Adaptive tracking of multiple sinusoids whose power levels are widely separated

The behavior of the gradient transversal filter (LMS), the gradient lattice (GL), and the least squares lattice (LSL) when used to track multiple sinusoidal (or narrow-band) components whose power levels are widely separated is investigated. These approaches to the realization of the pth-order one-step linear predictor of the time series are recursive in time. The lags of the instantaneous frequency estimates from their actual underlying values are of particular interest. The frequency tracking characteristics of the LMS, GL, and LSL algorithms are illustrated in several situations. Included are simulations of dual sinusoids undergoing a variety of frequency versus time dynamics and a formant tracking example of real speech.