Digital pre-compensation for faulty D/A converters : the "missing pixel" problem

Abstract

In some contexts, DACs fail in such a way that specific samples are dropped. The dropped samples lead to distortion in the analog reconstruction. We refer to this as the "missing pixel" problem. Under certain conditions, it may be possible to compensate for the dropped sample by pre-processing the digital signal, thereby reducing the analog reconstruction error. We develop three such compensation strategies in this thesis. The first strategy uses constrained minimization to calculate the optimal finite-length compensation signal. We develop a closed-form solution using the method of Lagrange multipliers. Next, we develop an approximation to the optimal solution using discrete prolate spheroidal sequences. We show that the optimal solution is a linear combination of the discrete prolates. The last compensation technique we develop is an iterative solution in class of projection-onto-convex-sets. We develop the algorithm and prove that it converges to the optimal solution found using constrained minimization. Each of the three strategies are analyzed and results from numerical simulations are presented.