On absolute value minimization approaches to tauberian modelling

Two methods to model a signal as the output of an all-pole linear filter driven by a sparse spike sequence are presented. These techniques can also be used to compute the filter coefficients when the input signal is assumed to be composed by pulses with a certain width. The linear system coefficients are obtained by minimizing the mean absolute value of the error for a forward-backward predictor. The advantages, in this particular case, of L1minimization over the well known least-squares optimization are shown.