On the performance analysis of ALE using an IIR lattice notch filter

An attempt is made at a quantitative understanding of the ALE (adaptive line enhancer) using an adaptive IIR (infinite impulse response) lattice notch filter. The stability of the algorithm is discussed, and an expression for the asymptotic bias of the frequency estimate is provided. The transient behavior of the algorithm is investigated. It is verified by simulation that the analysis substantiates the fast convergent properties shown by N.I. Cho et al. (1989). The cascade structure for retrieving multiple sinusoids is also discussed. The simulation results indicate that the cascade structure based on the lattice ALE algorithm provides results comparable to those described in the recent literature with much less computational complexity (i.e. O(N) versus O(N²)), where N is the number of input sinusoids