Tracking analysis of an adaptive lattice notch filter

In this paper, tracking properties of the adaptive lattice notch filter (ALNF) for input sinusoids with linearly and randomly varying frequencies are investigated. Expressions for the asymptotic tracking error and the mean square error (MSE) of the frequency estimate are derived. The expressions show that the forgetting factor, or the step-size constant of the algorithm, plays an important role in controlling the tracking error, the MSE of the frequency estimate, and the output SNR. It is shown that the tracking error decreases as the forgetting factor increases. However, the MSE of the frequency estimate becomes large either for large and small forgetting factor. The output SNR also becomes small either for too large and small forgetting factors. Hence, the optimal forgetting factors, which minimize the MSE and maximize the output SNR for given frequency variation models, are also derived from the expressions for MSE. Intensive computer simulations are performed to augment the theoretical analysis, and the results are discussed.