A Haar wavelet approach for solving the transient response of inhomogeneous transmission lines

This paper uses Haar wavelets to solve transient problems in transmission lines, both homogeneous and inhomogeneous. The feature of this newly developed approach is that it converts the original partial differential equations, the telegraphist's equations or the transmission-line equations, to a system of ordinary differential equations via Haar wavelets, which can be solved numerically. Examples of non-sinusoidal excitations, such as the unit step function and the rectangular pulse function for digital transmission in particular, are included to demonstrate the usefulness of this analysis tool.