In the paper, a parametric Fourier series based model (FSBM) for or as an approximation to an arbitrary nonminimum-phase linear time-invariant (LTI) system is proposed for statistical signal processing applications where a model for LTI systems is needed. Based on the FSBM, a (minimum-phase) linear prediction error (LPE) filter for amplitude estimation of the unknown LTI system together with the Cramer Rao (CR) bounds is presented. Then an iterative algorithm for obtaining the optimum mean-square LPE filter with finite data is presented which is also an approximate maximum likelihood algorithm when data are Gaussian. Then three iterative algorithms using higher-order statistics with finite non-Gaussian data are presented for estimating parameters of the FSBM followed by some simulation results to support the efficacy of the proposed algorithms. Finally, we draw some conclusions.