Following the approach described by A. V. Kryazhimskii and Yu. S. Osipov, we present a recursive algorithm which can be applied to solve the deconvolution problem of linear finite dimensional input output systems. The method gives an on line approximation of the unknown input, based on approximate samples of the output. Key features of this approach are the introduction of an associated singularly perturbed system and the use of a quasi canonical form due to Morse.