Mathematical examination of force reconstruction and the deconvolution problem

An important problem in engineering is the recovery of the input of a system from the measured output, which is an inherently difficult problem to solve. Solutions to this type of problem are abundant in the literature, but a clearly dictated examination of the problem and how solutions address the problem is lacking. Our aim with the work presented herein is to address this issue. In this paper, we examine the nature of the linear force reconstruction problem by mathematically modeling the nature of measurement noise in both the forward and inverse problems. We are able to definitely show the nature of the issue measurement noise presents to the force reconstruction. Additionally we take a look at the basic concepts that are generally applied resolve the measurement noise issue and produce examples to show how each resolves this issue.