Time-varying behavior of the PARCOR coefficients of lattice filters with nonstationary AR inputs

The authors describe the behavior of the partial correlation coefficients of lattice filters based on the recursive least squares (RLS) algorithm in the presence of a nonstationary input. The input is an autoregressive (AR) process and the coefficients of the generating filter are allowed to change with time, leading to a time-varying autocorrelation function at the input. For such an input the optimal Wiener-Hopf coefficients of a lattice filter are found. These are compared with the expected PARCOR coefficients of the RLS lattice filter, which are a function of the weighting parameter. It is shown that the PARCOR coefficients of the RLS lattice filter have two terms and tend to the Wiener-Hopf optimal weights asymptotically.<>