Comparing LS FIR filtering and l-step ahead linear prediction

This comparative study of the l-step-ahead linear prediction and least-squares finite impulse response (LS FIR) filtering problems emphasizes the numerical behavior of the resulting Toeplitz systems. It is shown that, although these systems are similar, the restraints on the autocorrelation coefficients fundamentally differentiate them. In the process of doing so, a new algorithmic scheme for the computation of the lagged lattice coefficients is developed, which exhibits fundamentally improved numerical behavior. Moreover, explicit formulas for the supremums of the absolute values of both the lagged lattice and filter coefficients are found theoretically and are experimentally confirmed by using the proposed algorithm. Finally, the bounds of the LS FIR filter coefficients are treated in comparison with the supremums of the lagged quantities