Separation of One-dimensional Waves - a Stochastic Systems Approach

In various applications it is of interest to extract the wave traveling in a certain direction of a medium. As waves that propagate in different directions generally overlap, it is not possible to directly measure the desired wave. This paper presents techniques for separation of broadband waves governed by the one-dimensional wave equation in the presence of measurement noise. The derived estimators are based on stochastic modeling of the waves and measurement noise, state space representations and optimal state estimation.