Adaptive lattice filter for multiple sinusoids in white noise

In this paper we present an analytical study of the lattice filter for an input time series consisting of multiple sinusoids in white noise. For this model, the method of undetermined coefficients is applied to derive the convergent solution. Further, expressions for the bias and misadjustment of the stochastic gradient (SG) lattice filter coefficients show that for inputs of moderate tonal-to-noise power ratios, the bias is negligible and the misadjustment is comparable to that of the LMS transversal filter. A heuristic approach to the derivation of the filter convergence time is presented.