On the adaptive lattice notch filter for the detection of sinusoids

A lattice notch filter for the detection and enchancement of sinusoids in noise is presented, and the convergence properties of the algorithm are investigated using ODE (ordinary differential equation) analysis. It is shown that the frequency estimate of the algorithm for a single sinusoid is unbiased, regardless of the pole-zero contraction factor and the noise variance. An expression for the MSE (mean square error) of the frequency estimate and the output SNR of the algorithm is derived. Simulation results are presented to verify the theoretical analysis. Based on cascading the proposed second-order adaptive notch filter, three different approaches for the detection of multiple sinusoids are presented. The first approach uses a linear cascade structure, and the second and third approaches use a triangular cascade structure. The performance of the algorithms for multiple sinusoids is investigated, and computer simulation results are presented and discussed.>