ON THE ADAPTIVE LATTICE NOTCH FILTER FOR THE DETECTION OF SINUSOIDS

In this paper, a lattice notch filter for the detection and enhancement of sinusoids in noise is presented. Also, the convergence properties of the algorithm are investigated by using the ODE (ordinary differential equation) analysis. It is. shown that the frequency estimate of the proposed algorithm for a single sinusoid is unbiased, regardless of the pole-zero contraction factor and the noise variance. We also derive an expression for the MSE (mean square error) of the frequency estimate and the output SNR of the proposed algorithm. The simulation results are presented to verify the theoretical analysis. Also,based on the cascade of the proposed second-order ANF, three different approaches for the detection of multiple sinusoids are presented. The first approach employs the linear cascade structure, and the second and third approaches employ the triangular cascade structure. The Performance of the proposed algorithms for multiple sinusoids are also investigated by using the ODE analysis, and the computer simulation results are presented and discussed.