A NEW ALGORITHM FOR THE DESIGN OF LINEAR PREDICTION ERROR FILTERS USING CUMULANT-BASED MSE CRITERIA

This correspondence proposes a new algorithm for the design of (minimum-phase) linear prediction error (LPE) filters using two new cumulant (higher order statistics) based MSE criteria when the given stationary random signal x(n) is nonGaussian and contaminated by Gaussian noise. It is shown that the designed LPE filters based on the proposed criteria are identical to the conventional correlation (second-order statistics) based LPE filter as if x(n) were noise-free measurements. As correlation-based LPE filters, coefficients of the designed cumulant-based LPE filters can be obtained by solving a set of symmetric Toeplitz linear equations using the well-known computationally efficient Levinson-Durbin recursion. Moreover, the proposed two criteria are applicable for any cumulant order M greater than or equal to 3, and one of the proposed criteria for M = 3 reduces to Delopoulos and Giannakis' third-order cumulant-based MSE criterion. Some simulation results are then provided to support the analytical results.