A spectral characterization of the ill-conditioning in numerical deconvolution

An important class of applications in digital signal processing involves the numerical solution of the convolution integral. These so-called numerical deconvolution problems are notoriously difficult to solve because of their inherent ill-conditioning. In this paper we present a characterization of this ill-conditioning based on a classical spectral decomposition of the discrete convolution. Factors prominently influencing the conditioning are identified and some explicit sensitivity measures are introduced.