipative and dispersive is modeled using the one-dimensional telegraph equation. Input signals are represented using impulsive, Heaviside unit step, Gaussian, rectangular pulse, and both unmodulated and modulated sinusoidal pulse type boundary data. Applications to coaxial transmission lines and freshwater signal propagation, for both digital and analog signals, are included. The analysis presented here supports the finding that digital transmission in dispersive media is generally superior to that of analog. The boundary data (input signals) give rise to solutions of the telegraph equation which contain propagating discontinuities. It is shown that the magnitudes of these discontinuities, as a function of distance, can be found without the need of solving the governing equation. Thus, for digital signals in particular, signal strength at a given distance from the input source can be easily determined. Furthermore, the magnitudes of these discontinuities are found to be independent of both the dispersion coefficient k and the elastic coefficient b. In addition, it is shown that, depending on the algebraic sign of k, one of two distinct forms of dispersion is possible and that for small-time intervals, solutions are approximately independent of k.