On the tracking properties of the ALNF (adaptive lattice notch filter)

The tracking properties of the ALNF (adaptive lattice notch filter) for linearly and randomly varying frequencies are investigated. Expressions for the asymptotic tracking error and MSE (mean square error) of the frequency estimate are derived. The results show that the forgetting factor plays an important role in controlling the tracking error, MSE, and output SNR. The optimal forgetting factor, which minimizes the MSE of the frequency estimate, is also derived from the expression for the MSE. Simulations are conducted to verify the theoretical expressions, and it is shown that the simulation results and theory are in close agreement.<>