New higher-order statistics based criteria for the design of linear prediction error filters

The authors propose two criteria for the design of (minimum-phase) linear prediction error (LPE) filters with a set of non-Gaussian measurements x(n). The first one requires a slice of Mth-order (M>or=3) cumulants of x(n) and the other requires a slice of third-order cumulants of the prediction error of x(n). They show that when x(n) is contaminated by additive Gaussian noise, the designed LPE filters based on the proposed criteria are identical to the conventional correlation-based LPE filter associated with the case that x(n) is noise-free. Moreover, as the conventional LPE filter, coefficients of the cumulant-based LPE filter associated with the first criterion can be obtained by solving a set of symmetric Toeplitz linear equations. Finally, some simulation results are provided to support the analytical results.