Adaptive filtering of exponentially damped, undamped and exponentially growing sinusoids

An analysis is presented of the output and parameter estimation errors of RLS (recursive least-squares) adaptive filters when they are applied to exponentially damped, undamped, and exponentially growing sinusoids. The authors show that the RLS adaptive filter guarantees zero output error for all three types of sinusoids. However, for undamped and exponentially growing sinusoids, unbiased parameter estimates of the signal models are also provided. A new method of estimating the parameters of an exponentially damped sinusoid is proposed. The method can accurately estimate the parameter values of the signal model provided the lower bound of the exponentially damping coefficient is known a priori and the measurement noise is negligible. The results are further verified through digital computer simulations